Details

Time bar (total: 18.4s)

analyze1.9s (10.3%)

Algorithm
search
egg-herbie
Rules
752×associate-*r/_binary64
481×*-commutative_binary64
271×cancel-sign-sub-inv_binary64
230×associate-/l*_binary64
224×neg-mul-1_binary64 neg-sub0_binary64
216×unswap-sqr_binary64
205×distribute-rgt-neg-in_binary64
185×distribute-lft-neg-in_binary64
140×distribute-rgt-in_binary64 distribute-lft-in_binary64
129×associate-*l*_binary64
118×associate-/r/_binary64
100×swap-sqr_binary64
94×distribute-neg-frac_binary64
87×sub-neg_binary64
85×sqr-pow_binary64
77×associate-*r*_binary64
72×times-frac_binary64
71×associate-/r*_binary64
48×associate-*l/_binary64
40×unsub-neg_binary64 distribute-lft-neg-out_binary64
29×*-rgt-identity_binary64 *-lft-identity_binary64
21×unpow1/2_binary64
20×div-sub_binary64 distribute-rgt-neg-out_binary64
18×associate-/l/_binary64
10×unpow2_binary64 sub0-neg_binary64 associate-+l-_binary64 +-commutative_binary64
unpow1_binary64 rem-sqrt-square_binary64
1-exp_binary64 swap-M-D
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 pow-plus_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 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-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 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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0122451
1393451
21448451
34121451
45362451
055
155
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14
Symmetry

(sort M D)

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample150.0ms (0.8%)

Algorithm
intervals
Results
36.0ms294×body128nan
34.0ms256×body128valid
26.0ms148×body128invalid
Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify38.0ms (0.2%)

Algorithm
egg-herbie
Rules
679×distribute-neg-frac_binary64
437×*-commutative_binary64
425×associate-/l*_binary64
347×cancel-sign-sub-inv_binary64
263×associate-/l/_binary64
212×associate-/r/_binary64
203×associate-/r*_binary64
201×neg-sub0_binary64
200×neg-mul-1_binary64
198×distribute-rgt-neg-in_binary64
195×distribute-lft-neg-in_binary64
188×times-frac_binary64
160×associate-*l*_binary64
141×associate-*r*_binary64
136×unswap-sqr_binary64
118×unsub-neg_binary64
107×associate-*l/_binary64
76×associate-*r/_binary64
67×distribute-rgt-in_binary64 distribute-lft-in_binary64
30×distribute-lft-neg-out_binary64
29×sub-neg_binary64
27×distribute-rgt-neg-out_binary64
24×div-sub_binary64
20×swap-sqr_binary64
19×sqr-pow_binary64
14×distribute-rgt-out_binary64 distribute-lft-out_binary64
12×mul0-rgt_binary64 mul0-lft_binary64
*-rgt-identity_binary64 *-lft-identity_binary64
cube-unmult_binary64
pow-plus_binary64
unpow1/2_binary64 +-commutative_binary64
div0_binary64
unpow2_binary64 unpow1_binary64 1-exp_binary64 fabs-mul_binary64 rem-sqrt-square_binary64 sub0-neg_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-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_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 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-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 fabs-div_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64 associate-+r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02441
16241
218841
3106041
4349041
5520741

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
25.7b
Counts
2 → 1
Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.7b
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
8.7b
(sqrt.f64 (/.f64 d h))
13.3b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
13.4b
(sqrt.f64 (/.f64 d l))

rewrite365.0ms (2%)

Algorithm
rewrite-expression-head
Error
14.8b
Rules
77×add-exp-log_binary64
41×prod-exp_binary64
32×add-sqr-sqrt_binary64
29×times-frac_binary64
26×add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
21×add-cbrt-cube_binary64
16×div-exp_binary64 associate-*r*_binary64
14×sqrt-div_binary64
13×pow1_binary64
10×pow-exp_binary64
cbrt-unprod_binary64 frac-times_binary64
associate-*r/_binary64 associate-*l/_binary64
add-log-exp_binary64 rem-sqrt-square_binary64 pow-prod-down_binary64 flip3--_binary64 flip--_binary64
div-inv_binary64
pow1/2_binary64 sqrt-pow1_binary64 pow-to-exp_binary64 cbrt-undiv_binary64 associate-*l*_binary64 *-commutative_binary64 sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64
Counts
4 → 127
Calls

4 calls:

22.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
3.0ms
(sqrt.f64 (/.f64 d l))
3.0ms
(sqrt.f64 (/.f64 d h))
Compiler

Compiled 4714 to 2207 computations (53.2% saved)

series374.0ms (2%)

Error
18.5b
Counts
4 → 50
Calls

4 calls:

202.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
126.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
18.0ms
(sqrt.f64 (/.f64 d h))
18.0ms
(sqrt.f64 (/.f64 d l))
Compiler

Compiled 2658 to 2317 computations (12.8% saved)

simplify162.0ms (0.9%)

Algorithm
egg-herbie
Rules
383×associate-*l*_binary64
313×associate-*r*_binary64
302×distribute-rgt-in_binary64
278×distribute-lft-in_binary64
200×*-commutative_binary64
193×distribute-rgt-neg-in_binary64
175×distribute-lft-neg-in_binary64
138×cancel-sign-sub-inv_binary64
134×log-prod_binary64
130×exp-prod_binary64
126×associate-/l*_binary64
110×associate-*r/_binary64
88×times-frac_binary64 associate-*l/_binary64
75×unswap-sqr_binary64
74×distribute-neg-frac_binary64
68×associate-/r*_binary64
60×sqr-pow_binary64
53×cube-prod_binary64
49×log-div_binary64
48×distribute-lft-neg-out_binary64
44×swap-sqr_binary64
40×neg-sub0_binary64
39×*-lft-identity_binary64
38×unpow3_binary64
37×distribute-rgt-neg-out_binary64
36×sub-neg_binary64 *-rgt-identity_binary64
35×+-commutative_binary64
33×neg-mul-1_binary64
31×associate-/l/_binary64
28×associate-/r/_binary64
21×associate-+l+_binary64
18×distribute-rgt-out_binary64
15×cube-div_binary64
14×distribute-lft-out_binary64
11×log-pow_binary64 unpow1/2_binary64
10×rem-sqrt-square_binary64
cube-unmult_binary64
/-rgt-identity_binary64 associate-+r-_binary64
pow-plus_binary64 associate-+r+_binary64
unpow2_binary64 unpow1_binary64 mul-1-neg_binary64
cube-mult_binary64 unsub-neg_binary64 distribute-rgt1-in_binary64
exp-sqrt_binary64 pow-sqr_binary64 associate--l+_binary64 associate--r+_binary64
exp-sum_binary64 rem-square-sqrt_binary64 distribute-neg-in_binary64
fabs-div_binary64 div-sub_binary64 distribute-lft1-in_binary64
exp-diff_binary64 1-exp_binary64 exp-1-e_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 unpow1/3_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 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-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-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_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
177 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03324611
17604377
228174371
347784371
449834371

prune113.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New9318111
Fresh000
Picked101
Done000
Total9418112
Error
14.6b
Counts
112 → 18
Compiler

Compiled 2476 to 1389 computations (43.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b
(/.f64 (*.f64 M D) (*.f64 d 2))
6.7b
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
8.7b
(sqrt.f64 (/.f64 d h))
13.3b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))

rewrite365.0ms (2%)

Algorithm
rewrite-expression-head
Error
10.6b
Rules
93×add-exp-log_binary64
48×prod-exp_binary64
37×add-cbrt-cube_binary64
29×frac-times_binary64
25×sqrt-div_binary64
22×add-sqr-sqrt_binary64
20×div-exp_binary64 times-frac_binary64
19×add-cube-cbrt_binary64 *-un-lft-identity_binary64
18×associate-*r/_binary64
16×pow1_binary64 cbrt-unprod_binary64 associate-*r*_binary64 associate-*l/_binary64
13×sqrt-prod_binary64
12×fabs-div_binary64
10×pow-exp_binary64
flip3--_binary64 flip--_binary64
pow-prod-down_binary64
cbrt-undiv_binary64
add-log-exp_binary64
div-inv_binary64
pow-to-exp_binary64 associate-*l*_binary64 *-commutative_binary64 rem-sqrt-square_binary64 sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64
pow1/2_binary64 sqrt-pow1_binary64 frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 associate-/r*_binary64
Counts
4 → 138
Calls

4 calls:

39.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
6.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
3.0ms
(sqrt.f64 (/.f64 d h))
Compiler

Compiled 6779 to 2606 computations (61.6% saved)

series593.0ms (3.2%)

Error
12.6b
Counts
4 → 51
Calls

4 calls:

380.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
130.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
40.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
20.0ms
(sqrt.f64 (/.f64 d h))
Compiler

Compiled 4526 to 3651 computations (19.3% saved)

simplify178.0ms (1%)

Algorithm
egg-herbie
Rules
753×associate-*l*_binary64
675×associate-*r*_binary64
201×times-frac_binary64
162×associate-/l*_binary64
152×associate-*l/_binary64
150×*-commutative_binary64
135×associate-*r/_binary64
126×distribute-rgt-in_binary64
125×distribute-lft-in_binary64
121×log-prod_binary64
97×associate-/r*_binary64
90×exp-prod_binary64
59×log-div_binary64
36×sqr-pow_binary64
30×associate-/r/_binary64
27×associate-/l/_binary64
26×distribute-rgt-neg-in_binary64
25×cancel-sign-sub-inv_binary64
24×swap-sqr_binary64
23×+-commutative_binary64
22×sub-neg_binary64 distribute-lft-neg-in_binary64
18×neg-sub0_binary64
16×neg-mul-1_binary64
14×associate-+l+_binary64
12×cube-unmult_binary64 *-rgt-identity_binary64
11×unswap-sqr_binary64
10×*-lft-identity_binary64
cube-prod_binary64
pow-plus_binary64 fabs-mul_binary64 associate-+r-_binary64
log-pow_binary64 distribute-lft-neg-out_binary64
unpow3_binary64 unpow1/2_binary64 exp-sqrt_binary64 exp-sum_binary64 rem-sqrt-square_binary64 distribute-neg-frac_binary64
unpow1/3_binary64 unpow2_binary64 unpow1_binary64 /-rgt-identity_binary64
fabs-div_binary64 fabs-sqr_binary64 mul-1-neg_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64
exp-diff_binary64 cube-div_binary64 rem-square-sqrt_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft-out_binary64 associate-+r+_binary64
log-rec_binary64 exp-neg_binary64 1-exp_binary64 cube-mult_binary64 sqr-abs_binary64 pow-sqr_binary64 distribute-frac-neg_binary64 distribute-neg-out_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 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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64
Counts
189 → 148
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04297190
111186368
246026367
349656367

prune162.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New13612148
Fresh41317
Picked101
Done000
Total14125166
Error
11.0b
Counts
166 → 25
Compiler

Compiled 4517 to 2220 computations (50.9% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 h)
4.6b
(/.f64 (*.f64 M D) (*.f64 d 2))
6.7b
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.3b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))

rewrite569.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
9.5b
Rules
102×add-exp-log_binary64
81×frac-times_binary64
55×prod-exp_binary64
48×sqrt-div_binary64 fabs-div_binary64 associate-*l/_binary64
46×add-cbrt-cube_binary64
36×associate-*r/_binary64
24×pow1_binary64
23×cbrt-unprod_binary64
20×div-exp_binary64
16×associate-*r*_binary64 flip3--_binary64 flip--_binary64
14×pow-prod-down_binary64
13×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
10×pow-exp_binary64 times-frac_binary64
cbrt-undiv_binary64
add-log-exp_binary64
cbrt-prod_binary64
pow-to-exp_binary64 associate-*l*_binary64 div-inv_binary64 *-commutative_binary64 sub-neg_binary64 distribute-rgt-in_binary64 cancel-sign-sub-inv_binary64 distribute-lft-in_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 associate-/r*_binary64 pow1/3_binary64
Counts
4 → 154
Calls

4 calls:

51.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
6.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
1.0ms
(cbrt.f64 h)
Compiler

Compiled 9671 to 3311 computations (65.8% saved)

series676.0ms (3.7%)

Error
10.7b
Counts
4 → 51
Calls

4 calls:

454.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
130.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
41.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
19.0ms
(cbrt.f64 h)
Compiler

Compiled 5721 to 4254 computations (25.6% saved)

simplify294.0ms (1.6%)

Algorithm
egg-herbie
Rules
257×distribute-rgt-in_binary64
256×distribute-lft-in_binary64
236×*-commutative_binary64
211×times-frac_binary64
185×associate-/l*_binary64
173×associate-*r/_binary64
160×log-div_binary64
158×associate-*l*_binary64
148×associate-*l/_binary64
116×associate-/r*_binary64
115×sqr-pow_binary64
109×unswap-sqr_binary64
103×associate-*r*_binary64
84×log-prod_binary64
80×exp-prod_binary64
72×sub-neg_binary64
61×cube-prod_binary64
56×neg-sub0_binary64
54×neg-mul-1_binary64
52×cube-div_binary64
51×*-rgt-identity_binary64 +-commutative_binary64
48×*-lft-identity_binary64
37×associate-+l+_binary64
34×distribute-rgt-neg-in_binary64
32×swap-sqr_binary64
30×cancel-sign-sub-inv_binary64
29×fabs-mul_binary64 distribute-lft-neg-in_binary64
25×div-sub_binary64
21×log-pow_binary64 exp-sum_binary64 cube-unmult_binary64
19×exp-diff_binary64 associate-/r/_binary64
17×unsub-neg_binary64
16×associate-+r+_binary64
15×associate-/l/_binary64 associate-+r-_binary64
14×fabs-sqr_binary64
13×fabs-div_binary64 pow-sqr_binary64
10×rem-sqrt-square_binary64
unpow1/3_binary64
distribute-lft-neg-out_binary64
associate-+l-_binary64
pow-plus_binary64 exp-neg_binary64 /-rgt-identity_binary64
unpow3_binary64 unpow1/2_binary64 exp-sqrt_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64
log-rec_binary64 unpow2_binary64 exp-to-pow_binary64 unpow1_binary64 distribute-neg-frac_binary64 associate--l+_binary64 associate--r+_binary64
cube-mult_binary64 sqr-abs_binary64 rem-square-sqrt_binary64
mul-1-neg_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft-out_binary64 associate--l-_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_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 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_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-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-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_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64
Counts
205 → 178
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
051411486
115299557
239449366
349519366
449889366

prune195.0ms (1.1%)

Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New1726178
Fresh22224
Picked101
Done000
Total17528203
Error
10.4b
Counts
203 → 28
Compiler

Compiled 6737 to 3285 computations (51.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b
(*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
3.3b
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
4.6b
(/.f64 (*.f64 M D) (*.f64 2 d))
13.3b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))

rewrite477.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
8.9b
Rules
113×add-exp-log_binary64
100×add-sqr-sqrt_binary64
94×associate-*l*_binary64
90×times-frac_binary64 sqrt-prod_binary64
80×cbrt-prod_binary64
65×add-cube-cbrt_binary64 *-un-lft-identity_binary64
63×prod-exp_binary64
49×unpow-prod-down_binary64 cube-prod_binary64
42×add-cbrt-cube_binary64
31×frac-times_binary64
27×sqrt-div_binary64
22×associate-*r/_binary64
20×div-exp_binary64
19×cbrt-unprod_binary64
17×associate-*r*_binary64
15×cube-div_binary64
14×unswap-sqr_binary64 associate-*l/_binary64
13×pow-exp_binary64
12×fabs-div_binary64
11×pow1_binary64
10×flip3--_binary64 flip--_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
cbrt-undiv_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
pow-to-exp_binary64
pow-prod-down_binary64 add-log-exp_binary64 div-inv_binary64
*-commutative_binary64
sqr-pow_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 associate-/r*_binary64 unpow3_binary64 cube-mult_binary64
Counts
4 → 250
Calls

4 calls:

42.0ms
(*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
34.0ms
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
11.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 11084 to 4513 computations (59.3% saved)

series756.0ms (4.1%)

Error
10.4b
Counts
4 → 66
Calls

4 calls:

385.0ms
(*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
172.0ms
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
132.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))
42.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 5759 to 4623 computations (19.7% saved)

simplify385.0ms (2.1%)

Algorithm
egg-herbie
Rules
535×*-commutative_binary64
245×times-frac_binary64
219×log-prod_binary64
207×associate-/l*_binary64
174×sqr-pow_binary64
156×associate-*r/_binary64
144×associate-*l/_binary64
135×log-div_binary64 associate-/r*_binary64
127×distribute-rgt-in_binary64
125×distribute-lft-in_binary64
104×unswap-sqr_binary64 associate-*r*_binary64
95×associate-*l*_binary64
88×swap-sqr_binary64
80×exp-prod_binary64
68×cube-prod_binary64
63×neg-sub0_binary64
55×neg-mul-1_binary64
53×*-rgt-identity_binary64
49×*-lft-identity_binary64
46×cube-div_binary64 sub-neg_binary64
41×+-commutative_binary64
33×distribute-rgt-neg-in_binary64
32×unpow3_binary64
29×rem-sqrt-square_binary64
28×cube-mult_binary64 cancel-sign-sub-inv_binary64
27×distribute-lft-neg-in_binary64 associate-+l+_binary64
25×log-pow_binary64
23×associate-/r/_binary64
22×rem-square-sqrt_binary64
18×fabs-mul_binary64
15×associate-/l/_binary64
14×cube-unmult_binary64 associate-+r+_binary64
11×distribute-lft-neg-out_binary64
10×pow-sqr_binary64
fabs-sqr_binary64 unsub-neg_binary64
mul-1-neg_binary64 distribute-rgt-neg-out_binary64 associate-+r-_binary64
unpow1/2_binary64
unpow2_binary64 unpow1_binary64 /-rgt-identity_binary64 distribute-neg-frac_binary64
pow-plus_binary64 fabs-div_binary64
unpow1/3_binary64 exp-sqrt_binary64 exp-sum_binary64 div-sub_binary64 associate--l+_binary64 associate--r+_binary64
distribute-rgt-out_binary64
rem-cube-cbrt_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft-out_binary64
exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 rem-cbrt-cube_binary64 sqr-abs_binary64 distribute-frac-neg_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-lft-sqr_binary64 exp-cbrt_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-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-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_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
316 → 269
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
052314864
1138613728
2381513674
3484513674
4501413674

prune215.0ms (1.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New2627269
Fresh72027
Picked101
Done000
Total27027297
Error
10.3b
Counts
297 → 27
Compiler

Compiled 6487 to 2775 computations (57.2% saved)

regimes5.5s (30.2%)

Accuracy

Total 2.8b remaining (22.2%)

Threshold costs 0b (0%)

Compiler

Compiled 90831 to 67657 computations (25.5% saved)

bsearch19.0ms (0.1%)

Compiler

Compiled 35 to 31 computations (11.4% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
18×*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
cancel-sign-sub-inv_binary64
1-exp_binary64 fabs-div_binary64 distribute-neg-frac_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-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 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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_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
049186
173186
292186
3104186
4113186
5117186
6118186
7115186

end15.0ms (0.1%)

Remove

(sort M D)

Compiler

Compiled 351 to 195 computations (44.4% saved)

sample4.7s (25.7%)

Algorithm
intervals
Results
1.1s8000×body128valid
1.1s8530×body128nan
651.0ms4670×body128invalid
Compiler

Compiled 1231 to 934 computations (24.1% saved)

Profiling

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