Details

Time bar (total: 2.2s)

analyze77.0ms (3.6%)

Algorithm
search
egg-herbie
Rules
78×sub-neg_binary64
74×cancel-sign-sub-inv_binary64
40×distribute-rgt-neg-in_binary64 associate--r+_binary64
38×unsub-neg_binary64
28×associate-+l-_binary64
26×neg-mul-1_binary64 distribute-neg-in_binary64 associate--r-_binary64
24×distribute-lft-neg-in_binary64
22×+-commutative_binary64
20×distribute-lft-neg-out_binary64 distribute-rgt-in_binary64
18×neg-sub0_binary64 sub0-neg_binary64 associate--l+_binary64
14×associate--l-_binary64
12×associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
10×*-lft-identity_binary64 distribute-lft-in_binary64 associate-*r*_binary64
mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt1-in_binary64
remove-double-neg_binary64 +-rgt-identity_binary64 distribute-rgt-neg-out_binary64
--rgt-identity_binary64
+-lft-identity_binary64 distribute-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01224
12624
26124
310024
420524
534324
638724
740724
841124
937224
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%74.9%25.1%4
18.7%56.2%25.1%5
28.1%34.3%37.6%6
34.3%28.1%37.6%7
39%17.2%43.8%8
41%13.7%45.4%9
43.1%8.4%48.5%10
44%6.7%49.3%11
45%4.1%50.8%12
45.4%3.3%51.2%13
45.9%2.1%52%14
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample20.0ms (0.9%)

Algorithm
intervals
Results
12.0ms256×body128valid
0.0msbody128nan
0.0msbody128invalid
Compiler

Compiled 17 to 17 computations (0% saved)

simplify16.0ms (0.7%)

Algorithm
egg-herbie
Rules
45×cancel-sign-sub-inv_binary64
44×sub-neg_binary64
31×unsub-neg_binary64
24×associate--r+_binary64
21×distribute-rgt-neg-in_binary64
18×neg-mul-1_binary64
17×associate--r-_binary64
16×distribute-neg-in_binary64
14×distribute-rgt-in_binary64 associate-+l-_binary64 +-commutative_binary64
13×neg-sub0_binary64 distribute-lft-neg-in_binary64
12×distribute-lft-neg-out_binary64
10×sub0-neg_binary64 associate--l+_binary64
distribute-lft-in_binary64
*-commutative_binary64
*-lft-identity_binary64
associate--l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
distribute-rgt-neg-out_binary64
remove-double-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 associate-*r*_binary64
+-rgt-identity_binary64 distribute-rgt1-in_binary64
*-rgt-identity_binary64 --rgt-identity_binary64 +-lft-identity_binary64
1-exp_binary64 distribute-neg-out_binary64 distribute-lft-out--_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11612
23512
35712
410912
519212
623112
723912
823812
920712

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Compiler

Compiled 8 to 7 computations (12.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b
(*.f64 y (sqrt.f64 x))

rewrite54.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
10×add-sqr-sqrt_binary64
add-log-exp_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64 associate-*r*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-prod_binary64 associate-+l+_binary64
associate-*l*_binary64 cancel-sign-sub-inv_binary64
unswap-sqr_binary64 sum-log_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64 diff-log_binary64 flip3-+_binary64 flip-+_binary64 associate-+l-_binary64 sub-neg_binary64 +-commutative_binary64
Counts
2 → 39
Calls

2 calls:

7.0ms
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
5.0ms
(*.f64 y (sqrt.f64 x))
Compiler

Compiled 512 to 234 computations (54.3% saved)

series40.0ms (1.8%)

Error
0.1b
Counts
2 → 15
Calls

2 calls:

17.0ms
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
15.0ms
(*.f64 y (sqrt.f64 x))
Compiler

Compiled 244 to 208 computations (14.8% saved)

simplify70.0ms (3.2%)

Algorithm
egg-herbie
Rules
768×unsub-neg_binary64
304×sub-neg_binary64
283×associate-*l*_binary64
258×distribute-rgt-in_binary64
253×neg-sub0_binary64
246×neg-mul-1_binary64
241×distribute-lft-in_binary64
232×associate-*r*_binary64
215×+-commutative_binary64
175×cancel-sign-sub-inv_binary64
155×times-frac_binary64 distribute-rgt-out_binary64
131×distribute-rgt-neg-out_binary64
122×distribute-lft-neg-out_binary64
109×exp-prod_binary64
97×exp-sum_binary64
87×associate-+l-_binary64
85×*-commutative_binary64
82×distribute-rgt-neg-in_binary64
75×associate--r+_binary64
60×distribute-lft-neg-in_binary64
59×associate-+r-_binary64
54×exp-diff_binary64
50×distribute-lft-out_binary64
44×sqr-pow_binary64
42×distribute-rgt-out--_binary64
41×unswap-sqr_binary64 associate-+l+_binary64
39×associate--l+_binary64
37×distribute-neg-in_binary64
35×associate-+r+_binary64
31×*-lft-identity_binary64
30×*-rgt-identity_binary64
20×cube-prod_binary64
19×log-prod_binary64 div-sub_binary64
18×associate--r-_binary64
15×swap-sqr_binary64 associate-/l*_binary64
13×distribute-neg-out_binary64
11×mul0-rgt_binary64 mul0-lft_binary64
10×associate-/r*_binary64
cube-unmult_binary64 sqr-neg_binary64 sub0-neg_binary64
rem-sqrt-square_binary64 remove-double-neg_binary64 +-rgt-identity_binary64
unpow3_binary64 div-exp_binary64 associate--l-_binary64
cube-neg_binary64 pow-sqr_binary64 associate-*r/_binary64
distribute-lft-out--_binary64 associate-*l/_binary64
--rgt-identity_binary64
unpow1/2_binary64 prod-exp_binary64 cube-mult_binary64 mul-1-neg_binary64 difference-of-sqr--1_binary64 difference-of-squares_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/r/_binary64
pow-plus_binary64 rec-exp_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 count-2_binary64 associate-/l/_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64
Counts
54 → 36
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
083590
1193557
2543552
31852552
43405552
55110552

prune25.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New31536
Fresh000
Picked011
Done000
Total31637
Error
0.0b
Counts
37 → 6
Compiler

Compiled 369 to 190 computations (48.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 y (fabs.f64 (cbrt.f64 x)))
0.4b
(*.f64 (*.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
0.7b
(cbrt.f64 x)
0.7b
(cbrt.f64 x)

rewrite95.0ms (4.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×add-sqr-sqrt_binary64
12×associate-*r*_binary64
11×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
cbrt-prod_binary64
sqrt-prod_binary64
add-log-exp_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
pow1/3_binary64 *-commutative_binary64
unswap-sqr_binary64
Counts
4 → 64
Calls

4 calls:

8.0ms
(*.f64 (*.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
5.0ms
(*.f64 y (fabs.f64 (cbrt.f64 x)))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
Compiler

Compiled 1123 to 393 computations (65% saved)

series110.0ms (5.1%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

50.0ms
(*.f64 (*.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
18.0ms
(cbrt.f64 x)
17.0ms
(cbrt.f64 x)
17.0ms
(*.f64 y (fabs.f64 (cbrt.f64 x)))
Compiler

Compiled 694 to 582 computations (16.1% saved)

simplify69.0ms (3.2%)

Algorithm
egg-herbie
Rules
592×unswap-sqr_binary64
581×associate-+l+_binary64
437×distribute-rgt-in_binary64
419×distribute-lft-in_binary64
311×*-commutative_binary64
164×associate-*l*_binary64
137×log-prod_binary64
134×sqr-pow_binary64
125×associate-*r*_binary64
119×distribute-rgt-neg-in_binary64
112×distribute-lft-neg-in_binary64
51×exp-prod_binary64
41×pow-sqr_binary64
40×associate-/l*_binary64
33×distribute-rgt-out_binary64
32×cancel-sign-sub-inv_binary64
30×count-2_binary64
27×cube-prod_binary64
26×rem-sqrt-square_binary64 neg-sub0_binary64 associate-+r+_binary64
25×neg-mul-1_binary64 associate-/l/_binary64
24×*-lft-identity_binary64
22×distribute-lft-out_binary64
21×log-pow_binary64 swap-sqr_binary64 associate-*r/_binary64
16×sub-neg_binary64 *-rgt-identity_binary64
15×associate-/r/_binary64
13×cube-unmult_binary64
12×associate-/r*_binary64
10×pow-plus_binary64
+-commutative_binary64
unpow3_binary64 unpow1/2_binary64 cube-mult_binary64
unpow1/3_binary64 associate-*l/_binary64
unpow2_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-+l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 unsub-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
82 → 54
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
093997
1196905
2673905
31008905
41747905
55203905

prune44.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New51354
Fresh134
Picked011
Done011
Total52860
Error
0b
Counts
60 → 8
Compiler

Compiled 634 to 280 computations (55.8% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 x)) y) (sqrt.f64 (cbrt.f64 (sqrt.f64 x))))
0.6b
(cbrt.f64 (sqrt.f64 x))
0.6b
(cbrt.f64 (sqrt.f64 x))
0.7b
(cbrt.f64 x)

rewrite108.0ms (5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
21×cbrt-prod_binary64
18×sqrt-prod_binary64
13×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
12×associate-*r*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64
pow1/3_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
associate-*l*_binary64 *-commutative_binary64
Counts
4 → 66
Calls

4 calls:

8.0ms
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 x)) y) (sqrt.f64 (cbrt.f64 (sqrt.f64 x))))
2.0ms
(cbrt.f64 (sqrt.f64 x))
2.0ms
(cbrt.f64 (sqrt.f64 x))
1.0ms
(cbrt.f64 x)
Compiler

Compiled 1516 to 461 computations (69.6% saved)

series95.0ms (4.4%)

Error
0b
Counts
4 → 15
Calls

4 calls:

42.0ms
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 x)) y) (sqrt.f64 (cbrt.f64 (sqrt.f64 x))))
19.0ms
(cbrt.f64 x)
14.0ms
(cbrt.f64 (sqrt.f64 x))
13.0ms
(cbrt.f64 (sqrt.f64 x))
Compiler

Compiled 744 to 590 computations (20.7% saved)

simplify141.0ms (6.5%)

Algorithm
egg-herbie
Rules
438×associate-+l+_binary64
377×associate-+r+_binary64
337×*-commutative_binary64
333×distribute-rgt-in_binary64
326×log-prod_binary64 distribute-lft-in_binary64
265×distribute-rgt-out_binary64
260×sqr-pow_binary64
238×unswap-sqr_binary64
213×pow-sqr_binary64
157×distribute-rgt-neg-in_binary64
152×distribute-lft-neg-in_binary64
147×associate-*l*_binary64
121×log-pow_binary64
110×associate-*r*_binary64
107×exp-prod_binary64
88×neg-mul-1_binary64
87×neg-sub0_binary64
75×cube-prod_binary64
72×rem-sqrt-square_binary64
69×cancel-sign-sub-inv_binary64
55×associate-/l*_binary64
32×sub-neg_binary64 swap-sqr_binary64 distribute-rgt1-in_binary64
26×unpow3_binary64
25×distribute-lft1-in_binary64
22×cube-mult_binary64 count-2_binary64
20×pow-plus_binary64 associate-/l/_binary64
19×cube-unmult_binary64
17×associate-*r/_binary64
16×+-commutative_binary64
13×times-frac_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 associate-/r*_binary64
12×unsub-neg_binary64
11×distribute-lft-out_binary64 associate-/r/_binary64
10×unpow1/2_binary64
unpow2_binary64
unpow1_binary64
mul0-rgt_binary64 mul0-lft_binary64
unpow1/3_binary64
rem-3cbrt-lft_binary64
1-exp_binary64 exp-1-e_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 sub0-neg_binary64 --rgt-identity_binary64 associate-*l/_binary64 associate-+l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 div-sub_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
81 → 32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0951020
1195956
2623950
3899950
41451950
53791950
64610950
74915950
84792950

prune28.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New32032
Fresh055
Picked011
Done022
Total32840
Error
0b
Counts
40 → 8
Compiler

Compiled 462 to 199 computations (56.9% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)

rewrite108.0ms (5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
pow1/3_binary64
add-exp-log_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 73
Calls

4 calls:

6.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 1351 to 437 computations (67.7% saved)

series82.0ms (3.8%)

Error
0b
Counts
4 → 12
Calls

4 calls:

20.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
18.0ms
(cbrt.f64 y)
17.0ms
(cbrt.f64 y)
17.0ms
(cbrt.f64 y)
Compiler

Compiled 564 to 418 computations (25.9% saved)

simplify107.0ms (5%)

Algorithm
egg-herbie
Rules
586×log-prod_binary64
416×sqr-pow_binary64
335×associate-*l*_binary64
309×*-commutative_binary64
277×distribute-rgt-neg-in_binary64
257×distribute-lft-neg-in_binary64
227×associate-*r*_binary64
188×exp-prod_binary64
161×log-pow_binary64
149×cube-prod_binary64
128×pow-sqr_binary64
124×unswap-sqr_binary64
111×swap-sqr_binary64
104×associate-/l*_binary64
81×cancel-sign-sub-inv_binary64
75×associate-+l+_binary64
69×associate-+r+_binary64
61×distribute-rgt-in_binary64
60×distribute-lft-out_binary64
57×distribute-lft-in_binary64
54×neg-sub0_binary64
53×neg-mul-1_binary64
48×distribute-rgt-out_binary64
45×+-commutative_binary64
43×pow-plus_binary64 rem-sqrt-square_binary64
41×times-frac_binary64 sub-neg_binary64
37×associate-/r/_binary64
35×associate-*r/_binary64
32×unpow3_binary64
31×*-rgt-identity_binary64 *-lft-identity_binary64 associate-/l/_binary64
29×count-2_binary64
27×cube-mult_binary64
24×associate-/r*_binary64
17×log-div_binary64 cube-div_binary64 distribute-neg-frac_binary64
13×cube-unmult_binary64 distribute-rgt1-in_binary64
11×distribute-rgt-neg-out_binary64
10×unpow1/2_binary64
distribute-lft-neg-out_binary64 distribute-lft1-in_binary64
unpow2_binary64 associate-*l/_binary64
unpow1_binary64
unpow1/3_binary64
exp-sqrt_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 mul-1-neg_binary64
exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 associate-+l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 unsub-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
85 → 50
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
056718
197666
2308646
31135632
42034548
53257548
64939548
74873548

prune31.0ms (1.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New50050
Fresh044
Picked011
Done033
Total50858
Error
0b
Counts
58 → 8
Compiler

Compiled 473 to 214 computations (54.8% saved)

regimes137.0ms (6.4%)

Accuracy

Total 0.1b remaining (71.1%)

Threshold costs 0.1b (71.1%)

Compiler

Compiled 1322 to 958 computations (27.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64 *-commutative_binary64
1-exp_binary64 neg-mul-1_binary64 neg-sub0_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11412
21812
32012
42112
52012

end1.0ms (0%)

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample651.0ms (30.3%)

Algorithm
intervals
Results
245.0ms7999×body128valid
3.0ms108×body128nan
2.0ms72×body128invalid
0.0msbody2048valid
Compiler

Compiled 140 to 112 computations (20% saved)

Profiling

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