Details

Time bar (total: 5.6min)

analyze12.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample21.0ms (0%)

Algorithm
1×intervals
Results
12.0ms256×body128valid
Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify128.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
046617
146617

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 11 to 10 computations (9.1% saved)

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite41.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
79×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
49×times-frac_binary64
30×sqrt-prod_binary64
26×add-cube-cbrt_binary64
18×difference-of-squares_binary64
13×distribute-lft-out_binary64
9×distribute-lft-out--_binary64
6×associate-/l*_binary64
5×add-exp-log_binary64 add-cbrt-cube_binary64
4×associate-/r*_binary64 pow1_binary64 associate-/r/_binary64
3×add-log-exp_binary64
2×flip3-+_binary64 associate-/l/_binary64 rem-sqrt-square_binary64 div-inv_binary64 flip-+_binary64
1×pow1/2_binary64 flip3--_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 flip--_binary64 sqrt-div_binary64
Counts
3 → 100
Calls

6 calls:

18.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
12.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series74.0ms (0%)

Counts
3 → 17
Calls

3 calls:

34.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
20.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
19.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
Compiler

Compiled 260 to 252 computations (3.1% saved)

simplify82.0ms (0%)

Algorithm
1×egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
064192047

prune435.0ms (0.1%)

Pruning

54 alts after pruning (53 fresh and 1 done)

PrunedKeptTotal
New6453117
Fresh000
Picked000
Done011
Total6454118
Error
0b
Counts
118 → 54
Compiler

Compiled 2368 to 1968 computations (16.9% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
0.0b
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
0.0b
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))

rewrite67.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
60×add-sqr-sqrt_binary64
49×times-frac_binary64
30×associate-*l*_binary64
28×add-cube-cbrt_binary64
18×difference-of-squares_binary64
14×distribute-lft-out_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
9×pow1_binary64 distribute-lft-out--_binary64
6×flip3-+_binary64 associate-/l*_binary64 flip-+_binary64
5×sqrt-div_binary64
4×associate-/r*_binary64 add-log-exp_binary64 associate-*r*_binary64 associate-*r/_binary64 associate-/r/_binary64 frac-times_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 associate-*l/_binary64
1×pow1/2_binary64 flip3--_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64 sqrt-prod_binary64 *-commutative_binary64
Counts
4 → 130
Calls

8 calls:

22.0ms
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
17.0ms
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
11.0ms
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
1.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))

series135.0ms (0%)

Counts
4 → 25
Calls

4 calls:

37.0ms
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
34.0ms
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
33.0ms
(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
29.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
Compiler

Compiled 568 to 510 computations (10.2% saved)

simplify83.0ms (0%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049613726
149613726

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 1 x) (+.f64 1 x))
0.0b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x))))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))))
0.0b
(sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x))))
0.0b
(*.f64 (+.f64 1 x) (+.f64 1 x))
0.0b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))

rewrite51.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×*-un-lft-identity_binary64
18×flip3-+_binary64 flip-+_binary64
16×associate-/r/_binary64 add-sqr-sqrt_binary64 sqrt-prod_binary64
12×pow1_binary64 add-cube-cbrt_binary64 frac-times_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
9×times-frac_binary64
6×swap-sqr_binary64 distribute-lft-out_binary64 associate-*r/_binary64 associate-*l/_binary64
4×add-log-exp_binary64 associate-*r*_binary64 associate-*l*_binary64 associate-/l*_binary64
3×difference-of-squares_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 rem-sqrt-square_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64
1×pow-prod-down_binary64 associate-/r*_binary64 pow1/2_binary64 flip3--_binary64 pow-prod-up_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 pow-plus_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 pow-sqr_binary64 flip--_binary64 pow2_binary64 sqrt-div_binary64 *-commutative_binary64
Counts
4 → 109
Calls

8 calls:

14.0ms
(/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))
13.0ms
(sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x))))
12.0ms
(*.f64 (+.f64 1 x) (+.f64 1 x))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))))

series96.0ms (0%)

Counts
4 → 22
Calls

4 calls:

29.0ms
(/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))
24.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x)))))
23.0ms
(sqrt.f64 (/.f64 (-.f64 (*.f64 1 1) (*.f64 x x)) (*.f64 (+.f64 1 x) (+.f64 1 x))))
19.0ms
(*.f64 (+.f64 1 x) (+.f64 1 x))
Compiler

Compiled 422 to 395 computations (6.4% saved)

simplify69.0ms (0%)

Algorithm
1×egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
054602130

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite122.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
377×*-un-lft-identity_binary64
234×add-sqr-sqrt_binary64
225×times-frac_binary64
212×sqrt-prod_binary64
95×add-cube-cbrt_binary64
68×difference-of-squares_binary64
64×distribute-lft-out_binary64
59×swap-sqr_binary64
46×distribute-lft-out--_binary64
33×associate-*r*_binary64 associate-*l*_binary64
20×pow1_binary64
14×associate-/r/_binary64
12×associate-/l*_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
9×pow1/2_binary64 sqrt-pow1_binary64 unswap-sqr_binary64
8×associate-/r*_binary64
7×flip3-+_binary64 div-inv_binary64 flip-+_binary64
6×rem-sqrt-square_binary64
5×pow-prod-up_binary64 sqrt-div_binary64
4×associate-/l/_binary64 add-log-exp_binary64
3×pow-prod-down_binary64 pow-sqr_binary64
2×flip3--_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 sqr-abs_binary64 div-exp_binary64 flip--_binary64
1×cbrt-unprod_binary64 rem-square-sqrt_binary64 associate-*r/_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 308
Calls

8 calls:

45.0ms
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series104.0ms (0%)

Counts
4 → 30
Calls

4 calls:

27.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
27.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
25.0ms
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
24.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
Compiler

Compiled 714 to 652 computations (8.7% saved)

simplify108.0ms (0%)

Algorithm
1×egg-herbie
Counts
338 → 338
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
051186212

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.9b
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.9b
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
1.0b
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

rewrite32.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
57×add-sqr-sqrt_binary64
55×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
24×times-frac_binary64 sqrt-prod_binary64
21×pow1_binary64
10×pow1/2_binary64 sqrt-pow1_binary64 difference-of-squares_binary64
8×swap-sqr_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
7×distribute-lft-out_binary64
6×associate-*r*_binary64 associate-*l*_binary64 associate-/l*_binary64
5×pow-prod-up_binary64 distribute-lft-out--_binary64
4×associate-/r*_binary64 add-log-exp_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64
3×pow-prod-down_binary64 pow-sqr_binary64
2×associate-/l/_binary64 associate-/r/_binary64
1×flip3-+_binary64 flip3--_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 div-sub_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64 sqr-abs_binary64 div-exp_binary64 flip--_binary64 flip-+_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 127
Calls

8 calls:

9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
7.0ms
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
1.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
1.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series120.0ms (0%)

Counts
4 → 17
Calls

4 calls:

38.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
35.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
28.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
19.0ms
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
Compiler

Compiled 582 to 518 computations (11% saved)

simplify83.0ms (0%)

Algorithm
1×egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
057892372

prune14.7s (4.4%)

Pruning

245 alts after pruning (240 fresh and 5 done)

PrunedKeptTotal
New559209768
Fresh173148
Picked000
Done156
Total577245822
Error
0b
Counts
822 → 245
Compiler

Compiled 19472 to 15458 computations (20.6% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0b
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
0.0b
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0b
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))

rewrite371.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
1312×times-frac_binary64
1190×*-un-lft-identity_binary64
839×add-sqr-sqrt_binary64
754×sqrt-prod_binary64
500×add-cube-cbrt_binary64
342×associate-*l*_binary64
210×difference-of-squares_binary64
188×distribute-lft-out_binary64
105×distribute-lft-out--_binary64
48×associate-/l*_binary64
39×sqrt-div_binary64
34×associate-/r/_binary64
21×flip3-+_binary64 flip-+_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
17×div-inv_binary64
9×pow1_binary64
7×associate-/r*_binary64 unswap-sqr_binary64
6×cbrt-undiv_binary64 div-exp_binary64
4×add-log-exp_binary64 associate-*r*_binary64 associate-*r/_binary64 frac-times_binary64
3×cbrt-unprod_binary64 prod-exp_binary64
2×pow-prod-down_binary64 sqrt-pow1_binary64 div-sub_binary64 associate-*l/_binary64
1×associate-/l/_binary64 pow1/2_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 807
Calls

8 calls:

92.0ms
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
49.0ms
(sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
36.0ms
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
1.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0ms
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3))))

series136.0ms (0%)

Counts
4 → 25
Calls

4 calls:

38.0ms
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
35.0ms
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
34.0ms
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))
29.0ms
(sqrt.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
Compiler

Compiled 568 to 510 computations (10.2% saved)

simplify318.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
832 → 832
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0567932225

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
0.0b
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1))
0.0b
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
0.0b
(atan.f64 (sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1)))
0.0b
(atan.f64 (sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1)))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
0.0b
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1))
0.0b
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))

rewrite61.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
84×*-un-lft-identity_binary64
62×add-sqr-sqrt_binary64
49×times-frac_binary64
30×associate-*l*_binary64
29×add-cube-cbrt_binary64
18×difference-of-squares_binary64
14×distribute-lft-out_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
9×distribute-lft-out--_binary64
6×pow1_binary64 associate-/l*_binary64
5×sqrt-prod_binary64
4×flip3-+_binary64 associate-/r*_binary64 add-log-exp_binary64 associate-*r*_binary64 associate-/r/_binary64 flip-+_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 sqr-pow_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 frac-times_binary64
1×pow-prod-down_binary64 pow1/2_binary64 flip3--_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 sqrt-pow1_binary64 div-sub_binary64 clear-num_binary64 unpow-prod-down_binary64 frac-2neg_binary64 flip--_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 130
Calls

8 calls:

22.0ms
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
20.0ms
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
3.0ms
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1))
1.0ms
(atan.f64 (sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1)))
0.0ms
(atan.f64 (sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1)))

series131.0ms (0%)

Counts
4 → 25
Calls

4 calls:

40.0ms
(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
35.0ms
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
29.0ms
(atan.f64 (sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1)))
27.0ms
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x))) 1))
Compiler

Compiled 568 to 510 computations (10.2% saved)

simplify88.0ms (0%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049793694
149793694

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0b
(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)

rewrite78.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
228×*-un-lft-identity_binary64
152×add-sqr-sqrt_binary64
144×times-frac_binary64
74×add-cube-cbrt_binary64
66×cbrt-prod_binary64
60×unpow-prod-down_binary64 cube-prod_binary64
52×difference-of-squares_binary64
38×distribute-lft-out_binary64
26×distribute-lft-out--_binary64
12×associate-/r/_binary64 associate-/l*_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×associate-/r*_binary64
6×flip3-+_binary64 div-inv_binary64 flip-+_binary64
5×pow1_binary64
4×associate-/l/_binary64 add-log-exp_binary64
3×pow-unpow_binary64 cbrt-undiv_binary64 div-exp_binary64
2×flip3--_binary64 sqr-pow_binary64 cube-div_binary64 div-sub_binary64 clear-num_binary64 rem-cube-cbrt_binary64 frac-2neg_binary64 flip--_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64
1×cbrt-div_binary64 pow-to-exp_binary64 rem-cbrt-cube_binary64 pow1/3_binary64 pow-pow_binary64
Counts
4 → 258
Calls

8 calls:

13.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
12.0ms
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series121.0ms (0%)

Counts
4 → 32
Calls

4 calls:

37.0ms
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
29.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
28.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
27.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 950 to 862 computations (9.3% saved)

simplify111.0ms (0%)

Algorithm
1×egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
054015265

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) 1))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) 1)) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))))))
0.0b
(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
0.0b
(/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x))
0.0b
(cbrt.f64 (-.f64 1 x))
0.0b
(cbrt.f64 (-.f64 1 x))
0.0b
(cbrt.f64 (-.f64 1 x))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
71×*-un-lft-identity_binary64
51×add-sqr-sqrt_binary64
48×cbrt-prod_binary64
36×times-frac_binary64
27×add-cube-cbrt_binary64
16×difference-of-squares_binary64
10×distribute-lft-out_binary64
9×associate-/l*_binary64
8×cbrt-div_binary64 distribute-lft-out--_binary64
6×add-exp-log_binary64
5×add-cbrt-cube_binary64
4×associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 flip--_binary64
3×pow1/3_binary64
2×associate-/l/_binary64 associate-/r/_binary64
1×flip3-+_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
Counts
4 → 113
Calls

8 calls:

9.0ms
(/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x))
4.0ms
(cbrt.f64 (-.f64 1 x))
4.0ms
(cbrt.f64 (-.f64 1 x))
3.0ms
(cbrt.f64 (-.f64 1 x))
0.0ms
(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))

series175.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

51.0ms
(/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x))
46.0ms
(cbrt.f64 (-.f64 1 x))
40.0ms
(cbrt.f64 (-.f64 1 x))
38.0ms
(cbrt.f64 (-.f64 1 x))
Compiler

Compiled 1326 to 1152 computations (13.1% saved)

simplify145.0ms (0%)

Algorithm
1×egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (118.0ms)

IterNodesCost
048152169
148152169

prune53.7s (16.1%)

Pruning

445 alts after pruning (435 fresh and 10 done)

PrunedKeptTotal
New11692451414
Fresh45190235
Picked000
Done01010
Total12144451659
Error
0b
Counts
1659 → 445
Compiler

Compiled 43793 to 35197 computations (19.6% saved)

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(atan.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x))))))
0.0b
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3))))
0.0b
(-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3)))
0.0b
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))
0.0b
(sqrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
0.0b
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3))))))
0.1b
(pow.f64 (pow.f64 x 3) 3)
0.1b
(*.f64 (pow.f64 x 3) (pow.f64 x 3))

rewrite373.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
650×times-frac_binary64
594×*-un-lft-identity_binary64
485×add-sqr-sqrt_binary64
382×sqrt-prod_binary64
354×associate-*l*_binary64
266×add-cube-cbrt_binary64
98×difference-of-squares_binary64
91×distribute-lft-out_binary64
49×distribute-lft-out--_binary64 sqrt-div_binary64
44×unpow-prod-down_binary64 cube-prod_binary64
30×unswap-sqr_binary64
27×add-exp-log_binary64
22×flip3-+_binary64 flip-+_binary64
19×associate-*r*_binary64
18×swap-sqr_binary64 frac-times_binary64
16×add-cbrt-cube_binary64 associate-/r/_binary64
15×sqr-pow_binary64
12×pow1_binary64 prod-exp_binary64
10×associate-*r/_binary64 pow-exp_binary64
9×associate-*l/_binary64
8×pow-to-exp_binary64 div-inv_binary64
7×unpow3_binary64 cube-mult_binary64
5×pow-prod-down_binary64
4×add-log-exp_binary64 cbrt-unprod_binary64
3×pow-unpow_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 div-exp_binary64
2×*-commutative_binary64
1×pow1/2_binary64 pow-prod-up_binary64 pow-pow_binary64 rem-cube-cbrt_binary64 pow-sqr_binary64 pow2_binary64
Counts
4 → 535
Calls

8 calls:

123.0ms
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3))))))
77.0ms
(sqrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
11.0ms
(*.f64 (pow.f64 x 3) (pow.f64 x 3))
5.0ms
(pow.f64 (pow.f64 x 3) 3)
0.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))

series228.0ms (0.1%)

Counts
4 → 19
Calls

4 calls:

76.0ms
(sqrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 1 1) (-.f64 (*.f64 x x) (*.f64 1 x)))))
54.0ms
(pow.f64 (pow.f64 x 3) 3)
53.0ms
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 x 3) 3)))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)) (*.f64 1 (pow.f64 x 3))))))
45.0ms
(*.f64 (pow.f64 x 3) (pow.f64 x 3))
Compiler

Compiled 957 to 822 computations (14.1% saved)

simplify232.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
554 → 554
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0505222841

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.0b
(+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2))
0.0b
(*.f64 (*.f64 x x) 1/2)
0.0b
(atan.f64 (+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2)))
0.0b
(atan.f64 (+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2)))
0.0b
(+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2))
0.0b
(*.f64 (*.f64 x x) 1/2)

rewrite20.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
8×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
6×add-sqr-sqrt_binary64
5×*-un-lft-identity_binary64 add-cube-cbrt_binary64
4×associate-+l+_binary64
3×pow-prod-down_binary64 cbrt-unprod_binary64 associate-*r*_binary64 cancel-sign-sub-inv_binary64 prod-exp_binary64
2×sum-log_binary64
1×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 associate-*l*_binary64 associate-+l-_binary64 unswap-sqr_binary64 +-commutative_binary64 flip-+_binary64 *-commutative_binary64
Counts
3 → 43
Calls

6 calls:

8.0ms
(+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2))
6.0ms
(*.f64 (*.f64 x x) 1/2)
3.0ms
(atan.f64 (+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2)))
0.0ms
(atan.f64 (+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2)))
0.0ms
(*.f64 (*.f64 x x) 1/2)

series110.0ms (0%)

Counts
3 → 15
Calls

3 calls:

58.0ms
(+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2))
33.0ms
(*.f64 (*.f64 x x) 1/2)
18.0ms
(atan.f64 (+.f64 (-.f64 1 x) (*.f64 (*.f64 x x) 1/2)))
Compiler

Compiled 262 to 243 computations (7.3% saved)

simplify73.0ms (0%)

Algorithm
1×egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04984722
14984722

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b
(atan.f64 (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))))
0.0b
(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))))
0.0b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
0.0b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))

rewrite134.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
413×sqrt-prod_binary64
326×*-un-lft-identity_binary64
272×times-frac_binary64
253×add-sqr-sqrt_binary64
127×add-cube-cbrt_binary64
74×distribute-lft-out_binary64
71×swap-sqr_binary64
62×difference-of-squares_binary64
41×associate-*r*_binary64 associate-*l*_binary64
20×pow1_binary64
16×unswap-sqr_binary64 associate-/l*_binary64
12×associate-/r/_binary64
11×rem-sqrt-square_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
9×pow1/2_binary64 sqrt-pow1_binary64
8×associate-/r*_binary64
6×flip3-+_binary64 div-inv_binary64 flip-+_binary64
5×pow-prod-up_binary64 sqr-abs_binary64
4×associate-/l/_binary64 add-log-exp_binary64
3×pow-prod-down_binary64 flip3--_binary64 pow-sqr_binary64 flip--_binary64
2×cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64
1×cbrt-unprod_binary64 rem-square-sqrt_binary64 associate-*r/_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 339
Calls

8 calls:

55.0ms
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))))
8.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
8.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms
(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))

series111.0ms (0%)

Counts
4 → 24
Calls

4 calls:

33.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
29.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
25.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
25.0ms
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))))
Compiler

Compiled 661 to 577 computations (12.7% saved)

simplify161.0ms (0%)

Algorithm
1×egg-herbie
Counts
363 → 363
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049669128
149669128

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.9b
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.9b
(sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
1.0b
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))

rewrite33.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
51×*-un-lft-identity_binary64
47×add-sqr-sqrt_binary64
24×times-frac_binary64
22×add-cube-cbrt_binary64
16×sqrt-prod_binary64
10×pow1_binary64 difference-of-squares_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
7×distribute-lft-out_binary64
6×associate-*r*_binary64 associate-*l*_binary64 associate-/l*_binary64
5×distribute-lft-out--_binary64
4×associate-/r*_binary64 add-log-exp_binary64 pow1/2_binary64 sqrt-pow1_binary64 unswap-sqr_binary64
3×pow-prod-down_binary64
2×associate-/l/_binary64 associate-/r/_binary64 rem-sqrt-square_binary64
1×flip3-+_binary64 flip3--_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 sqrt-unprod_binary64 div-sub_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64 flip-+_binary64 *-commutative_binary64
Counts
4 → 107
Calls

8 calls:

9.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
7.0ms
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))
1.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
1.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0ms
(atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series137.0ms (0%)

Counts
4 → 17
Calls

4 calls:

43.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
39.0ms
(sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
34.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
20.0ms
(*.f64 (sqrt.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (sqrt.f64 (atan.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))
Compiler

Compiled 742 to 646 computations (12.9% saved)

simplify84.0ms (0%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
057672238

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(atan.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))))))
0.0b
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
0.0b
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
0.0b
(*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3)))
0.0b
(sqrt.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3)))))
0.0b
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))))
0.0b
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))))
0.0b
(/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))

rewrite761.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
2993×sqrt-prod_binary64
2528×times-frac_binary64
1864×*-un-lft-identity_binary64
1590×add-sqr-sqrt_binary64
1131×add-cube-cbrt_binary64
586×associate-*l*_binary64
306×difference-of-squares_binary64
153×distribute-lft-out--_binary64
137×distribute-lft-out_binary64
100×unpow-prod-down_binary64 cube-prod_binary64
77×add-exp-log_binary64
67×associate-/l*_binary64
47×add-cbrt-cube_binary64
36×associate-/r*_binary64
30×div-exp_binary64
27×prod-exp_binary64
25×sqrt-div_binary64
24×div-inv_binary64
18×frac-times_binary64
16×cbrt-undiv_binary64
15×pow1_binary64 cbrt-unprod_binary64
14×associate-*r/_binary64
11×flip3-+_binary64 flip-+_binary64
10×sqr-pow_binary64 unpow3_binary64 associate-*l/_binary64 cube-mult_binary64
6×pow-prod-down_binary64 associate-/r/_binary64
4×pow-to-exp_binary64 add-log-exp_binary64 pow-exp_binary64
3×associate-/l/_binary64 sqrt-pow1_binary64
2×sqrt-undiv_binary64 cube-div_binary64 clear-num_binary64 frac-2neg_binary64
1×pow1/2_binary64 flip3--_binary64 associate-*r*_binary64 flip--_binary64 *-commutative_binary64
Counts
4 → 1000
Calls

8 calls:

153.0ms
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))))
96.0ms
(sqrt.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3)))))
35.0ms
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))))
29.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))
0.0ms
(*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3)))

series212.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

70.0ms
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))))
68.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))
40.0ms
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3))))
34.0ms
(sqrt.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) 3)))))
Compiler

Compiled 910 to 804 computations (11.6% saved)

simplify429.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1026 → 1026
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0505152108

prune2.3min (41.4%)

Pruning

796 alts after pruning (783 fresh and 13 done)

PrunedKeptTotal
New17174082125
Fresh55375430
Picked000
Done21315
Total17747962570
Error
0b
Counts
2570 → 796
Compiler

Compiled 51239 to 40953 computations (20.1% saved)

simplify2.2s (0.6%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
09108136295

regimes23.1s (6.9%)

Compiler

Compiled 336345 to 281984 computations (16.2% saved)

bsearch0.0ms (0%)

regimes17.5s (5.3%)

Compiler

Compiled 257430 to 214274 computations (16.8% saved)

bsearch0.0ms (0%)

regimes2.2s (0.7%)

Compiler

Compiled 29393 to 24575 computations (16.4% saved)

bsearch0.0ms (0%)

regimes284.0ms (0.1%)

Compiler

Compiled 2658 to 2391 computations (10% saved)

bsearch0.0ms (0%)

regimes200.0ms (0.1%)

Compiler

Compiled 1952 to 1744 computations (10.7% saved)

bsearch0.0ms (0%)

regimes29.0ms (0%)

Compiler

Compiled 187 to 167 computations (10.7% saved)

bsearch0.0ms (0%)

regimes25.0ms (0%)

Compiler

Compiled 147 to 130 computations (11.6% saved)

bsearch0.0ms (0%)

regimes18.0ms (0%)

Compiler

Compiled 81 to 74 computations (8.6% saved)

bsearch0.0ms (0%)

regimes12.0ms (0%)

Compiler

Compiled 33 to 34 computations (-3% saved)

bsearch0.0ms (0%)

regimes10.0ms (0%)

Compiler

Compiled 9 to 13 computations (-44.4% saved)

bsearch0.0ms (0%)

regimes7.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch11.0ms (0%)

Compiler

Compiled 182 to 159 computations (12.6% saved)

simplify5.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143276
1143276

end0.0ms (0%)

sample1.2min (22.2%)

Algorithm
1×intervals
Results
373.0ms8000×body128valid
Compiler

Compiled 66078 to 55358 computations (16.2% saved)

Pareto

0.9426412711672684

Profiling

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