Details

Time bar (total: 3.2s)

analyze377.0ms (12%)

Algorithm
search
egg-herbie
Rules
86×distribute-rgt-in_binary64
81×unsub-neg_binary64
60×distribute-lft-in_binary64
53×sub-neg_binary64
39×cancel-sign-sub-inv_binary64
37×neg-mul-1_binary64
33×neg-sub0_binary64
32×associate-*l*_binary64
30×distribute-rgt-neg-in_binary64 associate-*r*_binary64
28×associate--r+_binary64
22×+-lft-identity_binary64 distribute-lft-neg-out_binary64 associate-+l-_binary64
21×distribute-rgt-neg-out_binary64
20×sub0-neg_binary64
18×mul0-rgt_binary64 mul0-lft_binary64
17×+-commutative_binary64
16×*-commutative_binary64
10×--rgt-identity_binary64
*-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 distribute-rgt-out--_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
distribute-lft-neg-in_binary64
distribute-neg-in_binary64 associate--r-_binary64 associate--l+_binary64
1-exp_binary64 swap-y-z
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-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-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
01740
13940
27740
311740
421140
525340
627740
745540
842540
942340
1042040
1142040
1236140
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
12.5%87.4%0.1%7
31.2%68.6%0.1%8
39%57.7%3.3%9
47.6%46%6.4%10
58.1%35.5%6.4%11
62.2%29.1%8.7%12
66.2%22.7%11.1%13
71.3%17.6%11.1%14
Symmetry

(sort y z)

Compiler

Compiled 8 to 8 computations (0% saved)

sample25.0ms (0.8%)

Algorithm
intervals
Results
9.0ms256×body128valid
0.0ms11×body128invalid
Compiler

Compiled 15 to 18 computations (-20% saved)

simplify21.0ms (0.7%)

Algorithm
egg-herbie
Rules
46×distribute-rgt-in_binary64
45×associate-*r*_binary64
43×associate-*l*_binary64
41×cancel-sign-sub-inv_binary64
30×distribute-lft-in_binary64
29×unsub-neg_binary64 sub-neg_binary64
23×*-commutative_binary64
19×neg-sub0_binary64
18×associate--r+_binary64
17×distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
16×neg-mul-1_binary64
14×mul0-rgt_binary64 mul0-lft_binary64
11×+-lft-identity_binary64 distribute-rgt-neg-in_binary64
10×sub0-neg_binary64 associate-+l-_binary64
*-rgt-identity_binary64 *-lft-identity_binary64 +-commutative_binary64
--rgt-identity_binary64
remove-double-neg_binary64 distribute-neg-in_binary64
distribute-lft-neg-in_binary64
distribute-rgt-out--_binary64 associate-+l+_binary64 associate-+r+_binary64
associate--r-_binary64 associate-+r-_binary64
1-exp_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-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-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-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
0810
11710
23210
36610
415310
517410
618910
727410
826310
931110
1029210
1124110

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
3.3b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

3.2b
(*.f64 x (-.f64 1 (*.f64 y z)))

rewrite34.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
3.3b
Rules
add-sqr-sqrt_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64 associate-*l*_binary64 associate-*r*_binary64
sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64 associate-*r/_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64
Counts
1 → 24
Calls

1 calls:

6.0ms
(*.f64 x (-.f64 1 (*.f64 y z)))
Compiler

Compiled 322 to 168 computations (47.8% saved)

series31.0ms (1%)

Error
3.3b
Counts
1 → 15
Calls

1 calls:

27.0ms
(*.f64 x (-.f64 1 (*.f64 y z)))
Compiler

Compiled 178 to 159 computations (10.7% saved)

simplify75.0ms (2.4%)

Algorithm
egg-herbie
Rules
761×distribute-rgt-in_binary64
706×distribute-lft-in_binary64
618×distribute-neg-out_binary64
287×associate-*l*_binary64
262×*-commutative_binary64
224×associate-*r*_binary64
191×associate-+l+_binary64
181×neg-sub0_binary64
170×neg-mul-1_binary64
125×cancel-sign-sub-inv_binary64
123×distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
117×distribute-neg-in_binary64
108×associate-+r+_binary64
105×exp-prod_binary64
96×times-frac_binary64
83×sqr-pow_binary64
80×distribute-rgt-neg-in_binary64
73×distribute-lft-neg-in_binary64
59×sub-neg_binary64
53×unsub-neg_binary64
52×mul0-rgt_binary64 mul0-lft_binary64
50×unswap-sqr_binary64
47×*-lft-identity_binary64
46×exp-sum_binary64
42×*-rgt-identity_binary64
32×cancel-sign-sub_binary64
28×swap-sqr_binary64
20×cube-prod_binary64
19×exp-diff_binary64 associate-+l-_binary64
17×mul-1-neg_binary64
11×log-prod_binary64 sub0-neg_binary64
10×div-sub_binary64 pow-sqr_binary64 associate-+r-_binary64 +-commutative_binary64
cube-unmult_binary64 sqr-neg_binary64 rem-sqrt-square_binary64
+-rgt-identity_binary64
unpow1/2_binary64 difference-of-sqr-1_binary64 associate-/l*_binary64
unpow3_binary64
cube-mult_binary64
distribute-neg-frac_binary64
cube-neg_binary64 distribute-frac-neg_binary64 distribute-rgt-out--_binary64
pow-plus_binary64 --rgt-identity_binary64 difference-of-sqr--1_binary64
1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 +-lft-identity_binary64 distribute-rgt1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-*r/_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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 /-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-squares_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
39 → 31
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
058471
1133429
2411429
31126429
42879429
54779429
64868429

prune24.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New25631
Fresh000
Picked101
Done000
Total26632
Error
3.3b
Counts
32 → 6
Compiler

Compiled 352 to 206 computations (41.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (neg.f64 (*.f64 x (*.f64 z y))))
5.4b
(*.f64 x (*.f64 z y))

rewrite40.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64
*-un-lft-identity_binary64
pow-prod-down_binary64 prod-exp_binary64 add-cube-cbrt_binary64 cbrt-unprod_binary64 add-sqr-sqrt_binary64 associate-*l*_binary64
sum-log_binary64
associate-*r*_binary64 *-commutative_binary64 neg-log_binary64 flip3-+_binary64 unsub-neg_binary64 flip-+_binary64 distribute-lft-out_binary64 neg-sub0_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
2 → 33
Calls

2 calls:

5.0ms
(*.f64 x (*.f64 z y))
4.0ms
(+.f64 x (neg.f64 (*.f64 x (*.f64 z y))))
Compiler

Compiled 435 to 127 computations (70.8% saved)

series57.0ms (1.8%)

Error
3.3b
Counts
2 → 24
Calls

2 calls:

29.0ms
(+.f64 x (neg.f64 (*.f64 x (*.f64 z y))))
22.0ms
(*.f64 x (*.f64 z y))
Compiler

Compiled 343 to 296 computations (13.7% saved)

simplify104.0ms (3.3%)

Algorithm
egg-herbie
Rules
574×unsub-neg_binary64
445×distribute-rgt-neg-in_binary64
365×distribute-lft-neg-in_binary64
315×neg-sub0_binary64
303×neg-mul-1_binary64
256×distribute-rgt-in_binary64
246×*-commutative_binary64
216×distribute-lft-neg-out_binary64 distribute-rgt-out_binary64
202×distribute-lft-in_binary64
200×distribute-rgt-neg-out_binary64
179×cancel-sign-sub-inv_binary64
130×times-frac_binary64
124×exp-prod_binary64
123×distribute-rgt-out--_binary64
118×log-prod_binary64
117×cube-prod_binary64
110×associate-*r*_binary64
108×associate-*l*_binary64
93×distribute-lft-out_binary64
85×associate-+l-_binary64
81×distribute-neg-in_binary64
79×cancel-sign-sub_binary64
78×distribute-neg-out_binary64
66×sqr-pow_binary64
58×sub-neg_binary64
57×associate--r+_binary64
51×div-sub_binary64
48×exp-sum_binary64 unswap-sqr_binary64
42×swap-sqr_binary64
39×associate-/l*_binary64
36×associate--l+_binary64
34×exp-diff_binary64
33×remove-double-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64
31×distribute-lft-out--_binary64
28×associate-+l+_binary64
27×associate-+r+_binary64
26×distribute-rgt1-in_binary64
22×+-commutative_binary64
21×associate--l-_binary64
17×cube-neg_binary64 associate--r-_binary64
14×unpow3_binary64 associate-/r*_binary64
13×difference-of-squares_binary64
12×cube-mult_binary64 rem-sqrt-square_binary64 distribute-lft1-in_binary64
sqr-neg_binary64
sub0-neg_binary64
pow-sqr_binary64
associate-*r/_binary64
pow-plus_binary64 cube-unmult_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64
mul-1-neg_binary64 +-rgt-identity_binary64 distribute-frac-neg_binary64
rec-exp_binary64 associate-+r-_binary64
unpow1/2_binary64 div-exp_binary64 prod-exp_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 --rgt-identity_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-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_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 distribute-neg-frac_binary64 count-2_binary64
Counts
57 → 31
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
071628
1192555
2716548
31848548
44050548
54988548
64892548

prune20.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New29231
Fresh055
Picked011
Done000
Total29837
Error
3.2b
Counts
37 → 8
Compiler

Compiled 328 to 157 computations (52.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 z y))))
3.2b
(*.f64 x (-.f64 1 (*.f64 z y)))
3.2b
(*.f64 x (-.f64 1 (*.f64 z y)))
3.2b
(*.f64 x (-.f64 1 (*.f64 z y)))

rewrite100.0ms (3.2%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
16×add-sqr-sqrt_binary64
10×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64 associate-*r*_binary64
associate-*r/_binary64
sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64
add-log-exp_binary64 flip3--_binary64 flip--_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
cbrt-div_binary64
pow1/3_binary64 cbrt-prod_binary64
Counts
4 → 83
Calls

4 calls:

6.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
6.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
6.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
4.0ms
(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 z y))))
Compiler

Compiled 2558 to 1382 computations (46% saved)

series199.0ms (6.3%)

Error
3.2b
Counts
4 → 60
Calls

4 calls:

71.0ms
(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 z y))))
36.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
36.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
36.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
Compiler

Compiled 3571 to 2402 computations (32.7% saved)

simplify144.0ms (4.6%)

Algorithm
egg-herbie
Rules
572×prod-exp_binary64
458×times-frac_binary64
373×exp-sum_binary64
343×exp-prod_binary64
221×distribute-rgt-neg-in_binary64
219×exp-diff_binary64
210×*-commutative_binary64
202×log-prod_binary64 cancel-sign-sub-inv_binary64
201×unsub-neg_binary64
168×sub-neg_binary64
160×distribute-rgt-in_binary64
152×distribute-lft-in_binary64
110×neg-sub0_binary64
108×div-exp_binary64
106×distribute-neg-frac_binary64
103×neg-mul-1_binary64 distribute-lft-neg-in_binary64
95×div-sub_binary64
93×associate-*l*_binary64
92×associate-/l*_binary64
89×distribute-lft-neg-out_binary64
84×associate-*r*_binary64
83×distribute-rgt-neg-out_binary64
78×sqr-pow_binary64
72×associate-/r*_binary64
61×log-div_binary64
59×log-pow_binary64
58×distribute-neg-out_binary64
51×exp-to-pow_binary64 exp-neg_binary64
42×associate-+r-_binary64
41×unswap-sqr_binary64
40×associate-*r/_binary64 +-commutative_binary64
34×unpow1/3_binary64 distribute-neg-in_binary64
29×*-lft-identity_binary64
28×associate-+r+_binary64
27×associate--r-_binary64
24×associate-*l/_binary64 associate--l+_binary64 associate-+l+_binary64
23×swap-sqr_binary64 associate-+l-_binary64
22×pow-sqr_binary64
21×cube-prod_binary64
19×*-rgt-identity_binary64
18×rem-exp-log_binary64 sub0-neg_binary64
17×rec-exp_binary64 /-rgt-identity_binary64
16×log-rec_binary64
15×unpow3_binary64 cube-div_binary64 +-rgt-identity_binary64
13×associate--r+_binary64
12×pow-plus_binary64 mul0-rgt_binary64 mul0-lft_binary64
11×distribute-lft-out_binary64
10×cube-unmult_binary64
cube-mult_binary64
--rgt-identity_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-rgt-out_binary64
difference-of-sqr-1_binary64 associate-/l/_binary64 associate-/r/_binary64
rem-sqrt-square_binary64 mul-1-neg_binary64 remove-double-neg_binary64
unpow1/2_binary64 rem-log-exp_binary64 distribute-lft1-in_binary64 associate--l-_binary64
log-E_binary64 unpow2_binary64 pow-base-1_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 +-inverses_binary64 distribute-rgt-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 pow-base-0_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 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-lft-out--_binary64 count-2_binary64
Counts
143 → 87
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01281995
13221825
29881803
323921686
440411685
543691685
651781685

prune37.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New86187
Fresh066
Picked011
Done011
Total86995
Error
3.2b
Counts
95 → 9
Compiler

Compiled 1236 to 662 computations (46.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.7b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x)))
1.8b
(*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x))
3.2b
(*.f64 x (-.f64 1 (*.f64 z y)))
3.2b
(*.f64 x (-.f64 1 (*.f64 z y)))

rewrite126.0ms (4%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
22×pow1_binary64 add-exp-log_binary64
19×add-sqr-sqrt_binary64
15×add-cbrt-cube_binary64
13×associate-*r*_binary64
11×pow-prod-down_binary64 prod-exp_binary64 add-cube-cbrt_binary64 cbrt-unprod_binary64 *-un-lft-identity_binary64
10×associate-*l*_binary64
associate-*r/_binary64
add-log-exp_binary64 unswap-sqr_binary64 sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64 cbrt-prod_binary64 associate-*l/_binary64
Counts
4 → 96
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x)))
7.0ms
(*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x))
6.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
6.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
Compiler

Compiled 3584 to 1678 computations (53.2% saved)

series212.0ms (6.7%)

Error
3.2b
Counts
4 → 60
Calls

4 calls:

80.0ms
(*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x))
42.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 1 (*.f64 z y)) (cbrt.f64 x)))
38.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
38.0ms
(*.f64 x (-.f64 1 (*.f64 z y)))
Compiler

Compiled 3545 to 2216 computations (37.5% saved)

simplify127.0ms (4%)

Algorithm
egg-herbie
Rules
371×*-commutative_binary64
348×distribute-lft-neg-out_binary64
346×distribute-rgt-in_binary64
339×distribute-rgt-neg-out_binary64 distribute-lft-in_binary64
298×unswap-sqr_binary64
282×exp-prod_binary64
226×associate-*l*_binary64
202×associate-*r*_binary64
142×unsub-neg_binary64
127×log-prod_binary64
115×cancel-sign-sub-inv_binary64
107×sqr-pow_binary64
90×neg-sub0_binary64
83×neg-mul-1_binary64
70×distribute-rgt-neg-in_binary64
61×distribute-lft-neg-in_binary64
57×exp-sum_binary64
51×*-lft-identity_binary64
49×*-rgt-identity_binary64
46×cube-prod_binary64
44×sub-neg_binary64
34×distribute-neg-in_binary64
33×swap-sqr_binary64
26×associate-+l+_binary64
22×mul0-rgt_binary64 mul0-lft_binary64
21×distribute-neg-out_binary64
19×unpow3_binary64 pow-sqr_binary64
17×exp-diff_binary64
15×associate-+r+_binary64
14×+-commutative_binary64
13×pow-plus_binary64
11×log-pow_binary64 div-sub_binary64
10×cube-unmult_binary64
cube-mult_binary64 associate-/l*_binary64
remove-double-neg_binary64 associate-+l-_binary64
mul-1-neg_binary64
unpow1/2_binary64 sub0-neg_binary64
sqr-neg_binary64 rem-sqrt-square_binary64 difference-of-sqr-1_binary64
cube-neg_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64
unpow1/3_binary64 exp-neg_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 count-2_binary64 associate-+r-_binary64
unpow2_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 associate--r+_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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-cbrt-cube_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 /-rgt-identity_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-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64
Counts
156 → 102
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01242096
13081841
210231817
324281817
448151817
549231817

prune40.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1020102
Fresh066
Picked011
Done022
Total1029111
Error
3.2b
Counts
111 → 9
Compiler

Compiled 1504 to 718 computations (52.3% saved)

regimes632.0ms (20%)

Accuracy

Total -2.9b remaining (-1706.4%)

Threshold costs -2.9b (-1706.4%)

Compiler

Compiled 5607 to 4186 computations (25.3% saved)

bsearch2.0ms (0.1%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

simplify5.0ms (0.2%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
cancel-sign-sub-inv_binary64
if-if-or-not_binary64 1-exp_binary64 unsub-neg_binary64 distribute-lft-neg-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 if-if-and-not_binary64 if-if-and_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 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_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01940
14140
26040
37140
47840
58040
67940

end9.0ms (0.3%)

Remove

(sort y z)

Compiler

Compiled 81 to 51 computations (37% saved)

sample674.0ms (21.4%)

Algorithm
intervals
Results
205.0ms8000×body128valid
12.0ms534×body128invalid
Compiler

Compiled 211 to 163 computations (22.7% saved)

Profiling

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