Details

Time bar (total: 4.9s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.6%50.4%0%0%0%0
100%49.6%0%50.4%0%0%0%1
Compiler

Compiled 12 to 9 computations (25% saved)

sample3.9s (80.2%)

Results
2.8s4400×body2048valid
773.0ms2048×body1024valid
186.0ms1003×body512valid
116.0ms805×body256valid
Bogosity

preprocess35.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
12×fma-def
12×+-commutative
10×associate-+l-
8×sub-neg
6×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11111
21511
32211
42911
53911
65511
76511
86811
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(-.f64 1 (cos.f64 x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify13.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
12×fma-def
12×+-commutative
10×associate-+l-
8×sub-neg
6×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11111
21511
32211
42911
53911
65511
76511
86811
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(-.f64 1 (cos.f64 x))

eval0.0ms (0%)

Compiler

Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
30.2b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶30.2b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 5 to 4 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓3.0b
(-.f64 1 (cos.f64 x))
Compiler

Compiled 9 to 5 computations (44.4% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 1 (cos.f64 x))
0.0ms
x
@inf
(-.f64 1 (cos.f64 x))
0.0ms
x
@-inf
(-.f64 1 (cos.f64 x))

rewrite78.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
1402×add-sqr-sqrt
1386×*-un-lft-identity
1288×add-cube-cbrt
1276×add-cbrt-cube
1266×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114011
2168611
Stop Event
1×node limit
Counts
1 → 29
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))))

simplify54.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
932×associate-/l*
906×associate-*r*
896×times-frac
852×distribute-lft-in
792×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
095817
1232757
2782687
33180687
Stop Event
1×node limit
Counts
33 → 43
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(-.f64 1 (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (/.f64 1 (+.f64 1 (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) -1))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(-.f64 1 (cos.f64 x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(-.f64 1 (cos.f64 x))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(-.f64 1 (cos.f64 x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(-.f64 1 (cos.f64 x))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))

eval8.0ms (0.2%)

Compiler

Compiled 469 to 279 computations (40.5% saved)

prune8.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New40343
Fresh000
Picked011
Done000
Total40444
Error
0b
Counts
44 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶0b
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
✓30.2b
(-.f64 1 (cos.f64 x))
▶0.0b
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶0.3b
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize4.0ms (0.1%)

Compiler

Compiled 11 to 5 computations (54.5% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms
x
@-inf
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
0.0ms
x
@0
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

rewrite73.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
1792×add-sqr-sqrt
1766×*-un-lft-identity
1644×add-cube-cbrt
1624×add-cbrt-cube
182×pow1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
118721
2221421
Stop Event
1×node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))))))

simplify64.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1088×fma-def
952×distribute-lft-in
894×distribute-rgt-in
874×*-commutative
738×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069779
1152779
2419779
32320779
46397779
Stop Event
1×node limit
Counts
27 → 33
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))) 1)
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 1)
(pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 2)
(pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 3)
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 x 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3))
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
(exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (*.f64 1/720 (pow.f64 x 6))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))) 1)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 2)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 3)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3) 1/3)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 2))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 x 1/2))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2))) 3))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))) 1))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 x 1/2)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 -1/24 (pow.f64 x 4))
Compiler

Compiled 26 to 17 computations (34.6% saved)

series3.0ms (0.1%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 -1/24 (pow.f64 x 4))
0.0ms
x
@0
(*.f64 -1/24 (pow.f64 x 4))
0.0ms
x
@-inf
(*.f64 -1/24 (pow.f64 x 4))

rewrite52.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
1214×add-sqr-sqrt
1190×*-un-lft-identity
1132×pow1
1120×add-cube-cbrt
1112×add-cbrt-cube
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
114613
2158813
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 -1/24 (pow.f64 x 4))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/24) (*.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 4)) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))))))

simplify60.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1288×distribute-rgt-in
1264×distribute-lft-in
1002×log-prod
666×associate-*r*
640×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038275
193209
2328143
31794143
47731143
Stop Event
1×node limit
Counts
11 → 14
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) 1)
(pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)
(pow.f64 (*.f64 (sqrt.f64 -1/24) (*.f64 x x)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)
(pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 4)) -1/24))
(cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))
(exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))
(log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))
Outputs
(-.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) 1)
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (*.f64 (sqrt.f64 -1/24) (*.f64 x x)) 2)
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(pow.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 4)) -1/24))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(cbrt.f64 (pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 3))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(exp.f64 (log.f64 (*.f64 -1/24 (pow.f64 x 4))))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))
(log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))
(+.f64 (+.f64 1 (*.f64 -1/24 (pow.f64 x 4))) -1)
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) 0)
(*.f64 -1/24 (pow.f64 x 4))

eval12.0ms (0.2%)

Compiler

Compiled 564 to 387 computations (31.4% saved)

prune19.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New46147
Fresh000
Picked101
Done123
Total48351
Error
0b
Counts
51 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.2b
(-.f64 1 (cos.f64 x))
▶0b
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓0.3b
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 22 to 15 computations (31.8% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 x -1/24)
Compiler

Compiled 26 to 15 computations (42.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(*.f64 x -1/24)
0.0ms
x
@0
(*.f64 x -1/24)
0.0ms
x
@inf
(*.f64 x -1/24)

rewrite59.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
922×associate-*l*
904×add-sqr-sqrt
884×*-un-lft-identity
842×pow1
828×add-cube-cbrt
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11007
211127
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 x -1/24)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x -1/24) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x -1/24) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 x 1/576)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x -1/24)))))))

simplify63.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
840×log-prod
808×distribute-rgt-out
790×+-commutative
690×fma-def
624×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034161
185161
2261161
31816161
43918161
56091161
Stop Event
1×node limit
Counts
23 → 12
Calls
Call 1
Inputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(-.f64 (+.f64 (*.f64 x -1/24) 1) 1)
(pow.f64 (*.f64 x -1/24) 1)
(pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)
(pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)
(pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)
(sqrt.f64 (*.f64 x (*.f64 x 1/576)))
(log.f64 (pow.f64 (exp.f64 x) -1/24))
(cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))
(expm1.f64 (log1p.f64 (*.f64 x -1/24)))
(exp.f64 (log.f64 (*.f64 x -1/24)))
(log1p.f64 (expm1.f64 (*.f64 x -1/24)))
Outputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(-.f64 (+.f64 (*.f64 x -1/24) 1) 1)
(*.f64 -1/24 x)
(pow.f64 (*.f64 x -1/24) 1)
(*.f64 -1/24 x)
(pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)
(*.f64 -1/24 x)
(pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)
(*.f64 -1/24 x)
(pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)
(*.f64 -1/24 x)
(sqrt.f64 (*.f64 x (*.f64 x 1/576)))
(*.f64 -1/24 x)
(log.f64 (pow.f64 (exp.f64 x) -1/24))
(*.f64 -1/24 x)
(cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))
(*.f64 -1/24 x)
(expm1.f64 (log1p.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)
(exp.f64 (log.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)
(log1p.f64 (expm1.f64 (*.f64 x -1/24)))
(*.f64 -1/24 x)

eval3.0ms (0.1%)

Compiler

Compiled 151 to 91 computations (39.7% saved)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New12012
Fresh000
Picked011
Done022
Total12315
Error
0b
Counts
15 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.2b
(-.f64 1 (cos.f64 x))
✓0b
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓0.3b
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 22 to 15 computations (31.8% saved)

regimes12.0ms (0.2%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(-.f64 1 (cos.f64 x))
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
Outputs
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
Calls

3 calls:

7.0ms
x
2.0ms
(cos.f64 x)
2.0ms
(-.f64 1 (cos.f64 x))
Results
ErrorSegmentsBranch
0b1x
0b1(-.f64 1 (cos.f64 x))
0b1(cos.f64 x)
Compiler

Compiled 47 to 30 computations (36.2% saved)

regimes7.0ms (0.1%)

Accuracy

Total -30.0b remaining (-11864.7%)

Threshold costs -30.0b (-11864.7%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(-.f64 1 (cos.f64 x))
Outputs
(*.f64 1/2 (*.f64 x x))
Calls

3 calls:

3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(-.f64 1 (cos.f64 x))
0.3b1(cos.f64 x)
Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01140
11440
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(*.f64 1/2 (*.f64 x x))
Outputs
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 x x) 1/2)
Compiler

Compiled 17 to 11 computations (35.3% saved)

soundness242.0ms (5%)

Algorithm
2×egg-herbie
Rules
1088×fma-def
952×distribute-lft-in
932×associate-/l*
906×associate-*r*
896×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
095817
1232757
2782687
33180687
069779
1152779
2419779
32320779
46397779
Stop Event
1×node limit
1×node limit
Compiler

Compiled 198 to 133 computations (32.8% saved)

end49.0ms (1%)

Compiler

Compiled 16 to 9 computations (43.8% saved)

Profiling

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