Details

Time bar (total: 5.7s)

analyze0.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.8s (48.8%)

Results
1.3s2155×body2048valid
886.0ms4513×body256valid
422.0ms1069×body1024valid
180.0ms519×body512valid

preprocess22.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify31.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

eval0.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.9b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶14.9b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 8 to 6 computations (25% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.7b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
1.0ms
N
@0
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
N
@-inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
N
@inf
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite202.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
890×pow1_binary64
828×log1p-expm1-u_binary64
828×expm1-log1p-u_binary64
827×add-log-exp_binary64
810×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
115611
2221311
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))))

simplify67.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
52×fma-def_binary64
43×fma-neg_binary64
23×cancel-sign-sub-inv_binary64
18×sub-neg_binary64
14×associate--r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0952
12044
23144
36144
48844
513444
618244
721544
825844
929444
1032044
1132244
Stop Event
1×saturated
Counts
40 → 38
Calls
Call 1
Inputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
Outputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))

eval21.0ms (0.4%)

Compiler

Compiled 599 to 388 computations (35.2% saved)

prune42.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New35338
Fresh000
Picked011
Done000
Total35439
Error
13.8b
Counts
39 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶30.7b
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
▶14.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
▶47.8b
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
✓14.9b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 58 to 40 computations (31% saved)

localize55.0ms (1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(sqrt.f64 (atan.f64 N))
1.7b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓30.4b
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
Compiler

Compiled 54 to 20 computations (63% saved)

series6.0ms (0.1%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
2.0ms
N
@-inf
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
2.0ms
N
@0
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.0ms
N
@inf
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
0.0ms
N
@0
(sqrt.f64 (atan.f64 N))
0.0ms
N
@inf
(sqrt.f64 (atan.f64 N))

rewrite108.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
463×pow1_binary64
446×add-sqr-sqrt_binary64
438×*-un-lft-identity_binary64
427×add-log-exp_binary64
426×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0622
112213
2149013
Stop Event
1×node limit
Counts
2 → 53
Calls
Call 1
Inputs
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
(sqrt.f64 (atan.f64 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 N) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) (+.f64 (sqrt.f64 (atan.f64 N)) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 N) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 N) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (neg.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) (cbrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (neg.f64 (pow.f64 (atan.f64 N) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (atan.f64 N) 3/2)) (+.f64 0 (+.f64 (atan.f64 N) (*.f64 0 (sqrt.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (atan.f64 N)) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 N) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 N))))))))

simplify45.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
4×fma-def_binary64
3×+-commutative_binary64
3×sub-neg_binary64
2×*-commutative_binary64
1×associate-+l-_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0672
11312
21912
32012
42212
52612
63012
73512
Stop Event
1×saturated
Counts
65 → 55
Calls
Call 1
Inputs
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
Outputs
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0

localize33.0ms (0.6%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 N (+.f64 N 1))
✓0.0b
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓2.9b
(+.f64 N (-.f64 1 N))
Compiler

Compiled 39 to 26 computations (33.3% saved)

series6.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@-inf
(*.f64 N (+.f64 N 1))
1.0ms
N
@inf
(*.f64 N (+.f64 N 1))
1.0ms
N
@inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
1.0ms
N
@0
(*.f64 N (+.f64 N 1))
1.0ms
N
@-inf
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite157.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
616×fma-def_binary64
473×log-prod_binary64
352×pow-prod-down_binary64
297×fma-neg_binary64
270×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0933
121029
2307629
Stop Event
1×node limit
Counts
3 → 181
Calls
Call 1
Inputs
(+.f64 N (-.f64 1 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(*.f64 N (+.f64 N 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 N (-.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 N N) (+.f64 (+.f64 N -1) N)) (/.f64 (pow.f64 (-.f64 1 N) 2) (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 N (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (-.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (+.f64 (pow.f64 (-.f64 1 N) 2) (-.f64 (*.f64 N N) (*.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2)) (+.f64 (+.f64 N -1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) (neg.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))) (neg.f64 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 3) (pow.f64 N 3)) (+.f64 (pow.f64 (+.f64 N 1) 2) (fma.f64 N N (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 2) (*.f64 N N)) (+.f64 (+.f64 N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 N) 2) (*.f64 N N)) (-.f64 (-.f64 1 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (+.f64 N 1)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 N 1)) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x 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(cbrt.f64 N) N) (cbrt.f64 (*.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))))

simplify96.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
968×fma-neg_binary64
532×unswap-sqr_binary64
447×distribute-rgt-neg-in_binary64
354×cancel-sign-sub-inv_binary64
329×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019240
144198
267198
3163198
4583198
51634198
63616198
75643198
87339198
Stop Event
1×node limit
Counts
217 → 190
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
Outputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

localize26.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
✓1.0b
(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓28.1b
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
Compiler

Compiled 44 to 31 computations (29.5% saved)

series9.0ms (0.2%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
N
@0
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
2.0ms
N
@inf
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
2.0ms
N
@-inf
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
0.0ms
N
@-inf
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
0.0ms
N
@-inf
(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite109.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
886×pow1_binary64
821×add-log-exp_binary64
821×log1p-expm1-u_binary64
821×expm1-log1p-u_binary64
803×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01132
122630
2260830
Stop Event
1×node limit
Counts
3 → 58
Calls
Call 1
Inputs
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(cbrt.f64 (atan.f64 (+.f64 N 1)))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) 0) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3) (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))))

simplify140.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
1003×fma-def_binary64
772×fma-neg_binary64
506×associate-*l*_binary64
390×distribute-rgt-neg-in_binary64
361×associate-*r*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023396
168360
2104360
3168360
4286360
5664360
62252360
73256360
84885360
96855360
Stop Event
1×node limit
Counts
94 → 66
Calls
Call 1
Inputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
Outputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))

eval224.0ms (3.9%)

Compiler

Compiled 8177 to 4736 computations (42.1% saved)

prune57.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New4031404
Fresh000
Picked101
Done213
Total4062408
Error
0.5b
Counts
408 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓14.9b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 N (+.f64 N 1))
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 27 to 19 computations (29.6% saved)

series27.0ms (0.5%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
26.0ms
N
@inf
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms
N
@0
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms
N
@-inf
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite54.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
798×pow1_binary64
742×log1p-expm1-u_binary64
742×expm1-log1p-u_binary64
741×add-log-exp_binary64
727×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0713
115211
2205711
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

simplify80.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
968×fma-neg_binary64
532×unswap-sqr_binary64
451×distribute-rgt-neg-in_binary64
353×cancel-sign-sub-inv_binary64
312×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014104
13388
25488
315188
457588
5163888
6362788
7566288
8735988
Stop Event
1×node limit
Counts
24 → 19
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
Outputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (-.f64 1 (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))

eval66.0ms (1.2%)

Compiler

Compiled 1001 to 611 computations (39% saved)

prune15.0ms (0.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New73578
Fresh000
Picked011
Done011
Total73780
Error
0.5b
Counts
80 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
▶29.5b
(atan2.f64 1 (+.f64 1 N))
▶1.9b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓14.9b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶1.4b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
▶1.1b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
▶23.2b
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
Compiler

Compiled 130 to 96 computations (26.2% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.6b
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓14.3b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
Compiler

Compiled 42 to 22 computations (47.6% saved)

series6.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
N
@inf
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms
N
@-inf
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms
N
@0
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms
N
@0
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms
N
@inf
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite70.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
735×pow1_binary64
684×add-log-exp_binary64
683×log1p-expm1-u_binary64
683×expm1-log1p-u_binary64
669×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
118635
2192435
Stop Event
1×node limit
Counts
3 → 58
Calls
Call 1
Inputs
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/2) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

simplify34.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
25×fma-def_binary64
6×+-commutative_binary64
4×distribute-lft-in_binary64
3×distribute-rgt1-in_binary64
2×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07420
112420
218420
327420
435420
539420
651420
764420
869420
970420
Stop Event
1×saturated
Counts
94 → 45
Calls
Call 1
Inputs
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
Outputs
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(atan2.f64 1 (+.f64 1 N))
Compiler

Compiled 11 to 8 computations (27.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
N
@0
(atan2.f64 1 (+.f64 1 N))
0.0ms
N
@-inf
(atan2.f64 1 (+.f64 1 N))
0.0ms
N
@inf
(atan2.f64 1 (+.f64 1 N))

rewrite41.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
495×pow1_binary64
482×add-sqr-sqrt_binary64
460×add-log-exp_binary64
460×log1p-expm1-u_binary64
460×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
212437
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 N))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) (sqrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 N))))))))

simplify13.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
13×fma-def_binary64
11×fma-neg_binary64
7×cancel-sign-sub-inv_binary64
6×associate--r+_binary64
6×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0984
11984
22584
34884
46784
59784
611284
711684
Stop Event
1×saturated
Counts
28 → 19
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
Outputs
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 N))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
N
@0
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
0.0ms
N
@-inf
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
0.0ms
N
@inf
(atan2.f64 1 (+.f64 1 (*.f64 N N)))

rewrite48.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
563×pow1_binary64
525×add-log-exp_binary64
524×log1p-expm1-u_binary64
524×expm1-log1p-u_binary64
513×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0610
11218
214828
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 N N 1))))))))

simplify166.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
1366×sqr-pow_binary64
695×pow-sqr_binary64
617×cube-prod_binary64
613×fabs-mul_binary64
434×unswap-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07120
11496
22196
33296
46196
516096
658196
7144996
8163396
9181796
10202596
11231896
12271396
13319696
14376296
15444896
16528396
17568196
18597196
19625196
20632596
21636196
22730296
Stop Event
1×node limit
Counts
28 → 18
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
Outputs
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))
(atan2.f64 1 (+.f64 1 (pow.f64 N 2)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (fma.f64 N N 1))

localize27.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
✓12.4b
(-.f64 (pow.f64 N 4) (*.f64 N N))
✓34.2b
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
Compiler

Compiled 69 to 29 computations (58% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
N
@0
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@inf
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@-inf
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms
N
@-inf
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
0.0ms
N
@inf
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))

rewrite85.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
506×fma-def_binary64
469×log-prod_binary64
339×fma-neg_binary64
256×pow2_binary64
207×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01254
127124
2402724
Stop Event
1×node limit
Counts
3 → 272
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (/.f64 N (/.f64 (fma.f64 N N N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 N N 0) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (/.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (neg.f64 (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (neg.f64 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4)) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) 1) (pow.f64 (cbrt.f64 (fma.f64 N N N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) -2) (/.f64 (pow.f64 (fma.f64 N N N) 2) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) -1/2) (pow.f64 (fma.f64 N N N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) (hypot.f64 N (sqrt.f64 N))) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (fma.f64 N N N)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (pow.f64 (exp.f64 N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) 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simplify54.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
824×associate-/r*_binary64
749×fma-def_binary64
681×associate-*l*_binary64
377×associate-*l/_binary64
256×associate-/r/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
025593
157566
2101566
3280434
41636374
Stop Event
1×node limit
Counts
308 → 284
Calls
Call 1
Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(*.f64 -1 (pow.f64 N 2))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(*.f64 -1 (pow.f64 N 2))
(neg.f64 (*.f64 N N))
(*.f64 N (neg.f64 N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (*.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (*.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) N)) (-.f64 (/.f64 (*.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
0.5b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓14.7b
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
Compiler

Compiled 42 to 22 computations (47.6% saved)

series10.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
N
@-inf
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms
N
@0
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms
N
@inf
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms
N
@inf
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
1.0ms
N
@-inf
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)

rewrite67.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
761×pow1_binary64
714×add-log-exp_binary64
713×log1p-expm1-u_binary64
713×expm1-log1p-u_binary64
698×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
118824
2197624
Stop Event
1×node limit
Counts
2 → 39
Calls
Call 1
Inputs
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/3) (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3) (pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) 1) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2)) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6)) (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

simplify193.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
1290×sqr-pow_binary64
666×pow-sqr_binary64
625×cube-prod_binary64
558×fabs-mul_binary64
373×unpow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011324
127288
241288
361288
493288
5190288
6586288
71263288
81360288
91499288
101662288
111901288
122228288
132656288
143163288
153770288
164497288
174818288
185102288
195324288
205502288
215584288
226527288
237504288
247970288
Stop Event
1×node limit
Counts
63 → 43
Calls
Call 1
Inputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
Outputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(*.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

eval228.0ms (4%)

Compiler

Compiled 7551 to 4041 computations (46.5% saved)

prune59.0ms (1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New4086414
Fresh000
Picked101
Done246
Total41110421
Error
0.5b
Counts
421 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.8b
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
✓14.9b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
23.8b
(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))
2.0b
(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)
✓1.4b
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
1.8b
(*.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓29.5b
(atan2.f64 1 (+.f64 1 N))
15.6b
(atan2.f64 1 (+.f64 1 (*.f64 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.f64 1 (fma.f64 N N N))))))
2.7b
(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 3)
Compiler

Compiled 133 to 91 computations (31.6% saved)

regimes20.0ms (0.3%)

Counts
16 → 1
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 3)
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(atan2.f64 1 (+.f64 1 (*.f64 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.f64 1 (fma.f64 N N N))))))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
(*.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Calls

2 calls:

10.0ms
N
3.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Results
ErrorSegmentsBranch
0.5b1N
0.5b1(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 220 to 139 computations (36.8% saved)

regimes4.0ms (0.1%)

Accuracy

Total -28.3b remaining (-1993.3%)

Threshold costs -28.3b (-1993.3%)

Counts
2 → 1
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
Calls

1 calls:

3.0ms
N
Results
ErrorSegmentsBranch
1.4b1N
Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
1×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01230
11830
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 N))
Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 N))
Compiler

Compiled 24 to 19 computations (20.8% saved)

soundness0.0ms (0%)

end29.0ms (0.5%)

Compiler

Compiled 22 to 17 computations (22.7% saved)

Profiling

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