Details

Time bar (total: 11.8s)

analyze26.0ms (0.2%)

Algorithm
search
egg-herbie
Rules
+-commutative_binary64 swap-re-im
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 1-exp_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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_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 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01538
11238
21238
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
74.9%25%0.1%3
87.4%12.5%0.1%4
93.7%6.2%0.1%5
96.8%3.1%0.1%6
98.3%1.6%0.1%7
99.1%0.8%0.1%8
99.5%0.4%0.1%9
99.7%0.2%0.1%10
99.8%0.1%0.1%11
99.9%0%0.1%12
99.9%0%0.1%13
99.9%0%0.1%14
Symmetry

(sort re im)

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample30.0ms (0.3%)

Algorithm
intervals
Results
15.0ms256×body128valid
Compiler

Compiled 25 to 23 computations (8% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-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 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 1-exp_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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_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 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11219
21219

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
29.8b
Counts
1 → 1
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
27.5b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite93.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
29.6b
Rules
24×times-frac_binary64
22×log-pow_binary64
20×pow1_binary64
16×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1/2_binary64 sqrt-pow1_binary64 associate-/l*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64 associate-/r*_binary64
sqrt-prod_binary64
add-log-exp_binary64 flip3-+_binary64 flip-+_binary64 log-div_binary64 div-sub_binary64
rem-sqrt-square_binary64 div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
2 → 63
Calls

2 calls:

7.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 1160 to 427 computations (63.2% saved)

series105.0ms (0.9%)

Error
0.8b
Counts
2 → 30
Calls

2 calls:

46.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
39.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 1128 to 1004 computations (11% saved)

simplify115.0ms (1%)

Algorithm
egg-herbie
Rules
395×distribute-rgt-neg-in_binary64
378×distribute-lft-neg-in_binary64
302×unswap-sqr_binary64
291×times-frac_binary64
285×distribute-neg-frac_binary64
242×div-sub_binary64
240×associate-/l*_binary64
198×associate-*r*_binary64
173×associate-*l*_binary64
161×associate-/r*_binary64
159×sub-neg_binary64
108×associate-*l/_binary64
96×neg-sub0_binary64
94×*-commutative_binary64
87×cancel-sign-sub-inv_binary64 associate-*r/_binary64
85×neg-mul-1_binary64
51×associate-/l/_binary64
50×+-commutative_binary64
44×difference-of-squares_binary64
42×associate-/r/_binary64
40×sqr-pow_binary64
37×unsub-neg_binary64
35×associate-+r-_binary64
32×distribute-neg-in_binary64
28×distribute-lft-neg-out_binary64
27×associate-+l-_binary64
26×distribute-rgt-in_binary64
24×+-rgt-identity_binary64
22×cube-unmult_binary64
20×pow-plus_binary64
18×cube-prod_binary64 sub0-neg_binary64 distribute-lft-in_binary64
17×distribute-rgt-neg-out_binary64
15×log-div_binary64
13×associate-+l+_binary64
12×unpow3_binary64
10×mul-1-neg_binary64
log-prod_binary64 associate-+r+_binary64
associate--r-_binary64
distribute-rgt-out--_binary64
log-pow_binary64 remove-double-neg_binary64 associate--r+_binary64
cube-div_binary64 *-rgt-identity_binary64 distribute-frac-neg_binary64 associate--l+_binary64
log-rec_binary64 cube-mult_binary64 rem-sqrt-square_binary64 /-rgt-identity_binary64 *-lft-identity_binary64 pow-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt-out_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 distribute-neg-out_binary64 associate--l-_binary64
1-exp_binary64 rem-square-sqrt_binary64 div0_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_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-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-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_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 swap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64
Counts
93 → 52
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01612209
13482106
28592094
329952094
448392094
550692094

prune38.0ms (0.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New43952
Fresh000
Picked011
Done000
Total431053
Error
2.7b
Counts
53 → 10
Compiler

Compiled 769 to 453 computations (41.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3))
0.6b
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
0.7b
(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3)
27.5b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite195.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
2.6b
Rules
120×times-frac_binary64
94×log-pow_binary64
79×pow1_binary64
64×add-sqr-sqrt_binary64
63×add-cube-cbrt_binary64 *-un-lft-identity_binary64
62×cbrt-prod_binary64
56×unpow-prod-down_binary64 cube-prod_binary64
22×pow1/2_binary64 sqrt-pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l*_binary64
div-inv_binary64
add-log-exp_binary64 sqrt-div_binary64 associate-/r*_binary64
sqrt-prod_binary64 pow-unpow_binary64
flip3-+_binary64 flip-+_binary64 div-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64 cube-div_binary64 rem-cube-cbrt_binary64 cbrt-undiv_binary64 sqr-pow_binary64 log-div_binary64 div-sub_binary64
rem-sqrt-square_binary64 pow-pow_binary64 pow-to-exp_binary64 frac-2neg_binary64 clear-num_binary64 pow1/3_binary64 cbrt-div_binary64 rem-cbrt-cube_binary64
Counts
4 → 211
Calls

4 calls:

10.0ms
(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3)
8.0ms
(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3))
7.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 3344 to 1531 computations (54.2% saved)

series274.0ms (2.3%)

Error
0.5b
Counts
4 → 54
Calls

4 calls:

93.0ms
(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3)
46.0ms
(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10)) 3))
46.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 10))
44.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 2822 to 2554 computations (9.5% saved)

simplify247.0ms (2.1%)

Algorithm
egg-herbie
Rules
560×unswap-sqr_binary64
206×times-frac_binary64
173×sqr-pow_binary64
172×cancel-sign-sub-inv_binary64
142×associate-/l*_binary64
141×associate-/r*_binary64
133×log-div_binary64
113×associate-*l/_binary64
108×associate-*r/_binary64
107×associate-*r*_binary64
90×log-prod_binary64
84×associate-*l*_binary64
73×sub-neg_binary64 distribute-frac-neg_binary64
72×cube-div_binary64
66×*-commutative_binary64
58×exp-prod_binary64
57×distribute-neg-frac_binary64
55×cube-prod_binary64
53×neg-sub0_binary64
49×unpow3_binary64
48×cube-mult_binary64
47×distribute-rgt-neg-out_binary64
44×log-pow_binary64
36×div-sub_binary64
33×neg-mul-1_binary64 swap-sqr_binary64
31×+-commutative_binary64
27×rem-cbrt-cube_binary64
26×mul-1-neg_binary64
21×associate-/l/_binary64
18×distribute-rgt-neg-in_binary64
15×rem-sqrt-square_binary64 pow-sqr_binary64 distribute-lft-neg-in_binary64
13×pow-plus_binary64 *-rgt-identity_binary64
12×associate-/r/_binary64
unpow1/2_binary64 unpow1_binary64
unpow2_binary64 cube-unmult_binary64 distribute-neg-in_binary64 distribute-rgt-in_binary64
log-rec_binary64 *-lft-identity_binary64 difference-of-squares_binary64
unsub-neg_binary64 remove-double-neg_binary64 distribute-lft-neg-out_binary64 associate--r+_binary64
rem-square-sqrt_binary64 /-rgt-identity_binary64 distribute-lft-in_binary64 associate--l+_binary64
rem-cube-cbrt_binary64 associate-+r-_binary64 associate-+l+_binary64
cube-neg_binary64 sqr-neg_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64
1-exp_binary64 rem-3cbrt-lft_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-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 sqr-abs_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_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--r-_binary64 associate--l-_binary64 associate-+r+_binary64
Counts
265 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02957859
17627329
225467116
349017116
449717116

prune100.0ms (0.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New19412206
Fresh538
Picked101
Done011
Total20016216
Error
2.5b
Counts
216 → 16
Compiler

Compiled 2166 to 1255 computations (42.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10))))
0.5b
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10)))
27.5b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite235.0ms (2%)

Algorithm
rewrite-expression-head
Error
2.5b
Rules
127×times-frac_binary64
107×add-sqr-sqrt_binary64
78×sqrt-prod_binary64
66×*-un-lft-identity_binary64
61×log-pow_binary64
60×add-cube-cbrt_binary64
52×pow1_binary64
46×associate-*r*_binary64
27×add-exp-log_binary64
25×associate-*l*_binary64
17×add-cbrt-cube_binary64
16×pow1/2_binary64 sqrt-pow1_binary64
15×unswap-sqr_binary64
div-exp_binary64
prod-exp_binary64
associate-/r*_binary64
associate-/l*_binary64
cbrt-undiv_binary64
sqrt-div_binary64 cbrt-unprod_binary64
add-log-exp_binary64 div-inv_binary64
flip3-+_binary64 flip-+_binary64 log-div_binary64 div-sub_binary64 1-exp_binary64 rec-exp_binary64
rem-sqrt-square_binary64 frac-2neg_binary64 clear-num_binary64 pow-prod-down_binary64 frac-times_binary64 associate-*l/_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
3 → 194
Calls

3 calls:

31.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10))))
9.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 4410 to 2465 computations (44.1% saved)

series194.0ms (1.6%)

Error
0.3b
Counts
3 → 42
Calls

3 calls:

60.0ms
(/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10)))
47.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
46.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (sqrt.f64 (log.f64 10))))
Compiler

Compiled 2250 to 2076 computations (7.7% saved)

simplify221.0ms (1.9%)

Algorithm
egg-herbie
Rules
671×times-frac_binary64
356×associate-/r*_binary64
334×*-commutative_binary64
303×associate-/l/_binary64
231×unswap-sqr_binary64
227×sub-neg_binary64
183×associate-*r*_binary64
161×associate-/r/_binary64
143×associate-*l*_binary64
140×associate-/l*_binary64
138×associate-*r/_binary64
135×associate-*l/_binary64
117×neg-sub0_binary64
113×cancel-sign-sub-inv_binary64
109×neg-mul-1_binary64
94×distribute-rgt-neg-in_binary64
86×distribute-lft-neg-in_binary64
73×sqr-pow_binary64
71×unsub-neg_binary64
62×div-sub_binary64
57×associate-+l-_binary64 associate-+r-_binary64
47×*-lft-identity_binary64
44×difference-of-squares_binary64
43×distribute-neg-frac_binary64
34×log-div_binary64 distribute-rgt-in_binary64
32×associate-+r+_binary64
31×associate-+l+_binary64 +-commutative_binary64
27×+-rgt-identity_binary64
26×log-prod_binary64 distribute-lft-in_binary64
25×sub0-neg_binary64 associate--r+_binary64
24×associate--r-_binary64
23×cube-prod_binary64 *-rgt-identity_binary64
21×cube-div_binary64
18×exp-prod_binary64 distribute-lft-neg-out_binary64
17×/-rgt-identity_binary64
16×distribute-rgt-out_binary64
15×pow-sqr_binary64
14×cube-unmult_binary64 distribute-neg-in_binary64
12×mul-1-neg_binary64
11×unpow3_binary64 swap-sqr_binary64 distribute-rgt-out--_binary64
10×pow-plus_binary64
log-rec_binary64 distribute-frac-neg_binary64 distribute-rgt-neg-out_binary64 distribute-lft-out_binary64
cube-mult_binary64 remove-double-neg_binary64
rem-sqrt-square_binary64 associate--l+_binary64
log-pow_binary64 --rgt-identity_binary64 distribute-lft-out--_binary64
unpow1/2_binary64 associate--l-_binary64
exp-to-pow_binary64 rem-square-sqrt_binary64
unpow2_binary64 unpow1_binary64 +-lft-identity_binary64 div0_binary64 count-2_binary64
prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 +-inverses_binary64 remove-double-div_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_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 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_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 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-lft1-in_binary64
Counts
236 → 186
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02727128
16606403
219116295
342376295
450286295

prune117.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1806186
Fresh6814
Picked101
Done101
Total18814202
Error
0.3b
Counts
202 → 14
Compiler

Compiled 2860 to 1752 computations (38.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
0.2b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))))
3.8b
(pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
27.5b
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite241.0ms (2%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
58×add-sqr-sqrt_binary64
47×*-un-lft-identity_binary64
46×times-frac_binary64
45×add-cube-cbrt_binary64
41×sqrt-prod_binary64
30×log-prod_binary64
25×pow-unpow_binary64 associate-*l*_binary64
24×unpow-prod-down_binary64
16×add-exp-log_binary64
15×pow1_binary64
10×distribute-rgt-in_binary64 distribute-lft-in_binary64
add-cbrt-cube_binary64
log-pow_binary64
unswap-sqr_binary64
add-log-exp_binary64 sqr-pow_binary64 prod-exp_binary64 associate-*r*_binary64
pow-pow_binary64 rem-log-exp_binary64
pow1/2_binary64 sqrt-pow1_binary64 sqrt-div_binary64 div-inv_binary64 pow-to-exp_binary64 pow-exp_binary64 div-exp_binary64 cbrt-unprod_binary64
flip3-+_binary64 flip-+_binary64 rem-sqrt-square_binary64 sqrt-pow2_binary64 pow-prod-down_binary64 1-exp_binary64 rec-exp_binary64 cbrt-undiv_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 151
Calls

4 calls:

15.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))))
8.0ms
(pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
6.0ms
(log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 4371 to 2800 computations (35.9% saved)

series361.0ms (3.1%)

Error
0.3b
Counts
4 → 54
Calls

4 calls:

91.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))))
82.0ms
(pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
81.0ms
(log.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
46.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Compiler

Compiled 3974 to 3730 computations (6.1% saved)

simplify289.0ms (2.4%)

Algorithm
egg-herbie
Rules
609×times-frac_binary64
208×log-pow_binary64
191×associate-*l*_binary64
190×associate-*r*_binary64
151×associate-/l/_binary64
148×exp-prod_binary64
142×*-commutative_binary64
130×sqr-pow_binary64
129×associate-/r/_binary64
121×log-prod_binary64
112×distribute-rgt-in_binary64
105×associate-/l*_binary64
104×associate-*l/_binary64
101×unswap-sqr_binary64
100×distribute-lft-in_binary64
93×associate-*r/_binary64
87×cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
78×distribute-lft-neg-in_binary64
54×sub-neg_binary64
48×neg-sub0_binary64 pow-sqr_binary64 associate-/r*_binary64
41×log-div_binary64 exp-to-pow_binary64
39×+-commutative_binary64
36×neg-mul-1_binary64 distribute-rgt-out_binary64
32×*-rgt-identity_binary64 distribute-neg-frac_binary64
31×*-lft-identity_binary64
26×distribute-lft-neg-out_binary64
20×distribute-rgt-neg-out_binary64
19×pow-plus_binary64 unsub-neg_binary64
18×unpow3_binary64
17×exp-diff_binary64
15×distribute-neg-in_binary64
14×exp-neg_binary64
13×log-rec_binary64 distribute-lft-out_binary64
12×count-2_binary64
11×cube-unmult_binary64 cube-prod_binary64 swap-sqr_binary64 distribute-rgt-out--_binary64
mul-1-neg_binary64
prod-exp_binary64
cube-div_binary64 rem-sqrt-square_binary64 difference-of-squares_binary64 associate-+r-_binary64
/-rgt-identity_binary64 distribute-rgt1-in_binary64 associate--r+_binary64
unpow1/2_binary64 rem-log-exp_binary64 distribute-lft-out--_binary64 associate-+l+_binary64
pow-base-1_binary64 unpow1_binary64 cube-mult_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 associate--l+_binary64 associate-+r+_binary64
rem-square-sqrt_binary64 associate-+l-_binary64
unpow2_binary64 unpow-1_binary64 exp-sum_binary64 distribute-frac-neg_binary64
log-E_binary64 exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 sub0-neg_binary64 +-lft-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 pow-base-0_binary64 unpow1/3_binary64 unpow0_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_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 div-sub_binary64 --rgt-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 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
205 → 168
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02967033
17185856
221955401
347415361
448005361
549645361
649585361

prune113.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1644168
Fresh31013
Picked101
Done000
Total16814182
Error
0.3b
Counts
182 → 14
Compiler

Compiled 2544 to 1633 computations (35.8% saved)

regimes7.3s (61.9%)

Accuracy

Total 6.8b remaining (96%)

Threshold costs 0b (0%)

Compiler

Compiled 76766 to 56015 computations (27% saved)

bsearch53.0ms (0.4%)

Steps
ItersRangePoint
8
1.418218104034813e+119
1.759685704910558e+122
2.907640811759891e+120
9
1.5726615535625908e-159
3.4693918181042096e-150
3.5598012421053094e-159
Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02994
13894
24094
34194
44094

end12.0ms (0.1%)

Compiler

Compiled 174 to 156 computations (10.3% saved)

sample1.4s (11.7%)

Algorithm
intervals
Results
511.0ms8000×body128valid
Compiler

Compiled 389 to 322 computations (17.2% saved)

Profiling

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