Details

Time bar (total: 4.1s)

analyze207.0ms (5.1%)

Algorithm
1×search
2×egg-herbie
Rules
889×associate-/r*_binary64
839×neg-mul-1_binary64
735×sub-neg_binary64
637×neg-sub0_binary64
568×associate-/l/_binary64
553×distribute-rgt-in_binary64
548×distribute-rgt-neg-out_binary64
516×unsub-neg_binary64
509×distribute-lft-neg-out_binary64
439×distribute-lft-in_binary64
421×distribute-rgt-neg-in_binary64
303×associate--r+_binary64
292×distribute-neg-in_binary64
243×distribute-lft-out--_binary64
221×remove-double-neg_binary64
220×distribute-lft-out_binary64
195×*-commutative_binary64
183×associate--l+_binary64
147×--rgt-identity_binary64
133×associate-*l*_binary64
124×distribute-rgt-out--_binary64
123×associate--l-_binary64
121×associate-*r*_binary64
114×*-lft-identity_binary64
110×*-rgt-identity_binary64 +-commutative_binary64
108×distribute-lft-neg-in_binary64
107×cancel-sign-sub-inv_binary64
103×associate--r-_binary64
91×sub0-neg_binary64
86×associate-+l-_binary64
68×mul0-rgt_binary64 mul0-lft_binary64
53×distribute-rgt-out_binary64
47×+-lft-identity_binary64
46×distribute-neg-out_binary64
33×associate-+r+_binary64
28×distribute-rgt1-in_binary64
12×cancel-sign-sub_binary64 associate-+l+_binary64
11×/-rgt-identity_binary64 distribute-lft1-in_binary64 associate-+r-_binary64
10×+-rgt-identity_binary64
6×mul-1-neg_binary64
2×+-inverses_binary64
1×1-exp_binary64 sqr-neg_binary64 difference-of-sqr-1_binary64
0×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 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 div0_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-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 count-2_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-*l/_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01731
14228
210228
324728
462328
588328
6130128
7272628
8309528
9337028
10343128
11346028
12355228
13493528
14494828
15465528
16489528
17484328
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 21 to 17 computations (19% saved)

sample20.0ms (0.5%)

Algorithm
1×intervals
Results
13.0ms256×body128valid
Compiler

Compiled 41 to 34 computations (17.1% saved)

simplify188.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
889×associate-/r*_binary64
839×neg-mul-1_binary64
735×sub-neg_binary64
637×neg-sub0_binary64
568×associate-/l/_binary64
553×distribute-rgt-in_binary64
548×distribute-rgt-neg-out_binary64
516×unsub-neg_binary64
509×distribute-lft-neg-out_binary64
439×distribute-lft-in_binary64
421×distribute-rgt-neg-in_binary64
303×associate--r+_binary64
292×distribute-neg-in_binary64
243×distribute-lft-out--_binary64
221×remove-double-neg_binary64
220×distribute-lft-out_binary64
195×*-commutative_binary64
183×associate--l+_binary64
147×--rgt-identity_binary64
133×associate-*l*_binary64
124×distribute-rgt-out--_binary64
123×associate--l-_binary64
121×associate-*r*_binary64
114×*-lft-identity_binary64
110×*-rgt-identity_binary64 +-commutative_binary64
108×distribute-lft-neg-in_binary64
107×cancel-sign-sub-inv_binary64
103×associate--r-_binary64
91×sub0-neg_binary64
86×associate-+l-_binary64
68×mul0-rgt_binary64 mul0-lft_binary64
53×distribute-rgt-out_binary64
47×+-lft-identity_binary64
46×distribute-neg-out_binary64
33×associate-+r+_binary64
28×distribute-rgt1-in_binary64
12×cancel-sign-sub_binary64 associate-+l+_binary64
11×/-rgt-identity_binary64 distribute-lft1-in_binary64 associate-+r-_binary64
10×+-rgt-identity_binary64
6×mul-1-neg_binary64
2×+-inverses_binary64
1×1-exp_binary64 sqr-neg_binary64 difference-of-sqr-1_binary64
0×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 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 div0_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-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 count-2_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01731
14228
210228
324728
462328
588328
6130128
7272628
8309528
9337028
10343128
11346028
12355228
13493528
14494828
15465528
16489528
17484328

prune5.0ms (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 56 to 44 computations (21.4% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.0b
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
0.2b
(*.f64 (*.f64 v v) 6)

rewrite169.0ms (4.2%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
25×add-exp-log_binary64 add-cbrt-cube_binary64
22×associate-*r/_binary64
18×flip3--_binary64 sqrt-div_binary64 flip--_binary64
17×add-sqr-sqrt_binary64
16×pow1_binary64
12×*-un-lft-identity_binary64 frac-times_binary64
11×add-cube-cbrt_binary64
10×prod-exp_binary64 cbrt-unprod_binary64 associate-*r*_binary64
9×associate-*l*_binary64
8×associate-/r/_binary64
7×pow-prod-down_binary64
6×associate-*l/_binary64
4×add-log-exp_binary64 sqrt-prod_binary64
3×unswap-sqr_binary64 *-commutative_binary64 div-exp_binary64 cbrt-undiv_binary64 times-frac_binary64 associate-/l*_binary64
2×difference-of-squares_binary64
1×frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/r*_binary64
Counts
4 → 108
Calls

4 calls:

11.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
11.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
10.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
6.0ms
(*.f64 (*.f64 v v) 6)
Compiler

Compiled 3261 to 2040 computations (37.4% saved)

series100.0ms (2.5%)

Error
0b
Counts
4 → 21
Calls

4 calls:

30.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
18.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
17.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
8.0ms
(*.f64 (*.f64 v v) 6)
Compiler

Compiled 1392 to 1209 computations (13.1% saved)

simplify146.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
428×distribute-rgt-in_binary64
359×cancel-sign-sub-inv_binary64
265×associate-*r*_binary64
238×associate-*l*_binary64
229×neg-mul-1_binary64
223×distribute-rgt-neg-in_binary64
184×distribute-lft-neg-in_binary64
175×times-frac_binary64 associate-/r*_binary64
163×*-commutative_binary64
150×associate-/l*_binary64
147×sub-neg_binary64
98×+-commutative_binary64
78×distribute-neg-in_binary64
75×associate-+r+_binary64
69×exp-prod_binary64
66×associate-+l+_binary64
61×neg-sub0_binary64
50×distribute-neg-frac_binary64
49×sqr-pow_binary64
48×associate--r+_binary64
47×distribute-lft-neg-out_binary64
46×associate-*l/_binary64 associate-*r/_binary64
40×log-prod_binary64
39×associate--l+_binary64
37×cube-prod_binary64
35×distribute-lft-in_binary64
31×unsub-neg_binary64
27×unswap-sqr_binary64
26×distribute-rgt-out_binary64
25×distribute-rgt-neg-out_binary64
24×*-lft-identity_binary64
21×*-rgt-identity_binary64 swap-sqr_binary64
18×exp-sum_binary64 div-sub_binary64
17×unpow3_binary64
16×cube-div_binary64
15×cube-mult_binary64 associate-/r/_binary64
14×log-div_binary64
9×cube-unmult_binary64
7×/-rgt-identity_binary64 distribute-lft-out_binary64
5×pow-plus_binary64 distribute-rgt1-in_binary64
4×exp-diff_binary64 distribute-rgt-out--_binary64
3×unpow1/2_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64
2×log-pow_binary64 exp-neg_binary64 pow-sqr_binary64
1×unpow2_binary64 unpow1_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 sqr-neg_binary64 distribute-lft1-in_binary64 count-2_binary64
0×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 exp-sqrt_binary64 div-exp_binary64 rec-exp_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 sqr-abs_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-lft-out--_binary64 associate-/l/_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
129 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03083874
17723457
230633412
348293412
450773412

prune117.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1101111
Fresh011
Picked011
Done000
Total1103113
Error
0b
Counts
113 → 3
Compiler

Compiled 2660 to 1808 computations (32% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))))
0.2b
(*.f64 6 (*.f64 v v))
1.0b
(/.f64 1 (/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))))
1.0b
(/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

rewrite643.0ms (15.9%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
426×times-frac_binary64
171×add-sqr-sqrt_binary64
170×add-cube-cbrt_binary64 *-un-lft-identity_binary64
142×associate-/r/_binary64
102×flip3--_binary64 sqrt-div_binary64 flip--_binary64
68×frac-times_binary64
66×associate-/r*_binary64
57×add-exp-log_binary64
37×add-cbrt-cube_binary64
34×associate-*l/_binary64 associate-*r/_binary64
30×div-exp_binary64
23×div-inv_binary64
16×cbrt-undiv_binary64
10×pow1_binary64
9×associate-/l*_binary64
8×prod-exp_binary64
6×cbrt-unprod_binary64
4×add-log-exp_binary64 1-exp_binary64 rec-exp_binary64
3×frac-2neg_binary64 clear-num_binary64 pow-prod-down_binary64 associate-*l*_binary64
1×inv-pow_binary64 pow-flip_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64
Counts
4 → 360
Calls

4 calls:

21.0ms
(/.f64 1 (/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))))
17.0ms
(/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))))
10.0ms
(/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
6.0ms
(*.f64 6 (*.f64 v v))
Compiler

Compiled 15099 to 9678 computations (35.9% saved)

series112.0ms (2.8%)

Error
0b
Counts
4 → 21
Calls

4 calls:

29.0ms
(/.f64 1 (/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))))
26.0ms
(/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
22.0ms
(/.f64 PI.f64 (/.f64 4/3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))))
10.0ms
(*.f64 6 (*.f64 v v))
Compiler

Compiled 1572 to 1380 computations (12.2% saved)

simplify661.0ms (16.3%)

Algorithm
1×egg-herbie
Rules
548×associate-/r/_binary64
338×associate-*l/_binary64
307×associate-/l/_binary64
286×associate-/l*_binary64
273×associate-/r*_binary64
262×associate-*r/_binary64
207×times-frac_binary64
188×associate-*l*_binary64
70×*-commutative_binary64
69×distribute-rgt-in_binary64 distribute-lft-in_binary64
64×neg-mul-1_binary64
53×cancel-sign-sub-inv_binary64
51×sub-neg_binary64
46×log-div_binary64
44×+-commutative_binary64
42×log-prod_binary64
36×distribute-rgt-neg-in_binary64
30×distribute-lft-neg-in_binary64
27×associate-+r+_binary64
25×unpow3_binary64 neg-sub0_binary64
24×associate-*r*_binary64
21×exp-prod_binary64 cube-prod_binary64
19×sqr-pow_binary64 distribute-neg-in_binary64
16×cube-div_binary64
15×remove-double-div_binary64
14×div-sub_binary64
12×swap-sqr_binary64
11×log-rec_binary64 distribute-rgt-out_binary64
9×distribute-neg-frac_binary64
8×cube-unmult_binary64
7×/-rgt-identity_binary64
6×cube-mult_binary64 associate--l+_binary64 associate--r+_binary64
4×unswap-sqr_binary64
3×rem-square-sqrt_binary64 *-lft-identity_binary64 distribute-lft-neg-out_binary64 associate--r-_binary64
2×log-pow_binary64 pow-plus_binary64 *-rgt-identity_binary64 distribute-rgt1-in_binary64 distribute-lft-out_binary64
1×unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-sqrt-square_binary64 sub0-neg_binary64 count-2_binary64
0×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-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 unsub-neg_binary64 mul-1-neg_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 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-rgt-neg-out_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
Counts
381 → 359
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
062117368
1148616246
2483116246
3496016246
4496416246

prune339.0ms (8.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New3581359
Fresh101
Picked011
Done011
Total3593362
Error
0b
Counts
362 → 3
Compiler

Compiled 9892 to 6653 computations (32.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
0.0b
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
0.2b
(*.f64 6 (*.f64 v v))
1.0b
(/.f64 4/3 PI.f64)

rewrite180.0ms (4.4%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
40×times-frac_binary64
30×add-sqr-sqrt_binary64
28×add-cube-cbrt_binary64 *-un-lft-identity_binary64
23×add-exp-log_binary64 add-cbrt-cube_binary64
16×associate-/l*_binary64
10×pow1_binary64
8×sqrt-div_binary64 associate-/r/_binary64
7×div-exp_binary64 cbrt-undiv_binary64 flip3--_binary64 flip--_binary64
5×prod-exp_binary64 cbrt-unprod_binary64
4×add-log-exp_binary64 div-inv_binary64 associate-/r*_binary64 frac-times_binary64
3×pow-prod-down_binary64 associate-*l*_binary64 sqrt-prod_binary64
2×frac-2neg_binary64 clear-num_binary64 associate-*l/_binary64 associate-*r/_binary64
1×unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 associate-/l/_binary64
Counts
4 → 115
Calls

4 calls:

12.0ms
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
6.0ms
(*.f64 6 (*.f64 v v))
3.0ms
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
3.0ms
(/.f64 4/3 PI.f64)
Compiler

Compiled 3064 to 1950 computations (36.4% saved)

series67.0ms (1.7%)

Error
0b
Counts
4 → 15
Calls

4 calls:

30.0ms
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
12.0ms
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
8.0ms
(*.f64 6 (*.f64 v v))
0.0ms
(/.f64 4/3 PI.f64)
Compiler

Compiled 957 to 815 computations (14.8% saved)

simplify136.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
498×associate-/l/_binary64
337×associate-/r/_binary64
257×div-sub_binary64
189×distribute-rgt-in_binary64
184×cancel-sign-sub-inv_binary64
175×distribute-lft-in_binary64
162×distribute-rgt-neg-in_binary64 associate-/r*_binary64
158×times-frac_binary64
150×distribute-lft-neg-in_binary64
147×associate-/l*_binary64
124×associate-*r*_binary64
119×associate-*l*_binary64
113×*-commutative_binary64
86×sub-neg_binary64
62×+-commutative_binary64
58×associate-*l/_binary64
56×distribute-neg-frac_binary64
53×associate-+r+_binary64
47×associate-*r/_binary64
46×neg-sub0_binary64
45×log-div_binary64 log-prod_binary64
44×neg-mul-1_binary64
40×cube-prod_binary64
37×sqr-pow_binary64 associate-+l+_binary64
34×cube-div_binary64
27×distribute-lft-neg-out_binary64
25×distribute-rgt-out_binary64
23×distribute-neg-in_binary64
21×exp-prod_binary64 unswap-sqr_binary64
18×associate--l+_binary64
17×unpow3_binary64
16×*-rgt-identity_binary64 distribute-rgt-neg-out_binary64
15×cube-mult_binary64 unsub-neg_binary64
13×associate--r+_binary64
10×cube-unmult_binary64
7×*-lft-identity_binary64 swap-sqr_binary64
6×log-rec_binary64
5×/-rgt-identity_binary64 distribute-lft-out_binary64
4×pow-plus_binary64
3×rem-sqrt-square_binary64 rem-square-sqrt_binary64
2×log-pow_binary64 mul-1-neg_binary64 associate--l-_binary64
1×unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-diff_binary64 1-exp_binary64 cube-neg_binary64 sqr-neg_binary64 remove-double-neg_binary64 remove-double-div_binary64 pow-sqr_binary64 distribute-neg-out_binary64 count-2_binary64 associate-+l-_binary64
0×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-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 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate-+r-_binary64
Counts
130 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02883234
16992906
224312873
347872873
454682873

prune79.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New76076
Fresh000
Picked011
Done022
Total76379
Error
0b
Counts
79 → 3
Compiler

Compiled 1630 to 1109 computations (32% saved)

regimes120.0ms (3%)

Accuracy

Total 0.0b remaining (50.1%)

Threshold costs 0.0b (50.1%)

Compiler

Compiled 1538 to 1268 computations (17.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
5×sub-neg_binary64 *-commutative_binary64 +-commutative_binary64
3×neg-mul-1_binary64 neg-sub0_binary64 cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
2×distribute-lft-neg-in_binary64
1×1-exp_binary64 distribute-lft-neg-out_binary64
0×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_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
13131
24231
34831
45131
54931

end1.0ms (0%)

Compiler

Compiled 20 to 16 computations (20% saved)

sample724.0ms (17.8%)

Algorithm
1×intervals
Results
418.0ms8000×body128valid
0.0ms1×body128nan
Compiler

Compiled 100 to 84 computations (16% saved)

Profiling

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