Details

Time bar (total: 4.3s)

analyze796.0ms (18.4%)

Algorithm
search
egg-herbie
Rules
997×div-sub_binary64
387×cancel-sign-sub-inv_binary64
358×times-frac_binary64
329×distribute-rgt-in_binary64 associate-/l*_binary64
280×distribute-rgt-neg-in_binary64
263×neg-mul-1_binary64
253×distribute-neg-frac_binary64
246×distribute-lft-neg-in_binary64
218×sub-neg_binary64
201×neg-sub0_binary64
184×associate-/r/_binary64
105×associate-/l/_binary64
91×associate-*r*_binary64
89×distribute-frac-neg_binary64
78×*-commutative_binary64
70×associate-/r*_binary64
54×unsub-neg_binary64
45×distribute-neg-in_binary64
43×+-commutative_binary64
41×div0_binary64 associate-*l*_binary64
27×distribute-lft-in_binary64
22×associate-*l/_binary64
19×sub0-neg_binary64
18×*-rgt-identity_binary64 distribute-lft-neg-out_binary64
15×mul0-rgt_binary64 mul0-lft_binary64
13×associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
11×distribute-rgt-out--_binary64
/-rgt-identity_binary64 +-rgt-identity_binary64
*-inverses_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 *-lft-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt-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--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047175
1123175
2319175
3840154
42432133
54384133
64873133
75065133
044
144
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%99.8%0.2%7
9.4%90.4%0.2%8
9.4%90.4%0.2%9
10.9%88.9%0.2%10
25.9%73.9%0.2%11
47.1%52.7%0.2%12
55.3%44.5%0.2%13
59.2%40.6%0.2%14
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample23.0ms (0.5%)

Algorithm
intervals
Results
12.0ms256×body128valid
Compiler

Compiled 35 to 33 computations (5.7% saved)

simplify66.0ms (1.5%)

Algorithm
egg-herbie
Rules
504×associate-*l/_binary64
495×div-sub_binary64
454×cancel-sign-sub-inv_binary64
429×sub-neg_binary64
348×associate-*l*_binary64
337×neg-mul-1_binary64
323×distribute-neg-frac_binary64
293×distribute-lft-neg-in_binary64
282×distribute-rgt-neg-in_binary64
278×distribute-rgt-in_binary64
271×neg-sub0_binary64
226×distribute-lft-in_binary64
146×unsub-neg_binary64
145×associate-/l*_binary64
92×*-commutative_binary64
68×associate-/r/_binary64
65×distribute-rgt-neg-out_binary64
63×distribute-frac-neg_binary64
59×times-frac_binary64
58×swap-sqr_binary64
56×associate-/r*_binary64
53×distribute-lft-neg-out_binary64
51×associate-+r-_binary64
41×associate-*r*_binary64
35×associate-*r/_binary64
34×cube-prod_binary64
32×*-rgt-identity_binary64
30×distribute-neg-in_binary64
29×associate--r-_binary64
28×associate-/l/_binary64 +-commutative_binary64
25×distribute-lft-out--_binary64
24×div0_binary64
20×associate--r+_binary64
19×*-lft-identity_binary64
17×cube-div_binary64
16×sub0-neg_binary64 associate-+l-_binary64
12×mul0-lft_binary64
11×mul0-rgt_binary64
associate-+r+_binary64
+-lft-identity_binary64 associate--l-_binary64
/-rgt-identity_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 associate-+l+_binary64
distribute-rgt-out--_binary64
sqr-neg_binary64 *-inverses_binary64 distribute-lft-out_binary64
cube-unmult_binary64 remove-double-neg_binary64 associate--l+_binary64
unpow3_binary64 1-exp_binary64 cube-neg_binary64 lft-mult-inverse_binary64 remove-double-div_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 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-mult_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 mul-1-neg_binary64 +-inverses_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01425
12925
26825
316722
446019
599919
6228019
7426819
8505919

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
1.8b
Counts
2 → 2
Compiler

Compiled 43 to 36 computations (16.3% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

3.6b
(/.f64 (*.f64 y t) (*.f64 2 z))
6.0b
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))

rewrite110.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0.6b
Rules
20×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64 times-frac_binary64
12×add-cube-cbrt_binary64
associate-/r*_binary64
div-exp_binary64 cbrt-undiv_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64 associate-/l*_binary64 prod-exp_binary64 cbrt-unprod_binary64
pow1_binary64 add-log-exp_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/r/_binary64
flip3--_binary64 flip--_binary64
Counts
2 → 58
Calls

2 calls:

7.0ms
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
6.0ms
(/.f64 (*.f64 y t) (*.f64 2 z))
Compiler

Compiled 1262 to 639 computations (49.4% saved)

series75.0ms (1.7%)

Error
0.0b
Counts
2 → 22
Calls

2 calls:

38.0ms
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
29.0ms
(/.f64 (*.f64 y t) (*.f64 2 z))
Compiler

Compiled 623 to 543 computations (12.8% saved)

simplify81.0ms (1.9%)

Algorithm
egg-herbie
Rules
641×associate-/r*_binary64
500×associate-*l/_binary64
427×associate-*r/_binary64
406×associate-/l/_binary64
201×associate-/r/_binary64
173×neg-mul-1_binary64
172×neg-sub0_binary64
168×times-frac_binary64
147×cancel-sign-sub-inv_binary64
139×distribute-rgt-neg-in_binary64
136×distribute-lft-neg-in_binary64
110×associate-/l*_binary64
101×distribute-neg-frac_binary64
99×div-sub_binary64
59×log-div_binary64
52×cube-div_binary64
50×associate-*l*_binary64
40×associate-*r*_binary64
38×sub-neg_binary64
35×log-prod_binary64
32×*-commutative_binary64
27×cube-prod_binary64 distribute-rgt-in_binary64
24×distribute-lft-in_binary64
23×sqr-pow_binary64
16×unpow3_binary64
15×exp-prod_binary64
13×cube-mult_binary64
12×+-commutative_binary64
11×*-rgt-identity_binary64
10×unswap-sqr_binary64
swap-sqr_binary64 distribute-lft-neg-out_binary64
exp-sqrt_binary64
associate--r+_binary64
cube-unmult_binary64 /-rgt-identity_binary64 distribute-neg-in_binary64 associate--l+_binary64
unsub-neg_binary64 difference-of-squares_binary64 distribute-rgt-neg-out_binary64
log-pow_binary64 pow-plus_binary64 distribute-rgt-out--_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-diff_binary64 1-exp_binary64 cube-neg_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 *-lft-identity_binary64 remove-double-neg_binary64 div0_binary64 distribute-frac-neg_binary64 associate--r-_binary64 associate-+l+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 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 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 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-neg_binary64 --rgt-identity_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 pow-sqr_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--l-_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+r+_binary64
Counts
80 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01301508
13061439
211871438
344751438
449991438

prune59.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New64266
Fresh011
Picked101
Done000
Total65368
Error
0.6b
Counts
68 → 3
Compiler

Compiled 972 to 505 computations (48% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

6.0b
(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
7.2b
(/.f64 y (*.f64 2 (/.f64 z t)))

rewrite76.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.6b
Rules
22×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
18×times-frac_binary64
14×add-cube-cbrt_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l*_binary64 associate-/r*_binary64
div-exp_binary64 cbrt-undiv_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64
associate-/r/_binary64
pow1_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
associate-*r/_binary64 flip3--_binary64 flip--_binary64
Counts
2 → 61
Calls

2 calls:

7.0ms
(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
6.0ms
(/.f64 y (*.f64 2 (/.f64 z t)))
Compiler

Compiled 1291 to 646 computations (50% saved)

series73.0ms (1.7%)

Error
0.6b
Counts
2 → 22
Calls

2 calls:

37.0ms
(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
32.0ms
(/.f64 y (*.f64 2 (/.f64 z t)))
Compiler

Compiled 623 to 543 computations (12.8% saved)

simplify93.0ms (2.2%)

Algorithm
egg-herbie
Rules
613×times-frac_binary64
465×associate-/l*_binary64
400×cancel-sign-sub-inv_binary64
368×associate-/r*_binary64
332×associate-/r/_binary64
306×associate-/l/_binary64
281×associate-*l/_binary64
245×associate-*r/_binary64
191×associate-*l*_binary64
188×associate-*r*_binary64
113×div-sub_binary64
79×neg-sub0_binary64
75×neg-mul-1_binary64
62×distribute-neg-frac_binary64
54×sub-neg_binary64
53×distribute-rgt-neg-in_binary64
52×distribute-lft-neg-in_binary64
48×unswap-sqr_binary64
42×swap-sqr_binary64
41×log-div_binary64
37×*-rgt-identity_binary64 sqr-pow_binary64
34×cube-div_binary64
29×*-commutative_binary64
28×distribute-rgt-in_binary64
27×log-prod_binary64
25×cube-prod_binary64 distribute-lft-in_binary64
19×unsub-neg_binary64
17×exp-prod_binary64
15×*-lft-identity_binary64
13×+-commutative_binary64
11×unpow3_binary64
/-rgt-identity_binary64 distribute-neg-in_binary64
cube-unmult_binary64 distribute-lft-neg-out_binary64
cube-mult_binary64
difference-of-squares_binary64 associate--r+_binary64
remove-double-neg_binary64
distribute-rgt-neg-out_binary64 associate--r-_binary64
log-pow_binary64 exp-sqrt_binary64 *-inverses_binary64 distribute-rgt-out--_binary64
unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 unpow1_binary64 exp-diff_binary64 1-exp_binary64 cube-neg_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 div0_binary64 pow-sqr_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 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 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 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_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-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--l-_binary64 associate--l+_binary64 associate-+r+_binary64
Counts
83 → 39
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01351552
13041483
29271482
343011474
454141474

prune29.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New38139
Fresh202
Picked011
Done000
Total40242
Error
0.0b
Counts
42 → 2
Compiler

Compiled 455 to 230 computations (49.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t)))
0.4b
(/.f64 1/2 (/.f64 z t))
0.8b
(/.f64 1 (-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t))))

rewrite312.0ms (7.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
229×times-frac_binary64
201×add-sqr-sqrt_binary64
126×*-un-lft-identity_binary64
96×add-cube-cbrt_binary64
44×cancel-sign-sub-inv_binary64
30×difference-of-squares_binary64
24×associate-/r*_binary64
12×add-exp-log_binary64
10×add-cbrt-cube_binary64 distribute-lft-out--_binary64 div-inv_binary64
associate-/l*_binary64
div-exp_binary64 add-log-exp_binary64 associate-/r/_binary64
pow1_binary64 cbrt-undiv_binary64
frac-2neg_binary64 clear-num_binary64 frac-sub_binary64 flip3--_binary64 flip--_binary64
inv-pow_binary64 pow-flip_binary64 1-exp_binary64 rec-exp_binary64 diff-log_binary64 sub-neg_binary64
Counts
3 → 200
Calls

3 calls:

36.0ms
(/.f64 1 (-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t))))
36.0ms
(-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t)))
9.0ms
(/.f64 1/2 (/.f64 z t))
Compiler

Compiled 4809 to 2415 computations (49.8% saved)

series106.0ms (2.4%)

Error
0.0b
Counts
3 → 37
Calls

3 calls:

48.0ms
(-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t)))
36.0ms
(/.f64 1 (-.f64 (/.f64 z y) (/.f64 1/2 (/.f64 z t))))
15.0ms
(/.f64 1/2 (/.f64 z t))
Compiler

Compiled 868 to 796 computations (8.3% saved)

simplify201.0ms (4.7%)

Algorithm
egg-herbie
Rules
693×times-frac_binary64
294×div-sub_binary64
251×associate-*l/_binary64
232×*-commutative_binary64
226×cancel-sign-sub-inv_binary64
215×neg-mul-1_binary64
188×associate-*r/_binary64
184×associate-/r/_binary64
166×neg-sub0_binary64
133×sub-neg_binary64
132×associate-/l*_binary64 associate-*r*_binary64
125×associate-/l/_binary64
120×associate-*l*_binary64
111×exp-prod_binary64
75×distribute-lft-neg-out_binary64
71×distribute-rgt-neg-in_binary64
59×distribute-neg-frac_binary64
52×associate-/r*_binary64
46×*-rgt-identity_binary64
38×cube-prod_binary64
35×distribute-rgt-neg-out_binary64
32×log-prod_binary64
31×distribute-lft-neg-in_binary64
30×+-commutative_binary64
25×exp-diff_binary64
22×cube-div_binary64 *-lft-identity_binary64 sqr-pow_binary64
19×exp-sum_binary64
17×log-div_binary64
14×/-rgt-identity_binary64
13×unpow3_binary64
11×div0_binary64 swap-sqr_binary64
10×associate-+r-_binary64
cube-mult_binary64
cube-unmult_binary64 unswap-sqr_binary64
associate-+r+_binary64
+-rgt-identity_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
log-rec_binary64 unpow1/2_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 unsub-neg_binary64 remove-double-neg_binary64 remove-double-div_binary64 difference-of-squares_binary64
rem-3cbrt-lft_binary64 sqr-neg_binary64 distribute-neg-in_binary64 associate--r-_binary64 associate--r+_binary64 associate-+l+_binary64
log-pow_binary64 unpow2_binary64 pow-plus_binary64 unpow1_binary64 div-exp_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 +-lft-identity_binary64 distribute-rgt-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 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 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 mul-1-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--l-_binary64 associate--l+_binary64 associate-+l-_binary64
Counts
237 → 181
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03415255
19175141
231034622
344364621
449834621

prune104.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1801181
Fresh000
Picked011
Done011
Total1803183
Error
0b
Counts
183 → 3
Compiler

Compiled 2310 to 1136 computations (50.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
0.8b
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
15.1b
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))
15.1b
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))

rewrite212.0ms (4.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
42×add-sqr-sqrt_binary64
40×times-frac_binary64
36×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
32×sqrt-prod_binary64
12×add-exp-log_binary64 associate-/r/_binary64
10×pow1_binary64
add-cbrt-cube_binary64
sqrt-pow1_binary64 rem-sqrt-square_binary64 associate-/l*_binary64 associate-/r*_binary64
add-log-exp_binary64 inv-pow_binary64 pow-flip_binary64 div-inv_binary64 associate-*l/_binary64 frac-add_binary64 flip3-+_binary64 flip-+_binary64 div-exp_binary64
pow1/2_binary64 sqrt-div_binary64 1-exp_binary64 rec-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64
Counts
4 → 130
Calls

4 calls:

12.0ms
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))
11.0ms
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
10.0ms
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))
10.0ms
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
Compiler

Compiled 4710 to 2576 computations (45.3% saved)

series138.0ms (3.2%)

Error
0b
Counts
4 → 38
Calls

4 calls:

36.0ms
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))
36.0ms
(sqrt.f64 (/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y))))
30.0ms
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
28.0ms
(/.f64 1 (+.f64 (*.f64 (/.f64 t z) -1/2) (/.f64 z y)))
Compiler

Compiled 2250 to 1811 computations (19.5% saved)

simplify196.0ms (4.6%)

Algorithm
egg-herbie
Rules
662×associate-/l*_binary64
637×associate-*l/_binary64
540×div-sub_binary64
234×times-frac_binary64
217×associate-/l/_binary64
216×distribute-rgt-in_binary64
191×distribute-lft-in_binary64
165×associate-/r*_binary64
163×associate-/r/_binary64
143×associate-*r/_binary64
140×associate-*l*_binary64
103×associate-*r*_binary64
88×sub-neg_binary64
83×*-commutative_binary64
75×cancel-sign-sub-inv_binary64
74×distribute-neg-frac_binary64
66×distribute-rgt-neg-in_binary64
64×sqr-pow_binary64
57×neg-sub0_binary64
55×neg-mul-1_binary64
54×distribute-lft-neg-in_binary64
52×distribute-rgt-out_binary64
38×cube-div_binary64
36×cube-prod_binary64
35×unsub-neg_binary64
25×*-lft-identity_binary64
23×distribute-lft-out_binary64
21×unpow3_binary64
20×associate-+r+_binary64
19×/-rgt-identity_binary64 distribute-lft-neg-out_binary64
17×*-rgt-identity_binary64
16×associate-+r-_binary64
15×+-commutative_binary64
14×associate-+l+_binary64
13×unswap-sqr_binary64 distribute-neg-in_binary64
12×cube-unmult_binary64 cube-mult_binary64
11×+-rgt-identity_binary64 div0_binary64 distribute-rgt-out--_binary64
10×associate-+l-_binary64
rem-sqrt-square_binary64
distribute-rgt-neg-out_binary64
log-prod_binary64 pow-plus_binary64 exp-prod_binary64 sub0-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64
mul-1-neg_binary64 remove-double-neg_binary64 swap-sqr_binary64
pow-sqr_binary64
cube-neg_binary64 sqr-neg_binary64 +-lft-identity_binary64
log-div_binary64 unpow1/2_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 count-2_binary64
log-rec_binary64 unpow2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-square-sqrt_binary64 --rgt-identity_binary64 *-inverses_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 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 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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-frac-neg_binary64 distribute-neg-out_binary64 associate--r-_binary64
Counts
168 → 84
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01183622
12473402
26063402
315563396
446073396
547123396
655193396

prune62.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New84084
Fresh000
Picked011
Done022
Total84387
Error
0b
Counts
87 → 3
Compiler

Compiled 1805 to 965 computations (46.5% saved)

regimes632.0ms (14.6%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Compiler

Compiled 8294 to 6960 computations (16.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
sub-neg_binary64 +-commutative_binary64
*-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64 distribute-neg-frac_binary64
1-exp_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 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 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-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
01519
12219
23419
33819
44019
53619

end1.0ms (0%)

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample823.0ms (19.1%)

Algorithm
intervals
Results
390.0ms8000×body128valid
Compiler

Compiled 100 to 101 computations (-1% saved)

Profiling

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