Details

Time bar (total: 14.2s)

analyze363.0ms (2.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
25%74.9%0.1%8
25%74.9%0.1%9
25%64%11.1%10
31.2%54.6%14.2%11
39%44.1%16.9%12
Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.0s (28.1%)

Results
1.1s5457×body256valid
1.0s1889×body1024valid
928.0ms1706×body1024invalid
346.0ms902×body512valid
308.0ms1572×body256invalid
298.0ms802×body512invalid
8.0ms8×body2048valid

preprocess24.0ms (0.2%)

Algorithm
2×egg-herbie
Rules
96×fma-def_binary64
70×*-commutative_binary64
57×associate-/l*_binary64
30×associate-/r/_binary64
26×distribute-rgt-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02580
16972
216072
324372
432172
537572
642072
747472
848072
033
133
Stop Event
1×unsound
1×saturated
Calls
Call 1
Inputs
0
1
2
Outputs
0
1
0
2
Call 2
Inputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))
(+.f64 (*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (*.f64 th th)) (*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (*.f64 th th)))
Outputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (*.f64 th th)) (*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (*.f64 th th) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (*.f64 a2 a2)))
(*.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (*.f64 th th)))
(*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 th th)))
(*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 th th)))
(*.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (*.f64 a1 a1)))
(*.f64 (cos.f64 a2) (/.f64 (fma.f64 th th (*.f64 a1 a1)) (sqrt.f64 2)))
Symmetry

(sort a1 a2)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify11.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
32×fma-def_binary64
23×*-commutative_binary64
20×associate-/l*_binary64
11×associate-/r/_binary64
9×associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01320
12718
25818
38818
411518
513518
615218
717018
817218
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
Outputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))

eval1.0ms (0%)

Compiler

Compiled 34 to 20 computations (41.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.5b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.5b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Compiler

Compiled 15 to 10 computations (33.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
✓0.8b
(/.f64 (cos.f64 th) (sqrt.f64 2))
Compiler

Compiled 37 to 16 computations (56.8% saved)

series14.0ms (0.1%)

Counts
2 → 40
Calls

12 calls:

TimeVariablePointExpression
2.0ms
a2
@0
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
a2
@-inf
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
th
@-inf
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
a1
@0
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
th
@0
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite62.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
523×log-prod_binary64
407×exp-prod_binary64
343×pow-prod-down_binary64
283×pow2_binary64
198×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01126
122425
2273825
Stop Event
1×node limit
Counts
2 → 86
Calls
Call 1
Inputs
(/.f64 (cos.f64 th) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cos.f64 th)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (pow.f64 2 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (sqrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))

simplify54.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
821×unswap-sqr_binary64
749×associate-*l*_binary64
547×associate-/l/_binary64
515×fma-def_binary64
494×distribute-rgt-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
059925
1145857
2373853
31196821
44370806
Stop Event
1×node limit
Counts
126 → 109
Calls
Call 1
Inputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (*.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (*.f64 -1/720 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
Outputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 th (/.f64 (sqrt.f64 2) th)) (/.f64 1 (sqrt.f64 2)))
(fma.f64 -1/2 (*.f64 (/.f64 th (sqrt.f64 2)) th) (/.f64 1 (sqrt.f64 2)))
(fma.f64 -1/2 (*.f64 th (/.f64 th (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 th (/.f64 (sqrt.f64 2) th)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(fma.f64 -1/2 (*.f64 (/.f64 th (sqrt.f64 2)) th) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(fma.f64 -1/2 (*.f64 th (/.f64 th (sqrt.f64 2))) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(+.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 th (/.f64 th (sqrt.f64 2))) (+.f64 -1/2 (*.f64 th (*.f64 th 1/24)))))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (*.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 th (/.f64 (sqrt.f64 2) th)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (*.f64 (/.f64 th (sqrt.f64 2)) th) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (*.f64 th (/.f64 th (sqrt.f64 2))) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(+.f64 (/.f64 1 (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (*.f64 (*.f64 th (/.f64 th (sqrt.f64 2))) (+.f64 -1/2 (*.f64 th (*.f64 th 1/24))))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (*.f64 th th))))))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (fma.f64 -1/2 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (*.f64 th th)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (*.f64 (*.f64 th th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(fma.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (*.f64 -1/2 (*.f64 th th)) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 -1/2 (*.f64 (*.f64 th (/.f64 th (sqrt.f64 2))) (fma.f64 a2 a2 (*.f64 a1 a1))) (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (*.f64 th th))) (*.f64 1/24 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))))))
(+.f64 (fma.f64 1/24 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (pow.f64 th 4)) (/.f64 (*.f64 -1/2 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 (sqrt.f64 2) (*.f64 th th)))) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (*.f64 (*.f64 th th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (fma.f64 1/24 (*.f64 (pow.f64 th 4) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 1/24 (pow.f64 th 4))))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (*.f64 th (/.f64 th (sqrt.f64 2))) (+.f64 -1/2 (*.f64 th (*.f64 th 1/24)))))))
(+.f64 (*.f64 -1/720 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(fma.f64 -1/720 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (*.f64 th th))) (*.f64 1/24 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))))))
(+.f64 (+.f64 (fma.f64 -1/720 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 1/24 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (pow.f64 th 4)) (/.f64 (*.f64 -1/2 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 (sqrt.f64 2) (*.f64 th th)))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/720 (*.f64 (pow.f64 th 6) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (fma.f64 -1/2 (*.f64 (*.f64 th th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (fma.f64 1/24 (*.f64 (pow.f64 th 4) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))))
(fma.f64 -1/720 (*.f64 (pow.f64 th 6) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))) (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 1/24 (pow.f64 th 4)))))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 -1/2 (*.f64 th th)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a1) a1) (sqrt.f64 2))
(*.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a1) a1) (sqrt.f64 2))
(*.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a1) a1) (sqrt.f64 2))
(*.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))

eval37.0ms (0.3%)

Compiler

Compiled 1964 to 1149 computations (41.5% saved)

prune25.0ms (0.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New9910109
Fresh000
Picked011
Done000
Total9911110
Error
0b
Counts
110 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.4b
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
28.0b
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
15.2b
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
▶23.6b
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
▶1.1b
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
28.0b
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
0.5b
(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
▶27.1b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
▶27.1b
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
✓0.5b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
0.5b
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
Compiler

Compiled 305 to 234 computations (23.3% saved)

localize19.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
✓0.3b
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Compiler

Compiled 41 to 20 computations (51.2% saved)

series7.0ms (0%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
th
@0
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
th
@inf
(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms
th
@inf
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
th
@0
(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms
a1
@0
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite61.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
532×log-prod_binary64
408×exp-prod_binary64
373×pow-prod-down_binary64
299×pow2_binary64
208×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01228
124425
2279125
Stop Event
1×node limit
Counts
2 → 52
Calls
Call 1
Inputs
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1)) (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (pow.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1) (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) 1))))))

simplify60.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
837×distribute-rgt-in_binary64
820×distribute-lft-in_binary64
502×distribute-lft-out_binary64
488×unswap-sqr_binary64
450×associate-+l+_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
053958
1148884
2437838
31876810
45154806
Stop Event
1×node limit
Counts
100 → 75
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(sqrt.f64 1/2)
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
Outputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))
(fma.f64 -1/2 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2)))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (fma.f64 (sqrt.f64 1/2) (*.f64 -1/2 (*.f64 th th)) (sqrt.f64 1/2)))
(+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))
(fma.f64 1/24 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 -1/2 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))))
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(*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (*.f64 1/24 (pow.f64 th 4))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (+.f64 (sqrt.f64 1/2) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (fma.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 (sqrt.f64 1/2) (*.f64 1/24 (pow.f64 th 4)) (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 -1/2 (*.f64 th th)))))
(+.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))) (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
✓0.2b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
✓0.4b
(/.f64 a2 (sqrt.f64 2))
Compiler

Compiled 30 to 19 computations (36.7% saved)

series39.0ms (0.3%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
26.0ms
th
@inf
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
4.0ms
th
@-inf
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms
a2
@0
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
1.0ms
th
@inf
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
1.0ms
th
@-inf
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))

rewrite76.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
953×pow1_binary64
882×add-log-exp_binary64
882×log1p-expm1-u_binary64
882×expm1-log1p-u_binary64
862×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0931
118831
2238031
Stop Event
1×node limit
Counts
3 → 69
Calls
Call 1
Inputs
(/.f64 a2 (sqrt.f64 2))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 a2 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (*.f64 a2 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a2) 2) (*.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a2) (*.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) a2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 a2 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a2 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 a2 3) (pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 3) (pow.f64 a2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 a2) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))))

simplify115.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
1035×unswap-sqr_binary64
985×associate-*l/_binary64
967×fma-def_binary64
537×associate-/l*_binary64
469×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
053764
1135760
2350758
31142732
43628698
55294678
65470678
75679678
85894678
96098678
Stop Event
1×node limit
Counts
117 → 89
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 -1/720 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 -1/720 (/.f64 (*.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
Outputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
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(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
Compiler

Compiled 26 to 11 computations (57.7% saved)

series4.0ms (0%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
a2
@0
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
1.0ms
a2
@inf
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
1.0ms
a1
@inf
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
1.0ms
a1
@0
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
1.0ms
a2
@-inf
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))

rewrite63.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
765×pow1_binary64
708×add-log-exp_binary64
708×log1p-expm1-u_binary64
708×expm1-log1p-u_binary64
691×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
116412
2195812
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a2 a1) (*.f64 (hypot.f64 a2 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))))

simplify114.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
780×associate-/r/_binary64
600×associate-/l/_binary64
600×sqr-pow_binary64
566×*-commutative_binary64
372×cube-prod_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
010414
119414
232414
362378
4150378
5513378
62172378
73474378
83900378
94183378
104528378
115111378
126228378
137562378
Stop Event
1×node limit
Counts
55 → 37
Calls
Call 1
Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (pow.f64 a2 2) (cos.f64 th))
✓0.3b
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
Compiler

Compiled 28 to 18 computations (35.7% saved)

series5.0ms (0%)

Counts
2 → 20
Calls

12 calls:

TimeVariablePointExpression
1.0ms
th
@inf
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
1.0ms
a2
@0
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
0.0ms
th
@0
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
0.0ms
a2
@inf
(*.f64 (pow.f64 a2 2) (cos.f64 th))
0.0ms
a2
@inf
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))

rewrite69.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
921×pow1_binary64
854×add-log-exp_binary64
854×log1p-expm1-u_binary64
854×expm1-log1p-u_binary64
834×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
118923
2233223
Stop Event
1×node limit
Counts
2 → 54
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (/.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (*.f64 (cos.f64 th) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2) 2)) (cbrt.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2)) (*.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (*.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2)) 1) (/.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 1) (/.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (*.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (cbrt.f64 2)) (/.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 (*.f64 a2 (cos.f64 th)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a2 (*.f64 a2 (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 a2 a2) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (*.f64 a2 a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (*.f64 a2 (cos.f64 th)))))))))

simplify71.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
952×fma-def_binary64
617×associate-*l/_binary64
520×distribute-rgt-out_binary64
494×*-commutative_binary64
488×associate-/l*_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
043358
1111339
2327326
31336299
44865280
56771266
67997266
Stop Event
1×node limit
Counts
74 → 72
Calls
Call 1
Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 -1/720 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (+.f64 (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))) (*.f64 1/24 (*.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 th 4) (pow.f64 a2 2))) (*.f64 -1/720 (*.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (*.f64 th th)))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 th th)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(fma.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 -1/2 (*.f64 th th)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)) (sqrt.f64 2)) (+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (*.f64 th th))))))
(fma.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (fma.f64 -1/2 (/.f64 (*.f64 th th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (pow.f64 th 4)) (fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 th th)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 (*.f64 th th) (fma.f64 (*.f64 th th) 1/24 -1/2))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 th (*.f64 th (fma.f64 (*.f64 th th) 1/24 -1/2)))))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 1/24 (pow.f64 th 4) (fma.f64 -1/2 (*.f64 th th) 1)))
(+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (*.f64 -1/720 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(fma.f64 1/24 (/.f64 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)) (sqrt.f64 2)) (+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (*.f64 th th))) (*.f64 -1/720 (/.f64 (*.f64 (*.f64 a2 a2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (fma.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (fma.f64 -1/2 (/.f64 (*.f64 th th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))) (*.f64 -1/720 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (pow.f64 th 6))))
(fma.f64 1/24 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (pow.f64 th 4)) (fma.f64 -1/720 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (pow.f64 th 6)) (fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 th th)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(fma.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (*.f64 -1/2 (*.f64 th th)) (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))))))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) 1/24 -1/2) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (+.f64 (fma.f64 1/24 (pow.f64 th 4) 1) (fma.f64 -1/2 (*.f64 th th) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (*.f64 a2 a2) (cos.f64 th))
(*.f64 a2 (*.f64 a2 (cos.f64 th)))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 (*.f64 a2 a2) (*.f64 th th))))
(*.f64 (+.f64 (*.f64 -1/2 (*.f64 th th)) 1) (*.f64 a2 a2))
(*.f64 (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 a2 (fma.f64 -1/2 (*.f64 a2 (*.f64 th th)) a2))
(*.f64 a2 (fma.f64 (*.f64 -1/2 th) (*.f64 a2 th) a2))
(+.f64 (pow.f64 a2 2) (+.f64 (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))) (*.f64 1/24 (*.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (*.f64 a2 a2) (*.f64 th th)) (*.f64 1/24 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)))))
(fma.f64 a2 a2 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (*.f64 a2 a2) (+.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 1/24 (pow.f64 th 4))))
(*.f64 (*.f64 a2 a2) (fma.f64 1/24 (pow.f64 th 4) (fma.f64 -1/2 (*.f64 th th) 1)))
(+.f64 (pow.f64 a2 2) (+.f64 (*.f64 -1/2 (*.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 th 4) (pow.f64 a2 2))) (*.f64 -1/720 (*.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(+.f64 (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (*.f64 a2 a2) (*.f64 th th)) (fma.f64 1/24 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)) (*.f64 -1/720 (*.f64 (*.f64 a2 a2) (pow.f64 th 6))))))
(fma.f64 a2 a2 (fma.f64 -1/2 (*.f64 (*.f64 a2 a2) (*.f64 th th)) (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))
(fma.f64 a2 a2 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 -1/2 (*.f64 th th)) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))))))
(*.f64 (*.f64 a2 a2) (+.f64 (fma.f64 -1/2 (*.f64 th th) 1) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (*.f64 a2 a2) (+.f64 (fma.f64 1/24 (pow.f64 th 4) 1) (fma.f64 -1/2 (*.f64 th th) (*.f64 -1/720 (pow.f64 th 6)))))

localize59.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6)))
✓0.3b
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
✓1.0b
(/.f64 1 (cbrt.f64 2))
✓1.0b
(cbrt.f64 2)
Compiler

Compiled 64 to 41 computations (35.9% saved)

series99.0ms (0.7%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
81.0ms
th
@inf
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
5.0ms
a2
@0
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
4.0ms
a1
@0
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
2.0ms
th
@0
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms
th
@-inf
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite85.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
731×log-prod_binary64
384×pow2_binary64
268×pow1/3_binary64
263×expm1-udef_binary64
263×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01647
133234
2414134
Stop Event
1×node limit
Counts
4 → 151
Calls
Call 1
Inputs
(cbrt.f64 2)
(/.f64 1 (cbrt.f64 2))
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6)))
Outputs
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(*.f64 (cos.f64 th) (pow.f64 2 -1/6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) (pow.f64 2 -1/6)) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (cbrt.f64 2)) 3) (pow.f64 (*.f64 (cos.f64 th) (pow.f64 2 -1/6)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (cos.f64 th) (pow.f64 2 -1/6)) 3) (pow.f64 (/.f64 1 (cbrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))))

simplify165.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
558×associate-*l/_binary64
461×associate-*r/_binary64
412×associate-/r/_binary64
370×associate-*l*_binary64
345×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0701328
11991224
26461189
330311153
472761147
575301147
676841147
778501147
Stop Event
1×node limit
Counts
199 → 178
Calls
Call 1
Inputs
(*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/720 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6))))
(+.f64 (*.f64 -1/720 (*.f64 (/.f64 (pow.f64 th 6) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 1/24 (*.f64 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6)))))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
Outputs
(*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(fma.f64 -1/2 (*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (*.f64 th th)))) (*.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 th th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2))))
(*.f64 (pow.f64 1/2 1/6) (fma.f64 -1/2 (/.f64 (*.f64 th th) (/.f64 (cbrt.f64 2) (fma.f64 a2 a2 (*.f64 a1 a1)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (+.f64 (pow.f64 1/2 1/6) (*.f64 (pow.f64 1/2 1/6) (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (+.f64 (*.f64 -1/2 (*.f64 th th)) 1) (pow.f64 1/2 1/6)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (pow.f64 1/2 1/6)))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))))
(fma.f64 1/24 (*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (pow.f64 th 4)))) (fma.f64 -1/2 (*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (*.f64 th th)))) (*.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 2)) (pow.f64 1/2 1/6))))
(fma.f64 1/24 (*.f64 (pow.f64 1/2 1/6) (/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 th 4)) (cbrt.f64 2))) (*.f64 (pow.f64 1/2 1/6) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 th th))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (fma.f64 -1/2 (/.f64 (*.f64 th th) (/.f64 (cbrt.f64 2) (fma.f64 a2 a2 (*.f64 a1 a1)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2))) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (+.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/2 (*.f64 th th))))))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/720 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))))
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(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(/.f64 (*.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (pow.f64 1/2 1/6)) (cbrt.f64 2))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (cbrt.f64 2)) (pow.f64 1/2 1/6)) (*.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(*.f64 (pow.f64 1/2 1/6) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (cos.f64 th)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 1 (cbrt.f64 2)))
(/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2))
(+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6)))
(fma.f64 -1/2 (*.f64 (pow.f64 1/2 1/6) (/.f64 (*.f64 th th) (cbrt.f64 2))) (*.f64 (pow.f64 1/2 1/6) (/.f64 1 (cbrt.f64 2))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 1 (cbrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 th th) (cbrt.f64 2)))))
(*.f64 (pow.f64 1/2 1/6) (fma.f64 -1/2 (*.f64 (/.f64 th (cbrt.f64 2)) th) (/.f64 1 (cbrt.f64 2))))
(*.f64 (pow.f64 1/2 1/6) (fma.f64 -1/2 (/.f64 th (/.f64 (cbrt.f64 2) th)) (/.f64 1 (cbrt.f64 2))))
(+.f64 (*.f64 1/24 (*.f64 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6))))
(fma.f64 1/24 (*.f64 (pow.f64 1/2 1/6) (/.f64 (pow.f64 th 4) (cbrt.f64 2))) (fma.f64 -1/2 (*.f64 (pow.f64 1/2 1/6) (/.f64 (*.f64 th th) (cbrt.f64 2))) (*.f64 (pow.f64 1/2 1/6) (/.f64 1 (cbrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (*.f64 (pow.f64 1/2 1/6) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2))) (*.f64 -1/2 (/.f64 (*.f64 th th) (cbrt.f64 2))))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 1 (cbrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (/.f64 (*.f64 -1/2 (*.f64 th th)) (cbrt.f64 2)))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 1 (cbrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (*.f64 -1/2 (/.f64 th (/.f64 (cbrt.f64 2) th))))))
(+.f64 (*.f64 -1/720 (*.f64 (/.f64 (pow.f64 th 6) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 1/24 (*.f64 (/.f64 (pow.f64 th 4) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (+.f64 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 th 2) (cbrt.f64 2)) (pow.f64 1/2 1/6))) (*.f64 (/.f64 1 (cbrt.f64 2)) (pow.f64 1/2 1/6)))))
(fma.f64 -1/720 (*.f64 (pow.f64 1/2 1/6) (/.f64 (pow.f64 th 6) (cbrt.f64 2))) (fma.f64 1/24 (*.f64 (pow.f64 1/2 1/6) (/.f64 (pow.f64 th 4) (cbrt.f64 2))) (fma.f64 -1/2 (*.f64 (pow.f64 1/2 1/6) (/.f64 (*.f64 th th) (cbrt.f64 2))) (*.f64 (pow.f64 1/2 1/6) (/.f64 1 (cbrt.f64 2))))))
(+.f64 (*.f64 (pow.f64 1/2 1/6) (+.f64 (/.f64 1 (cbrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 th th) (cbrt.f64 2))))) (*.f64 (pow.f64 1/2 1/6) (+.f64 (*.f64 -1/720 (/.f64 (pow.f64 th 6) (cbrt.f64 2))) (*.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2))))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (fma.f64 -1/2 (*.f64 (/.f64 th (cbrt.f64 2)) th) (/.f64 1 (cbrt.f64 2))) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (cbrt.f64 2)) (*.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2))))))
(*.f64 (pow.f64 1/2 1/6) (+.f64 (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (cbrt.f64 2)) (*.f64 1/24 (/.f64 (pow.f64 th 4) (cbrt.f64 2)))) (fma.f64 -1/2 (/.f64 th (/.f64 (cbrt.f64 2) th)) (/.f64 1 (cbrt.f64 2)))))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 1/2 1/6))
(*.f64 (pow.f64 1/2 1/6) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 1/2 1/6) (cbrt.f64 2)) (cos.f64 th))

eval339.0ms (2.4%)

Compiler

Compiled 7688 to 4779 computations (37.8% saved)

prune110.0ms (0.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

PrunedKeptTotal
New43516451
Fresh325
Picked101
Done325
Total44220462
Error
0b
Counts
462 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
▶37.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
41.1b
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
28.0b
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
37.2b
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
28.0b
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
27.1b
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
27.1b
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
▶28.0b
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
44.7b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
28.0b
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
23.7b
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
41.1b
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓0.5b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
27.1b
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
27.1b
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
27.1b
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
▶43.9b
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
▶23.6b
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
▶27.1b
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
✓27.1b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
Compiler

Compiled 467 to 361 computations (22.7% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
Compiler

Compiled 26 to 11 computations (57.7% saved)

series3.0ms (0%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
a2
@0
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
0.0ms
a2
@inf
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
0.0ms
a1
@inf
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
0.0ms
a1
@0
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
0.0ms
a2
@-inf
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))

rewrite50.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
674×pow1_binary64
620×add-log-exp_binary64
620×log1p-expm1-u_binary64
620×expm1-log1p-u_binary64
605×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
115812
2175312
Stop Event
1×node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 1/2 1/4) (hypot.f64 a2 a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))))))

simplify161.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1040×sqr-pow_binary64
784×cube-prod_binary64
743×fabs-mul_binary64
484×unswap-sqr_binary64
360×pow-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011324
125288
249288
394288
4226288
5687288
61068288
71891288
82108288
92348288
102661288
113107288
123703288
134412288
145296288
155988288
166446288
176882288
187038288
197108288
207935288
Stop Event
1×node limit
Counts
39 → 21
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (*.f64 a2 a2)))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
✓0.5b
(/.f64 a1 (sqrt.f64 2))
Compiler

Compiled 17 to 13 computations (23.5% saved)

series3.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
a1
@inf
(/.f64 a1 (sqrt.f64 2))
1.0ms
a1
@0
(/.f64 a1 (sqrt.f64 2))
1.0ms
a1
@inf
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
1.0ms
a1
@0
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.0ms
a1
@-inf
(/.f64 a1 (sqrt.f64 2))

rewrite65.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
618×pow1_binary64
576×add-log-exp_binary64
576×log1p-expm1-u_binary64
576×expm1-log1p-u_binary64
564×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
112715
2156615
Stop Event
1×node limit
Counts
2 → 50
Calls
Call 1
Inputs
(/.f64 a1 (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (*.f64 a1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a1) (*.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 a1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 a1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))))

simplify116.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
759×sqr-pow_binary64
434×unswap-sqr_binary64
423×*-commutative_binary64
423×associate-*r/_binary64
393×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06108
111108
220108
337108
483108
5266108
61091108
73478108
84280108
94465108
104681108
115028108
125456108
135935108
146584108
157273108
Stop Event
1×node limit
Counts
62 → 52
Calls
Call 1
Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (*.f64 th (*.f64 th -1/2)))
✓0.2b
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
0.4b
(/.f64 a2 (sqrt.f64 2))
✓8.3b
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
Compiler

Compiled 49 to 35 computations (28.6% saved)

series6.0ms (0%)

Counts
3 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
a2
@0
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
1.0ms
th
@inf
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
1.0ms
th
@0
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
0.0ms
a2
@inf
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
0.0ms
a2
@0
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

rewrite129.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
949×prod-diff_binary64
680×log-prod_binary64
443×fma-def_binary64
230×expm1-udef_binary64
230×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01340
127836
2363036
Stop Event
1×node limit
Counts
3 → 175
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 1 (*.f64 th (*.f64 th -1/2)))
Outputs
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1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th th) -1/2 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 th (*.f64 th -1/2))) (cbrt.f64 (pow.f64 (*.f64 th (*.f64 th -1/2)) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 th (*.f64 th -1/2)) 2)) (cbrt.f64 (*.f64 th (*.f64 th -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 th) 2) (*.f64 (cbrt.f64 th) (*.f64 th -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 th -1/2) 2)) (*.f64 (cbrt.f64 (*.f64 th -1/2)) th) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th (sqrt.f64 -1/2)) (*.f64 th (sqrt.f64 -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 th) (*.f64 (sqrt.f64 th) (*.f64 th -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 th -1/2)) (*.f64 (sqrt.f64 (*.f64 th -1/2)) th) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th (cbrt.f64 (pow.f64 (*.f64 th -1/2) 2))) (cbrt.f64 (*.f64 th -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th (sqrt.f64 (*.f64 th -1/2))) (sqrt.f64 (*.f64 th -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 th -1/2) (pow.f64 (cbrt.f64 th) 2)) (cbrt.f64 th) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 th -1/2) (sqrt.f64 th)) (sqrt.f64 th) 1)))))

simplify123.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
1380×associate-/l/_binary64
1044×fma-def_binary64
539×associate-*r/_binary64
451×associate-/r/_binary64
402×distribute-lft-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
018699
139639
2101639
3350639
41739639
54008639
65018639
76654639
87076639
97206639
107359639
Stop Event
1×node limit
Counts
223 → 187
Calls
Call 1
Inputs
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(*.f64 -1/2 (pow.f64 th 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(*.f64 -1/2 (pow.f64 th 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
Outputs
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(/.f64 (*.f64 -1/2 (*.f64 (*.f64 th th) (*.f64 a2 a2))) (sqrt.f64 2))
(*.f64 -1/2 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (*.f64 th th)))
(*.f64 (/.f64 -1/2 (sqrt.f64 2)) (*.f64 (*.f64 th a2) (*.f64 th a2)))
(/.f64 (*.f64 (*.f64 th a2) (*.f64 th a2)) (/.f64 (sqrt.f64 2) -1/2))
(*.f64 th (/.f64 -1/2 (/.f64 (/.f64 (sqrt.f64 2) th) (*.f64 a2 a2))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(/.f64 (*.f64 -1/2 (*.f64 (*.f64 th th) (*.f64 a2 a2))) (sqrt.f64 2))
(*.f64 -1/2 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (*.f64 th th)))
(*.f64 (/.f64 -1/2 (sqrt.f64 2)) (*.f64 (*.f64 th a2) (*.f64 th a2)))
(/.f64 (*.f64 (*.f64 th a2) (*.f64 th a2)) (/.f64 (sqrt.f64 2) -1/2))
(*.f64 th (/.f64 -1/2 (/.f64 (/.f64 (sqrt.f64 2) th) (*.f64 a2 a2))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) (fma.f64 -1/2 (*.f64 th th) 1))
(*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(*.f64 (fma.f64 th (*.f64 -1/2 th) 1) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (*.f64 th th))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (*.f64 th th))
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 th th)))
(fma.f64 -1/2 (*.f64 th th) 1)
(fma.f64 th (*.f64 -1/2 th) 1)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
0.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.5b
(/.f64 a1 (sqrt.f64 2))
Compiler

Compiled 29 to 19 computations (34.5% saved)

series4.0ms (0%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
th
@inf
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
1.0ms
a1
@0
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
1.0ms
th
@-inf
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
1.0ms
th
@0
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
0.0ms
a1
@inf
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))

rewrite56.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
931×pow1_binary64
861×add-log-exp_binary64
861×log1p-expm1-u_binary64
861×expm1-log1p-u_binary64
842×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
118714
2233014
Stop Event
1×node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a1 (pow.f64 2 1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a1) (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))))))))

simplify97.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
1132×unswap-sqr_binary64
659×associate-*l/_binary64
607×fma-def_binary64
494×associate-*r/_binary64
372×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
032424
183424
2230424
3857406
42734387
54348375
65665375
75970375
86198375
96407375
Stop Event
1×node limit
Counts
39 → 25
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 -1/720 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (*.f64 th th))) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 th th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(fma.f64 -1/2 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 th th)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (*.f64 th (*.f64 th -1/2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(*.f64 (+.f64 (*.f64 -1/2 (*.f64 th th)) 1) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (*.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (*.f64 th th))) (fma.f64 1/24 (/.f64 (*.f64 (*.f64 a1 a1) (pow.f64 th 4)) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 th th)) (fma.f64 1/24 (/.f64 (*.f64 (*.f64 a1 a1) (pow.f64 th 4)) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 -1/2 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 th th)) (fma.f64 1/24 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (pow.f64 th 4)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4)))))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (fma.f64 th (*.f64 th -1/2) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (+.f64 (fma.f64 th (*.f64 th -1/2) (*.f64 1/24 (pow.f64 th 4))) 1) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (+.f64 1 (fma.f64 th (*.f64 th -1/2) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (+.f64 1 (fma.f64 th (*.f64 th -1/2) (*.f64 1/24 (pow.f64 th 4)))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (*.f64 -1/720 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (*.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (*.f64 th th))) (fma.f64 -1/720 (/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (fma.f64 1/24 (/.f64 (*.f64 (*.f64 a1 a1) (pow.f64 th 4)) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(fma.f64 -1/2 (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 th th)) (fma.f64 -1/720 (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (pow.f64 th 6)) (fma.f64 1/24 (/.f64 (*.f64 (*.f64 a1 a1) (pow.f64 th 4)) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(fma.f64 -1/2 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 th th)) (fma.f64 1/24 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (pow.f64 th 4)) (fma.f64 -1/720 (*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (pow.f64 th 6)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))))
(fma.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (*.f64 1/24 (pow.f64 th 4)) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 -1/720 (pow.f64 th 6))))))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (+.f64 (*.f64 -1/2 (*.f64 th th)) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))))))
(*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (+.f64 (+.f64 1 (*.f64 -1/2 (*.f64 th th))) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (+.f64 (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))) (+.f64 1 (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (fma.f64 -1/720 (pow.f64 th 6) (*.f64 1/24 (pow.f64 th 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)
(*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 a1 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 a1 (*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2))))

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th))
✓0.2b
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
✓0.4b
(*.f64 (pow.f64 2 -1/2) a2)
Compiler

Compiled 35 to 24 computations (31.4% saved)

series8.0ms (0.1%)

Counts
3 → 60
Calls

15 calls:

TimeVariablePointExpression
1.0ms
a2
@0
(*.f64 (pow.f64 2 -1/2) a2)
1.0ms
th
@-inf
(*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th))
1.0ms
a2
@inf
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
1.0ms
th
@0
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
1.0ms
th
@-inf
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))

rewrite83.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
949×pow1_binary64
876×add-log-exp_binary64
875×log1p-expm1-u_binary64
875×expm1-log1p-u_binary64
856×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01034
120831
2242631
Stop Event
1×node limit
Counts
3 → 39
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 -1/2) a2)
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
(*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 a2 a2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) 1/2) (pow.f64 a2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 a2 3) (*.f64 (sqrt.f64 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) a2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 a2 3) (pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) (pow.f64 a2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 a2) (sqrt.f64 1/2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))))

simplify250.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
841×distribute-lft-out_binary64
697×sqr-pow_binary64
645×*-commutative_binary64
524×distribute-rgt-in_binary64
368×pow-sqr_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
056830
1143830
2410790
31763769
43229758
53851758
64498758
75464758
85621758
95804758
106095758
116397758
126738758
137148758
147633758
Stop Event
1×node limit
Counts
99 → 59
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) a2))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4)))) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 6)))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
Outputs
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 th) (*.f64 a2 th))) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(*.f64 (*.f64 a2 a2) (+.f64 (sqrt.f64 1/2) (*.f64 (*.f64 th th) (*.f64 (sqrt.f64 1/2) -1/2))))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (+.f64 a2 (*.f64 th (*.f64 -1/2 (*.f64 a2 th))))))
(*.f64 (*.f64 a2 a2) (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) (sqrt.f64 1/2)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 4))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 th) (*.f64 a2 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 (*.f64 a2 (pow.f64 th 4))) 1/24))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (*.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (*.f64 a2 a2) (+.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 a2 (*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4)))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (fma.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 6))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 4)))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 th) (*.f64 a2 th))) (fma.f64 -1/720 (*.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)) (pow.f64 th 6)) (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 (*.f64 a2 (pow.f64 th 4))) 1/24)))))
(+.f64 (*.f64 (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 -1/2 (*.f64 th th)))) (*.f64 (*.f64 a2 a2) (+.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 th 4) (*.f64 (sqrt.f64 1/2) 1/24)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 a2 (+.f64 a2 (*.f64 th (*.f64 -1/2 (*.f64 a2 th))))) (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (+.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (+.f64 (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 th (*.f64 th -1/2))) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) a2))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 th th))) (*.f64 (sqrt.f64 1/2) a2))
(fma.f64 (sqrt.f64 1/2) a2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 (*.f64 th th)) -1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 a2 (*.f64 a2 (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (sqrt.f64 1/2) (+.f64 a2 (*.f64 th (*.f64 -1/2 (*.f64 a2 th)))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 th th))) (fma.f64 (sqrt.f64 1/2) a2 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 th th))) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))) (*.f64 (sqrt.f64 1/2) a2)))
(fma.f64 (sqrt.f64 1/2) a2 (*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/2 (*.f64 th th)))))
(*.f64 (sqrt.f64 1/2) (+.f64 a2 (*.f64 a2 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (*.f64 th (*.f64 th -1/2)) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4)))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4)))) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 6)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 th th))) (fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 6)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 th th))) (fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (pow.f64 th 4))) (*.f64 (*.f64 (sqrt.f64 1/2) a2) (*.f64 (pow.f64 th 6) -1/720)))))
(+.f64 (*.f64 (sqrt.f64 1/2) (+.f64 a2 (*.f64 a2 (*.f64 -1/2 (*.f64 th th))))) (*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 a2 (*.f64 a2 (*.f64 -1/720 (pow.f64 th 6)))) (*.f64 a2 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (*.f64 (sqrt.f64 1/2) a2) (+.f64 (+.f64 (*.f64 -1/720 (pow.f64 th 6)) (*.f64 th (*.f64 th -1/2))) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (cos.f64 th)))

eval154.0ms (1.1%)

Compiler

Compiled 7055 to 4985 computations (29.3% saved)

prune129.0ms (0.9%)

Pruning

28 alts after pruning (23 fresh and 5 done)

PrunedKeptTotal
New41017427
Fresh7613
Picked101
Done156
Total41928447
Error
0b
Counts
447 → 28
Alt Table
Click to see full alt table
StatusErrorProgram
✓37.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
▶41.1b
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
41.1b
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
27.1b
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
▶37.2b
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
▶27.1b
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
✓28.0b
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
37.2b
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
▶42.2b
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
41.1b
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
✓27.1b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
28.0b
(*.f64 (*.f64 a1 (*.f64 (pow.f64 2 -1/2) a1)) (cos.f64 th))
41.1b
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
56.9b
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
✓0.5b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
54.2b
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
37.2b
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
27.1b
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
27.1b
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
▶37.2b
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
40.2b
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
✓23.6b
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
28.0b
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
37.3b
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
56.5b
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
28.0b
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
37.2b
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
43.9b
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
Compiler

Compiled 610 to 469 computations (23.1% saved)

localize28.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓0.3b
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
Compiler

Compiled 27 to 15 computations (44.4% saved)

series6.0ms (0%)

Counts
2 → 28
Calls

9 calls:

TimeVariablePointExpression
1.0ms
th
@-inf
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
1.0ms
th
@inf
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
1.0ms
a2
@0
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
1.0ms
th
@0
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
1.0ms
th
@0
(*.f64 (sqrt.f64 1/2) (cos.f64 th))

rewrite79.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
811×pow1_binary64
746×add-log-exp_binary64
746×log1p-expm1-u_binary64
746×expm1-log1p-u_binary64
727×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0922
118122
2209822
Stop Event
1×node limit
Counts
2 → 26
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 1/2 (pow.f64 (cos.f64 th) 2)) (pow.f64 a2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 a2 a2) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) (pow.f64 (*.f64 a2 a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (*.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 1/2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))

simplify209.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
840×unswap-sqr_binary64
741×distribute-lft-out_binary64
539×sqr-pow_binary64
405×*-commutative_binary64
289×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
048510
1125508
2358478
31597458
42729454
54272454
64491454
74719454
84972454
95244454
106662454
117026454
127478454
137995454
Stop Event
1×node limit
Counts
54 → 44
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(sqrt.f64 1/2)
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
Outputs
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (*.f64 (*.f64 (*.f64 a2 a2) (*.f64 th th)) (*.f64 (sqrt.f64 1/2) -1/2)))
(*.f64 (*.f64 a2 a2) (fma.f64 (sqrt.f64 1/2) (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (+.f64 (*.f64 -1/2 (*.f64 a2 (*.f64 th th))) a2)))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 4))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)) (*.f64 (sqrt.f64 1/2) 1/24))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (+.f64 1 (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))))
(+.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (fma.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 6))) (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (pow.f64 th 4)))))))
(fma.f64 (sqrt.f64 1/2) (*.f64 a2 a2) (fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (*.f64 th th))) (fma.f64 -1/720 (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (pow.f64 th 6)))) (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 th 4)) (*.f64 (sqrt.f64 1/2) 1/24)))))
(+.f64 (*.f64 (*.f64 a2 a2) (fma.f64 (sqrt.f64 1/2) (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(*.f64 (*.f64 a2 a2) (+.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 -1/720 (pow.f64 th 6)))))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 -1/720 (pow.f64 th 6))))))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(sqrt.f64 1/2)
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (sqrt.f64 1/2))
(fma.f64 (sqrt.f64 1/2) (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (*.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (+.f64 (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)) (*.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (fma.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 (sqrt.f64 1/2) (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(+.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 th (*.f64 th -1/2)) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))
(*.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (*.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 1 (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 -1/720 (pow.f64 th 6))))))
(*.f64 (sqrt.f64 1/2) (+.f64 1 (+.f64 (*.f64 1/24 (pow.f64 th 4)) (+.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 -1/720 (pow.f64 th 6))))))

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
✓0.4b
(*.f64 (sqrt.f64 1/2) a2)
Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
0.0ms
a2
@inf
(*.f64 (sqrt.f64 1/2) a2)
0.0ms
a2
@0
(*.f64 (sqrt.f64 1/2) a2)
0.0ms
a2
@inf
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
0.0ms
a2
@0
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
0.0ms
a2
@-inf
(*.f64 (sqrt.f64 1/2) a2)

rewrite47.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
511×pow1_binary64
490×add-sqr-sqrt_binary64
471×add-log-exp_binary64
471×log1p-expm1-u_binary64
471×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
112015
2131615
Stop Event
1×node limit
Counts
2 → 22
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) a2)
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) a2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) a2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (*.f64 (sqrt.f64 1/2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))))

simplify176.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
554×fabs-mul_binary64
523×pow-sqr_binary64
441×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07108
113108
223108
344108
4107108
5328108
61230108
72107108
82271108
92455108
102663108
112959108
123352108
133833108
144401108
155091108
165926108
176320108
186610108
196884108
206954108
216988108
227929108
Stop Event
1×node limit
Counts
34 → 24
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
a1
@0
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
0.0ms
a1
@inf
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
0.0ms
a1
@-inf
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

rewrite62.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
610×pow1_binary64
570×add-log-exp_binary64
570×log1p-expm1-u_binary64
570×expm1-log1p-u_binary64
556×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11279
215839
Stop Event
1×node limit
Counts
1 → 32
Calls
Call 1
Inputs
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (*.f64 a1 (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 a1) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)) (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 a1 4)) (*.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 1) (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 a1 a1) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 a1 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))))))

simplify152.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
759×sqr-pow_binary64
434×unswap-sqr_binary64
423×*-commutative_binary64
423×associate-*r/_binary64
393×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06108
111108
220108
337108
483108
5266108
61091108
73478108
84280108
94465108
104681108
115028108
125456108
135935108
146584108
157273108
Stop Event
1×node limit
Counts
44 → 34
Calls
Call 1
Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

localize37.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.5b
(/.f64 a1 (sqrt.f64 2))
✓1.6b
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
Compiler

Compiled 36 to 28 computations (22.2% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
a1
@0
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
0.0ms
a1
@inf
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
0.0ms
a1
@-inf
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)

rewrite117.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
986×pow1_binary64
926×add-log-exp_binary64
925×log1p-expm1-u_binary64
925×expm1-log1p-u_binary64
102×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0915
12039
227939
Stop Event
1×node limit
Counts
1 → 60
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 a1) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) 2)) (*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cbrt.f64 a1) (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 2) (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (*.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a1) (*.f64 (sqrt.f64 a1) (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) -1) (/.f64 1 (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 1) (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (/.f64 a1 (pow.f64 2 1/4))) 1) (-.f64 (hypot.f64 1 (/.f64 a1 (pow.f64 2 1/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (cbrt.f64 (/.f64 (*.f64 a1 a1) 2))) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (sqrt.f64 (/.f64 a1 (sqrt.f64 2)))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) (sqrt.f64 a1)) (sqrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2)) (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2) (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 a1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) (-.f64 1 (*.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) -1) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) -1) (-.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) 2) -1)) (neg.f64 (+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1))) (-.f64 1 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1)) 2) (cbrt.f64 (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 a1 (pow.f64 2 1/4))) (hypot.f64 1 (/.f64 a1 (pow.f64 2 1/4))) -1)))))

simplify135.0ms (1%)

Algorithm
1×egg-herbie
Rules
759×sqr-pow_binary64
434×unswap-sqr_binary64
423×*-commutative_binary64
423×associate-*r/_binary64
393×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06108
111108
220108
337108
483108
5266108
61091108
73478108
84280108
94465108
104681108
115028108
125456108
135935108
146584108
157273108
Stop Event
1×node limit
Counts
72 → 61
Calls
Call 1
Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

localize30.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
✓0.3b
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
✓0.4b
(/.f64 (sqrt.f64 2) a1)
Compiler

Compiled 26 to 21 computations (19.2% saved)

series7.0ms (0%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
a1
@-inf
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
1.0ms
a1
@0
(/.f64 (sqrt.f64 2) a1)
1.0ms
a1
@-inf
(/.f64 (sqrt.f64 2) a1)
1.0ms
a1
@0
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
1.0ms
a1
@inf
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)

rewrite121.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
760×pow1_binary64
707×add-log-exp_binary64
707×log1p-expm1-u_binary64
707×expm1-log1p-u_binary64
691×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
116721
2197321
Stop Event
1×node limit
Counts
3 → 85
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 2) a1)
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (sqrt.f64 2) a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (/.f64 1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) a1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a1)) (cbrt.f64 (/.f64 2 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (*.f64 a1 a1))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a1)) (sqrt.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (/.f64 1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 a1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 a1 a1))) (/.f64 (sqrt.f64 2) (cbrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (*.f64 a1 a1))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (*.f64 a1 a1))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 a1)) (/.f64 (sqrt.f64 2) (sqrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 a1)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 a1 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) a1)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 2) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 2) -1) (pow.f64 (/.f64 1 a1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 a1 a1))) -1) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a1)) -1) (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 a1 a1)) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 a1 a1)) (cbrt.f64 2)) (/.f64 (cbrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 a1 a1)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) (pow.f64 2 1/4)) (/.f64 (sqrt.f64 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (neg.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (sqrt.f64 2) a1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cbrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 2) (sqrt.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 a1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 a1 (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 a1 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 a1 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (*.f64 a1 a1)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a1 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))) a1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 a1 3) (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) (pow.f64 a1 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))))

simplify132.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
760×sqr-pow_binary64
444×associate-*r/_binary64
434×unswap-sqr_binary64
415×*-commutative_binary64
393×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07180
112180
221180
338180
486180
5274180
61103180
73496180
84318180
94503180
104719180
115069180
125499180
135982180
146634180
157323180
Stop Event
1×node limit
Counts
109 → 87
Calls
Call 1
Inputs
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
Outputs
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

eval92.0ms (0.7%)

Compiler

Compiled 3661 to 2708 computations (26% saved)

prune65.0ms (0.5%)

Pruning

30 alts after pruning (21 fresh and 9 done)

PrunedKeptTotal
New2957302
Fresh41418
Picked101
Done099
Total30030330
Error
0b
Counts
330 → 30
Alt Table
Click to see full alt table
StatusErrorProgram
46.5b
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
40.2b
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
✓37.2b
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
✓41.1b
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
37.2b
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
41.1b
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
27.1b
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
✓37.2b
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
37.2b
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
41.1b
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
✓27.1b
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
✓28.0b
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
✓27.1b
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
28.0b
(*.f64 (*.f64 a1 (*.f64 (pow.f64 2 -1/2) a1)) (cos.f64 th))
37.3b
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
28.0b
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
41.1b
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
56.9b
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
✓0.5b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
54.2b
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
37.2b
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
27.1b
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
37.2b
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
27.1b
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
✓23.6b
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
28.0b
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
✓42.2b
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
56.5b
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
37.3b
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
43.9b
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
Compiler

Compiled 355 to 273 computations (23.1% saved)

regimes289.0ms (2%)

Counts
52 → 1
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (*.f64 (pow.f64 2 -1/2) a1)) (cos.f64 th))
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
Outputs
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Calls

10 calls:

66.0ms
a1
29.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
27.0ms
a2
25.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
25.0ms
th
Results
ErrorSegmentsBranch
0.4b1a1
0.4b1a2
0.4b1th
0.4b1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.4b1(/.f64 (cos.f64 th) (sqrt.f64 2))
0.4b1(/.f64 (cos.f64 th) (sqrt.f64 2))
0.4b1(cos.f64 th)
0.4b1(*.f64 a1 a1)
0.4b1(*.f64 a1 a1)
0.4b1(*.f64 a2 a2)
Compiler

Compiled 576 to 365 computations (36.6% saved)

regimes266.0ms (1.9%)

Counts
45 → 1
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (*.f64 (pow.f64 2 -1/2) a1)) (cos.f64 th))
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Outputs
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
Calls

8 calls:

73.0ms
a1
53.0ms
(cos.f64 th)
34.0ms
(*.f64 a1 a1)
23.0ms
a2
22.0ms
th
Results
ErrorSegmentsBranch
0.5b1a1
0.5b1a2
0.5b1th
0.5b1(/.f64 (cos.f64 th) (sqrt.f64 2))
0.5b1(cos.f64 th)
0.5b1(*.f64 a1 a1)
0.5b1(*.f64 a1 a1)
0.5b1(*.f64 a2 a2)
Compiler

Compiled 447 to 286 computations (36% saved)

regimes950.0ms (6.7%)

Counts
44 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(*.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(*.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (*.f64 a1 (*.f64 (pow.f64 2 -1/2) a1)) (cos.f64 th))
(*.f64 a2 (*.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
(*.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
Outputs
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
Calls

10 calls:

158.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
144.0ms
th
137.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
120.0ms
(cos.f64 th)
103.0ms
(*.f64 a1 a1)
Results
ErrorSegmentsBranch
6.6b2a1
6.9b2a2
9.0b5th
9.2b4(/.f64 (cos.f64 th) (sqrt.f64 2))
9.2b4(/.f64 (cos.f64 th) (sqrt.f64 2))
9.2b4(cos.f64 th)
11.0b4(*.f64 a1 a1)
11.0b4(*.f64 a1 a1)
11.3b4(*.f64 a2 a2)
11.3b4(*.f64 a2 a2)
Compiler

Compiled 449 to 292 computations (35% saved)

bsearch62.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
61.0ms
-2.2240413927052555e-147
-9.095573415959815e-148
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes608.0ms (4.3%)

Counts
32 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
Outputs
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
Calls

10 calls:

180.0ms
th
94.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
58.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
48.0ms
a2
45.0ms
(cos.f64 th)
Results
ErrorSegmentsBranch
6.6b2a1
6.9b2a2
17.0b9th
21.4b4(/.f64 (cos.f64 th) (sqrt.f64 2))
21.4b4(/.f64 (cos.f64 th) (sqrt.f64 2))
21.4b4(cos.f64 th)
11.0b4(*.f64 a1 a1)
11.0b4(*.f64 a1 a1)
11.3b4(*.f64 a2 a2)
11.3b4(*.f64 a2 a2)
Compiler

Compiled 335 to 228 computations (31.9% saved)

bsearch57.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
57.0ms
-2.2240413927052555e-147
-9.095573415959815e-148
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes798.0ms (5.6%)

Counts
31 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
Outputs
(/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
Calls

10 calls:

206.0ms
th
91.0ms
(cos.f64 th)
83.0ms
a2
82.0ms
(*.f64 a1 a1)
68.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))
Results
ErrorSegmentsBranch
6.6b2a1
6.9b2a2
17.0b9th
21.4b4(/.f64 (cos.f64 th) (sqrt.f64 2))
21.4b4(/.f64 (cos.f64 th) (sqrt.f64 2))
21.4b4(cos.f64 th)
11.0b4(*.f64 a1 a1)
11.0b4(*.f64 a1 a1)
11.3b4(*.f64 a2 a2)
11.3b4(*.f64 a2 a2)
Compiler

Compiled 326 to 224 computations (31.3% saved)

bsearch63.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
63.0ms
-2.2240413927052555e-147
-9.095573415959815e-148
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes316.0ms (2.2%)

Counts
28 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
Outputs
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th))))
Calls

8 calls:

87.0ms
th
52.0ms
(*.f64 a1 a1)
42.0ms
a2
41.0ms
(*.f64 a1 a1)
26.0ms
a1
Results
ErrorSegmentsBranch
15.5b2a1
13.8b2a2
18.4b7th
22.6b2(cos.f64 th)
16.6b6(*.f64 a1 a1)
16.6b6(*.f64 a1 a1)
19.0b2(*.f64 a2 a2)
19.0b2(*.f64 a2 a2)
Compiler

Compiled 283 to 197 computations (30.4% saved)

bsearch57.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
57.0ms
3.1303225098756238e-152
1.708562226319729e-150
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes178.0ms (1.3%)

Counts
27 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a1 (*.f64 (/.f64 1 (sqrt.f64 2)) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (sqrt.f64 (/.f64 (*.f64 a1 a1) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(*.f64 a1 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a1)))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(*.f64 th (*.f64 -1/2 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 th a2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (*.f64 -1/2 (*.f64 th th)))
(/.f64 (*.f64 (+.f64 1 (*.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (*.f64 th (*.f64 th -1/2)))))
(*.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (*.f64 th (*.f64 th -1/2))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
Outputs
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
Calls

7 calls:

52.0ms
th
28.0ms
a1
27.0ms
a2
16.0ms
(*.f64 a2 a2)
15.0ms
(*.f64 a1 a1)
Results
ErrorSegmentsBranch
27.1b2a1
27.5b2a2
34.8b4th
29.7b2(*.f64 a1 a1)
29.7b2(*.f64 a1 a1)
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 269 to 187 computations (30.5% saved)

bsearch99.0ms (0.7%)

Algorithm
1×binary-search
Steps
TimeLeftRight
98.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes154.0ms (1.1%)

Counts
10 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
Outputs
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
Calls

6 calls:

49.0ms
th
26.0ms
a1
25.0ms
a2
17.0ms
(*.f64 a2 a2)
16.0ms
(*.f64 a1 a1)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
29.7b2(*.f64 a1 a1)
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 93 to 61 computations (34.4% saved)

bsearch111.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
111.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes146.0ms (1%)

Counts
9 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
Outputs
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
Calls

6 calls:

45.0ms
th
24.0ms
a2
24.0ms
a1
16.0ms
(*.f64 a2 a2)
16.0ms
(*.f64 a1 a1)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
29.7b2(*.f64 a1 a1)
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 87 to 58 computations (33.3% saved)

bsearch108.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
108.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes121.0ms (0.9%)

Counts
8 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
Outputs
(*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
Calls

6 calls:

43.0ms
th
18.0ms
a2
15.0ms
(*.f64 a2 a2)
14.0ms
(*.f64 a2 a2)
14.0ms
(*.f64 a1 a1)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
29.7b2(*.f64 a1 a1)
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 81 to 54 computations (33.3% saved)

bsearch57.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
57.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes60.0ms (0.4%)

Counts
6 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))
Outputs
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
Calls

6 calls:

18.0ms
th
10.0ms
a2
9.0ms
a1
7.0ms
(*.f64 a2 a2)
6.0ms
(*.f64 a2 a2)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
29.7b2(*.f64 a1 a1)
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 69 to 47 computations (31.9% saved)

bsearch58.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
58.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes39.0ms (0.3%)

Counts
3 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
Outputs
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (*.f64 (sqrt.f64 1/2) a2))
Calls

5 calls:

14.0ms
th
7.0ms
a1
7.0ms
a2
5.0ms
(*.f64 a2 a2)
5.0ms
(*.f64 a2 a2)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
30.3b2(*.f64 a2 a2)
30.3b2(*.f64 a2 a2)
Compiler

Compiled 45 to 32 computations (28.9% saved)

bsearch59.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
59.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes31.0ms (0.2%)

Accuracy

Total -27.4b remaining (-100.8%)

Threshold costs -27.4b (-100.8%)

Counts
2 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
Outputs
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
Calls

4 calls:

12.0ms
th
6.0ms
a1
6.0ms
a2
4.0ms
(*.f64 a2 a2)
Results
ErrorSegmentsBranch
27.2b2a1
27.5b2a2
34.8b4th
30.3b2(*.f64 a2 a2)
Compiler

Compiled 33 to 24 computations (27.3% saved)

bsearch60.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
60.0ms
-6.106381439212111e-127
-2.9121755179734557e-133
Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify14.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
16×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059351
177351
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 7383574706152289/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
Outputs
(*.f64 (*.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a1 -8004616401021389/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (/.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(if (<=.f64 a1 -8004616401021389/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (/.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)) (*.f64 (*.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))))
(if (<=.f64 a1 -128073862416342224/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a1 -8004616401021389/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (/.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 (cos.f64 th) a2))))
(if (<=.f64 a2 7383574706152289/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 7383574706152289/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (*.f64 (sqrt.f64 1/2) (*.f64 a2 (*.f64 (cos.f64 th) a2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -1906258740553689088/3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a1 -930790400660981/1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711624327585667956874652483059712) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))
(*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))
Compiler

Compiled 274 to 197 computations (28.1% saved)

soundness11.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
32×fma-def_binary64
23×*-commutative_binary64
20×associate-/l*_binary64
11×associate-/r/_binary64
9×associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01320
12718
25818
38818
411518
513518
615218
717018
817218
Stop Event
1×saturated
Compiler

Compiled 53 to 36 computations (32.1% saved)

end186.0ms (1.3%)

Remove

(sort a1 a2)

Compiler

Compiled 267 to 158 computations (40.8% saved)

Profiling

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