Details

Time bar (total: 3.0s)

analyze398.0ms (13.1%)

Algorithm
search
egg-herbie
Rules
15×*-commutative_binary64
14×associate-+l+_binary64
12×associate-*r*_binary64 +-commutative_binary64
associate-+r+_binary64
distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64 associate-*l*_binary64
distribute-rgt-out_binary64
1-exp_binary64 swap-x-y
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 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 mul0-rgt_binary64 mul0-lft_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-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 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02388
14076
26852
39552
410652
510952
610752
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
25%74.9%0.1%8
31.2%64%4.8%9
31.2%42.1%26.7%10
35.9%37.1%27.1%11
38.2%32.2%29.6%12
47.8%21.6%30.6%13
50.2%19%30.8%14
Symmetry

(sort x y)

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample23.0ms (0.8%)

Algorithm
intervals
Results
7.0ms256×body128valid
0.0ms13×body128invalid
Compiler

Compiled 31 to 20 computations (35.5% saved)

simplify9.0ms (0.3%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*r*_binary64 associate-+l+_binary64
associate-+r+_binary64 +-commutative_binary64
distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64 associate-*l*_binary64
1-exp_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 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 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 mul0-rgt_binary64 mul0-lft_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-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 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
1 → 1
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0922
11619
22613
33713
44213
54313
64113

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 33 to 24 computations (27.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 x y) (*.f64 z z))
0.0b
(+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))
0.1b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z)) (*.f64 z z))

rewrite52.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
19×add-log-exp_binary64
10×sum-log_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 *-un-lft-identity_binary64 flip-+_binary64 +-commutative_binary64
associate-+l+_binary64
Counts
3 → 38
Calls

3 calls:

12.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))
9.0ms
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z)) (*.f64 z z))
4.0ms
(+.f64 (*.f64 x y) (*.f64 z z))
Compiler

Compiled 1006 to 149 computations (85.2% saved)

series116.0ms (3.8%)

Error
0.0b
Counts
3 → 54
Calls

3 calls:

38.0ms
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z)) (*.f64 z z))
38.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))
30.0ms
(+.f64 (*.f64 x y) (*.f64 z z))
Compiler

Compiled 954 to 757 computations (20.6% saved)

simplify98.0ms (3.2%)

Algorithm
egg-herbie
Rules
548×associate--r+_binary64
450×associate--l+_binary64
387×distribute-rgt-in_binary64
335×distribute-lft-in_binary64
267×associate-*l*_binary64
234×associate-*r*_binary64
207×associate-+l+_binary64
177×unswap-sqr_binary64
161×sub-neg_binary64
154×associate-+r+_binary64
117×distribute-rgt-out--_binary64
116×*-commutative_binary64
111×distribute-neg-in_binary64
110×distribute-rgt-neg-in_binary64
107×exp-sum_binary64
99×distribute-lft-neg-in_binary64
87×associate--r-_binary64
84×cancel-sign-sub-inv_binary64
78×exp-diff_binary64
76×exp-prod_binary64
73×unsub-neg_binary64
70×distribute-lft-out--_binary64
62×associate--l-_binary64
56×+-commutative_binary64
48×sqr-pow_binary64
44×associate-+r-_binary64
41×distribute-rgt-out_binary64
37×distribute-lft-neg-out_binary64
35×neg-sub0_binary64
34×neg-mul-1_binary64 associate-+l-_binary64
31×difference-of-squares_binary64
21×distribute-rgt-neg-out_binary64
20×+-rgt-identity_binary64
16×unpow3_binary64 sub0-neg_binary64
14×distribute-lft-out_binary64
12×distribute-lft1-in_binary64
11×pow-sqr_binary64 distribute-rgt1-in_binary64
10×cube-unmult_binary64 swap-sqr_binary64
cube-prod_binary64 cancel-sign-sub_binary64
pow-plus_binary64
mul0-rgt_binary64 mul0-lft_binary64 associate-/l*_binary64
prod-exp_binary64 cube-mult_binary64 +-inverses_binary64
count-2_binary64
associate-/l/_binary64
distribute-neg-out_binary64 associate-*r/_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 1-exp_binary64 rem-sqrt-square_binary64 associate-/r/_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 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 --rgt-identity_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-sqr-1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 associate-*l/_binary64
Counts
92 → 68
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0711316
12251230
26831115
325421115
447651115
548601115

prune30.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New66268
Fresh011
Picked011
Done000
Total66470
Error
0.0b
Counts
70 → 4
Compiler

Compiled 613 to 224 computations (63.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x y) (*.f64 z (*.f64 z 3)))
0.2b
(*.f64 z (*.f64 z 3))

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
pow-prod-down_binary64 prod-exp_binary64 add-cube-cbrt_binary64 cbrt-unprod_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64 associate-*l*_binary64
associate-*r*_binary64 *-commutative_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
2 → 29
Calls

2 calls:

5.0ms
(*.f64 z (*.f64 z 3))
4.0ms
(+.f64 (*.f64 x y) (*.f64 z (*.f64 z 3)))
Compiler

Compiled 443 to 235 computations (47% saved)

series44.0ms (1.5%)

Error
0.0b
Counts
2 → 21
Calls

2 calls:

34.0ms
(+.f64 (*.f64 x y) (*.f64 z (*.f64 z 3)))
7.0ms
(*.f64 z (*.f64 z 3))
Compiler

Compiled 277 to 282 computations (-1.8% saved)

simplify111.0ms (3.7%)

Algorithm
egg-herbie
Rules
534×associate-*l*_binary64
526×unswap-sqr_binary64
354×associate-*r*_binary64
347×cancel-sign-sub-inv_binary64
322×distribute-rgt-in_binary64
296×distribute-lft-in_binary64
198×distribute-rgt-neg-in_binary64
163×distribute-lft-neg-in_binary64
154×distribute-rgt-out_binary64
129×neg-mul-1_binary64
123×*-commutative_binary64
92×sqr-pow_binary64
87×associate-+l+_binary64
85×neg-sub0_binary64 unsub-neg_binary64
83×sub-neg_binary64 associate-+r+_binary64
68×distribute-lft-out_binary64
57×log-prod_binary64
47×cube-prod_binary64
46×exp-prod_binary64 distribute-lft-neg-out_binary64
33×+-commutative_binary64
29×distribute-rgt-out--_binary64
28×unpow3_binary64 pow-sqr_binary64
18×log-pow_binary64 cube-unmult_binary64
17×pow-plus_binary64
16×swap-sqr_binary64
15×associate-+l-_binary64
14×mul0-rgt_binary64 mul0-lft_binary64
13×distribute-rgt-neg-out_binary64
12×sub0-neg_binary64
11×prod-exp_binary64 associate-+r-_binary64
10×cube-mult_binary64
associate-/l*_binary64
distribute-neg-in_binary64 distribute-lft-out--_binary64
+-rgt-identity_binary64
exp-lft-cube_binary64 exp-sum_binary64 associate-/l/_binary64 associate-*r/_binary64 associate--r+_binary64
sqr-neg_binary64 difference-of-squares_binary64 count-2_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-sqrt-square_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 associate-/r/_binary64 associate-/r*_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 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_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-sqr-1_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 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
50 → 38
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
059598
1170568
2562547
31600545
43526545
54856545
64994545
74926545

prune21.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New36238
Fresh112
Picked011
Done011
Total37542
Error
0.0b
Counts
42 → 5
Compiler

Compiled 347 to 176 computations (49.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 3 (*.f64 z z))
0.3b
(*.f64 (sqrt.f64 (*.f64 3 (*.f64 z z))) (sqrt.f64 (*.f64 3 (*.f64 z z))))
23.4b
(sqrt.f64 (*.f64 3 (*.f64 z z)))
23.4b
(sqrt.f64 (*.f64 3 (*.f64 z z)))

rewrite149.0ms (4.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
148×pow1_binary64
80×pow-prod-down_binary64
66×sqrt-pow1_binary64
17×pow-prod-up_binary64
14×pow1/2_binary64
12×add-sqr-sqrt_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64 pow-sqr_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64
sqrt-prod_binary64
associate-*r*_binary64
add-log-exp_binary64 prod-exp_binary64 cbrt-unprod_binary64 swap-sqr_binary64
unswap-sqr_binary64 *-commutative_binary64
pow2_binary64 pow-plus_binary64 sqrt-unprod_binary64 rem-square-sqrt_binary64
Counts
4 → 109
Calls

4 calls:

14.0ms
(*.f64 (sqrt.f64 (*.f64 3 (*.f64 z z))) (sqrt.f64 (*.f64 3 (*.f64 z z))))
6.0ms
(*.f64 3 (*.f64 z z))
4.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
4.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
Compiler

Compiled 1588 to 855 computations (46.2% saved)

series47.0ms (1.6%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

12.0ms
(*.f64 (sqrt.f64 (*.f64 3 (*.f64 z z))) (sqrt.f64 (*.f64 3 (*.f64 z z))))
8.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
8.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
8.0ms
(*.f64 3 (*.f64 z z))
Compiler

Compiled 455 to 385 computations (15.4% saved)

simplify113.0ms (3.7%)

Algorithm
egg-herbie
Rules
545×associate-*r*_binary64
378×unswap-sqr_binary64
317×sqr-pow_binary64
282×associate-/l*_binary64
225×associate-/l/_binary64
197×associate-/r/_binary64
196×log-prod_binary64
134×distribute-rgt-in_binary64 *-commutative_binary64
123×exp-prod_binary64
115×pow-sqr_binary64
108×distribute-lft-in_binary64
93×swap-sqr_binary64
92×cube-prod_binary64
90×+-commutative_binary64
86×associate-*l*_binary64
68×distribute-lft-out_binary64
59×log-div_binary64
55×associate-+l+_binary64
52×associate-+r+_binary64
42×distribute-rgt-out_binary64
39×times-frac_binary64
37×pow-plus_binary64
36×associate-*r/_binary64
35×log-pow_binary64 rem-sqrt-square_binary64
32×unpow3_binary64
29×*-lft-identity_binary64 distribute-rgt-neg-in_binary64
27×cube-mult_binary64
23×distribute-lft-neg-in_binary64 count-2_binary64
18×associate-/r*_binary64
17×neg-sub0_binary64
15×neg-mul-1_binary64
13×sub-neg_binary64 *-rgt-identity_binary64
unpow1/2_binary64 cube-unmult_binary64
unpow2_binary64 prod-exp_binary64
cube-div_binary64 cancel-sign-sub-inv_binary64
unpow1_binary64 distribute-rgt1-in_binary64
exp-lft-cube_binary64 rem-square-sqrt_binary64 unsub-neg_binary64
log-rec_binary64 mul-1-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-neg-out_binary64 distribute-lft1-in_binary64
exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 /-rgt-identity_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 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 div-exp_binary64 rec-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 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-rgt-out--_binary64 distribute-lft-out--_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
121 → 91
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0781061
1134907
2402884
31226871
42319772
53072772
64889772
74997772

prune47.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New88391
Fresh202
Picked101
Done022
Total91596
Error
0.0b
Counts
96 → 5
Compiler

Compiled 676 to 392 computations (42% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3))
0.5b
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3)
23.4b
(sqrt.f64 (*.f64 3 (*.f64 z z)))
23.4b
(sqrt.f64 (*.f64 3 (*.f64 z z)))

rewrite172.0ms (5.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
38×add-sqr-sqrt_binary64
37×sqrt-prod_binary64
25×pow1_binary64
20×associate-*r*_binary64
18×unpow-prod-down_binary64 cube-prod_binary64
16×add-cube-cbrt_binary64 *-un-lft-identity_binary64
14×sqrt-pow1_binary64
12×unswap-sqr_binary64
10×add-exp-log_binary64
pow-prod-down_binary64
add-cbrt-cube_binary64 pow-pow_binary64 associate-*l*_binary64
pow1/2_binary64 add-log-exp_binary64 sqr-pow_binary64
pow-unpow_binary64 prod-exp_binary64
pow-to-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64
rem-cube-cbrt_binary64 sqrt-pow2_binary64 pow-prod-up_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 114
Calls

4 calls:

17.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3))
7.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3)
7.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
4.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
Compiler

Compiled 2352 to 1463 computations (37.8% saved)

series49.0ms (1.6%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

14.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3)
11.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 3 (*.f64 z z)))) 3))
9.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
9.0ms
(sqrt.f64 (*.f64 3 (*.f64 z z)))
Compiler

Compiled 569 to 504 computations (11.4% saved)

simplify110.0ms (3.6%)

Algorithm
egg-herbie
Rules
535×sqr-pow_binary64
523×distribute-rgt-in_binary64
407×*-commutative_binary64
263×log-prod_binary64
259×exp-prod_binary64
205×cube-prod_binary64
199×pow-sqr_binary64
180×associate-/l*_binary64
177×associate-*l*_binary64
173×swap-sqr_binary64
159×associate-*r*_binary64
111×associate-/r*_binary64
86×times-frac_binary64
78×distribute-lft-out_binary64
77×distribute-rgt-out_binary64
70×distribute-lft-in_binary64
62×unpow3_binary64
59×cube-mult_binary64
56×log-pow_binary64
54×pow-plus_binary64
48×unswap-sqr_binary64
37×rem-sqrt-square_binary64
36×associate-/l/_binary64
31×associate-*r/_binary64
27×*-rgt-identity_binary64
26×*-lft-identity_binary64 associate-/r/_binary64
20×count-2_binary64 associate-+l+_binary64 associate-+r+_binary64
cube-unmult_binary64 +-commutative_binary64
distribute-rgt-neg-in_binary64
unpow2_binary64 unpow1/2_binary64 rem-square-sqrt_binary64 neg-sub0_binary64 distribute-lft-neg-in_binary64
/-rgt-identity_binary64
neg-mul-1_binary64 sub-neg_binary64 distribute-rgt1-in_binary64
unpow1_binary64 associate-*l/_binary64
rem-cbrt-cube_binary64
exp-lft-cube_binary64 mul-1-neg_binary64
prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-cube-cbrt_binary64 sqr-abs_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 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-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-3cbrt-lft_binary64 sqr-neg_binary64 div-sub_binary64 unsub-neg_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-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-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
126 → 110
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01032124
12161817
28931604
316621527
431001523
550461523

prune93.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1100110
Fresh022
Picked011
Done022
Total1105115
Error
0.0b
Counts
115 → 5
Compiler

Compiled 1279 to 847 computations (33.8% saved)

regimes585.0ms (19.3%)

Accuracy

Total 0.1b remaining (79.3%)

Threshold costs 0.1b (79.3%)

Compiler

Compiled 7479 to 5567 computations (25.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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
0913
11213
21213

end6.0ms (0.2%)

Remove

(sort x y)

Compiler

Compiled 27 to 24 computations (11.1% saved)

sample680.0ms (22.4%)

Algorithm
intervals
Results
252.0ms8000×body128valid
14.0ms479×body128invalid
Compiler

Compiled 118 to 103 computations (12.7% saved)

Profiling

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