Details

Time bar (total: 5.9s)

analyze403.0ms (6.8%)

Algorithm
search
egg-herbie
Rules
715×div-sub_binary64
690×sub-neg_binary64
581×neg-mul-1_binary64
491×neg-sub0_binary64
476×associate-/r*_binary64
402×distribute-neg-frac_binary64
321×distribute-rgt-neg-in_binary64
280×distribute-rgt-neg-out_binary64
252×distribute-lft-neg-out_binary64
251×distribute-lft-neg-in_binary64
232×+-commutative_binary64
226×associate-/r/_binary64
220×associate-/l*_binary64
217×associate-*l/_binary64
201×associate-+l-_binary64
198×remove-double-neg_binary64
195×distribute-rgt-in_binary64
184×cancel-sign-sub-inv_binary64
144×times-frac_binary64
141×unsub-neg_binary64
131×associate-/l/_binary64
119×associate-*r/_binary64
117×associate--r+_binary64
106×distribute-lft-in_binary64
93×distribute-frac-neg_binary64
88×sub0-neg_binary64
76×cancel-sign-sub_binary64
72×*-lft-identity_binary64
71×associate--l-_binary64
68×distribute-neg-in_binary64
63×*-commutative_binary64
61×+-lft-identity_binary64
57×associate--r-_binary64
54×/-rgt-identity_binary64
53×+-rgt-identity_binary64
45×associate-*r*_binary64
41×associate-+r-_binary64
40×associate-+l+_binary64
36×div0_binary64
26×associate-*l*_binary64
24×--rgt-identity_binary64
18×mul0-rgt_binary64 mul0-lft_binary64 associate--l+_binary64
17×associate-+r+_binary64
*-rgt-identity_binary64
sqr-neg_binary64 swap-sqr_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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_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 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038104
19596
217196
332396
448096
578696
6138496
7244896
8354696
9433996
10461496
11487196
12496196
13513296
033
133
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 30 to 24 computations (20% saved)

sample38.0ms (0.6%)

Algorithm
intervals
Results
12.0ms244×body128valid
8.0ms284×pre128true
2.0ms28×body128nan
1.0ms12×body256valid
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify344.0ms (5.8%)

Algorithm
egg-herbie
Rules
1261×associate-/l*_binary64
1150×div-sub_binary64
772×distribute-rgt-in_binary64
702×distribute-lft-in_binary64
619×times-frac_binary64
576×associate-/r*_binary64
479×associate-/r/_binary64
467×cancel-sign-sub-inv_binary64
429×*-commutative_binary64
426×sub-neg_binary64
423×unsub-neg_binary64
407×associate-/l/_binary64
225×distribute-rgt-neg-in_binary64
208×distribute-rgt-out--_binary64
201×neg-mul-1_binary64
197×distribute-lft-neg-in_binary64
192×distribute-neg-frac_binary64
188×associate-*l/_binary64
163×neg-sub0_binary64
156×distribute-rgt-out_binary64
136×distribute-rgt-neg-out_binary64
121×associate--r+_binary64
112×+-commutative_binary64
99×distribute-lft-neg-out_binary64
80×distribute-lft-out_binary64
77×associate--r-_binary64
73×distribute-frac-neg_binary64
72×distribute-lft-out--_binary64
68×*-lft-identity_binary64 distribute-neg-out_binary64
66×associate-*r/_binary64
62×mul0-rgt_binary64
60×associate-*r*_binary64
59×associate--l-_binary64
55×div0_binary64
54×mul0-lft_binary64
51×associate-*l*_binary64
33×remove-double-neg_binary64
32×associate-+r-_binary64
30×+-lft-identity_binary64
28×/-rgt-identity_binary64 associate--l+_binary64
27×remove-double-div_binary64
22×distribute-neg-in_binary64
19×sub0-neg_binary64 --rgt-identity_binary64
17×*-rgt-identity_binary64
14×mul-1-neg_binary64 associate-+l+_binary64
13×associate-+l-_binary64
associate-+r+_binary64
+-rgt-identity_binary64
swap-sqr_binary64
1-exp_binary64 sqr-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 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_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-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13224
26524
312824
417824
528724
646024
775424
8112024
9114224
10179924
11216224
12195324
13204124
14210524
15213124
16284324
17260324
18284124
19295124
20307124
21311324
22318324
23317124
24317124
25219124
26214124
27210524
28210724
29210724
30210724
31210724
32183424

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
28.8b
Counts
2 → 1
Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
28.7b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite109.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
26.3b
Rules
21×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 add-cube-cbrt_binary64
difference-of-squares_binary64 sqrt-prod_binary64 times-frac_binary64 associate-/l*_binary64
pow1_binary64
flip3--_binary64 flip--_binary64 cancel-sign-sub-inv_binary64
distribute-lft-out--_binary64
diff-log_binary64 sub-neg_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-/l/_binary64 sqrt-div_binary64
prod-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 div-sub_binary64 clear-num_binary64 div-inv_binary64 associate-/r*_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
Counts
4 → 74
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
Compiler

Compiled 1900 to 1105 computations (41.8% saved)

series227.0ms (3.8%)

Error
1.1b
Counts
4 → 72
Calls

4 calls:

73.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
48.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
45.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
37.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2358 to 1932 computations (18.1% saved)

simplify132.0ms (2.2%)

Algorithm
egg-herbie
Rules
794×times-frac_binary64
230×distribute-rgt-in_binary64
199×distribute-lft-in_binary64
182×cancel-sign-sub-inv_binary64
181×div-sub_binary64
165×distribute-rgt-neg-in_binary64
151×distribute-lft-neg-in_binary64
127×exp-prod_binary64
119×associate-*r*_binary64
111×associate-*l*_binary64
98×sub-neg_binary64
92×*-commutative_binary64
91×unswap-sqr_binary64
80×associate-/l*_binary64
71×neg-sub0_binary64
69×neg-mul-1_binary64
65×distribute-neg-frac_binary64
63×distribute-neg-in_binary64
58×associate-/r*_binary64
52×sqr-pow_binary64
45×+-commutative_binary64
44×cube-prod_binary64
31×distribute-rgt-out_binary64
30×associate-*l/_binary64
27×unsub-neg_binary64 distribute-lft-neg-out_binary64 associate-*r/_binary64
25×exp-sum_binary64
23×associate--r+_binary64
22×associate-+r+_binary64
20×associate-+l+_binary64
17×unpow3_binary64
16×exp-diff_binary64 distribute-lft-out_binary64
15×swap-sqr_binary64
14×associate-/r/_binary64
12×distribute-rgt-neg-out_binary64
11×cube-mult_binary64
10×cube-unmult_binary64
associate-+r-_binary64
pow-plus_binary64 difference-of-squares_binary64
+-rgt-identity_binary64
rem-sqrt-square_binary64
log-div_binary64 unpow2_binary64 mul-1-neg_binary64
log-prod_binary64 exp-sqrt_binary64 pow-sqr_binary64
unpow1/2_binary64 unpow1_binary64 exp-lft-sqr_binary64 cube-div_binary64 associate--l+_binary64 associate-+l-_binary64
log-pow_binary64 div-exp_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 distribute-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64
prod-exp_binary64 1-exp_binary64 cube-neg_binary64 rem-3cbrt-lft_binary64 fabs-mul_binary64 remove-double-neg_binary64 div0_binary64 *-inverses_binary64 cancel-sign-sub_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-cbrt_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 sub0-neg_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 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64
Counts
146 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02063603
15503323
218583272
347533272
452093272

prune77.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10913122
Fresh000
Picked101
Done000
Total11013123
Error
0.7b
Counts
123 → 13
Compiler

Compiled 2063 to 1170 computations (43.3% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
0.3b
(*.f64 (*.f64 a a) (pow.f64 c 3))
0.3b
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
0.4b
(*.f64 (pow.f64 a 3) (pow.f64 c 4))

rewrite336.0ms (5.7%)

Algorithm
rewrite-expression-head
Error
0.7b
Rules
109×add-exp-log_binary64
54×prod-exp_binary64
42×add-sqr-sqrt_binary64
30×div-exp_binary64
29×add-cbrt-cube_binary64 unpow-prod-down_binary64
24×pow-to-exp_binary64 pow-exp_binary64
22×add-cube-cbrt_binary64 *-un-lft-identity_binary64
19×associate-*r*_binary64 times-frac_binary64 associate-/r*_binary64
16×unswap-sqr_binary64 cube-prod_binary64
15×sqr-pow_binary64
13×associate-*l*_binary64
10×cbrt-unprod_binary64
cbrt-undiv_binary64
pow1_binary64 add-log-exp_binary64 unpow3_binary64 cube-mult_binary64
*-commutative_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64
Counts
4 → 178
Calls

4 calls:

10.0ms
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
9.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
9.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
8.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
Compiler

Compiled 6755 to 4045 computations (40.1% saved)

series185.0ms (3.1%)

Error
0.7b
Counts
4 → 30
Calls

4 calls:

64.0ms
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
54.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
32.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
29.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
Compiler

Compiled 2583 to 1992 computations (22.9% saved)

simplify150.0ms (2.5%)

Algorithm
egg-herbie
Rules
615×log-prod_binary64
394×associate-*l*_binary64
324×times-frac_binary64
322×associate-*r*_binary64
316×associate-/l*_binary64
277×log-div_binary64
186×associate-/r*_binary64
146×swap-sqr_binary64
129×cube-prod_binary64 distribute-rgt-neg-in_binary64
107×exp-prod_binary64
98×*-commutative_binary64
97×sqr-pow_binary64
85×cancel-sign-sub-inv_binary64
76×associate-/l/_binary64
74×unswap-sqr_binary64 associate-*l/_binary64
56×log-pow_binary64
54×cube-div_binary64
47×*-rgt-identity_binary64 associate-*r/_binary64
45×associate-/r/_binary64
38×sub-neg_binary64
27×distribute-neg-frac_binary64
23×cube-unmult_binary64
22×rem-sqrt-square_binary64 neg-mul-1_binary64 neg-sub0_binary64 *-lft-identity_binary64
21×distribute-lft-neg-in_binary64
20×/-rgt-identity_binary64 pow-sqr_binary64
19×pow-plus_binary64
18×+-commutative_binary64
17×associate--l+_binary64
15×log-rec_binary64
14×unpow3_binary64
12×fabs-mul_binary64
11×cube-mult_binary64
associate-+l+_binary64
fabs-sqr_binary64 distribute-neg-in_binary64
distribute-lft-neg-out_binary64
unpow2_binary64 unpow1_binary64 unsub-neg_binary64 distribute-rgt-neg-out_binary64
rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 rem-square-sqrt_binary64 div-sub_binary64
unpow1/2_binary64 mul-1-neg_binary64 count-2_binary64 associate-+r+_binary64
1-exp_binary64 exp-1-e_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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-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 associate--r-_binary64 associate--l-_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
208 → 157
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02633437
15723061
233832982
346602982
454482982

prune100.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1570157
Fresh01212
Picked011
Done000
Total15713170
Error
0.7b
Counts
170 → 13
Compiler

Compiled 2575 to 1543 computations (40.1% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.4b
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
0.5b
(*.f64 (*.f64 a c) (*.f64 a c))
0.7b
(pow.f64 (*.f64 a c) 3)

rewrite359.0ms (6.1%)

Algorithm
rewrite-expression-head
Error
0.7b
Rules
56×times-frac_binary64
51×add-exp-log_binary64
48×unpow-prod-down_binary64
47×add-sqr-sqrt_binary64
46×pow1_binary64
35×add-cube-cbrt_binary64 *-un-lft-identity_binary64
26×sqr-pow_binary64
23×add-cbrt-cube_binary64
21×prod-exp_binary64
19×pow-prod-down_binary64
18×pow-exp_binary64
14×pow-to-exp_binary64
12×div-exp_binary64
10×cbrt-unprod_binary64
unpow3_binary64 cube-mult_binary64 cube-prod_binary64 unswap-sqr_binary64
associate-*l*_binary64 associate-*r*_binary64 associate-/l*_binary64
associate-/r*_binary64
add-log-exp_binary64 pow-prod-up_binary64 pow-sqr_binary64
pow-unpow_binary64
pow-pow_binary64 rem-cube-cbrt_binary64 pow-plus_binary64 *-commutative_binary64
pow2_binary64 swap-sqr_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
4 → 192
Calls

4 calls:

10.0ms
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
7.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
7.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
4.0ms
(pow.f64 (*.f64 a c) 3)
Compiler

Compiled 8985 to 5208 computations (42% saved)

series167.0ms (2.8%)

Error
0.7b
Counts
4 → 27
Calls

4 calls:

71.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
32.0ms
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
31.0ms
(pow.f64 (*.f64 a c) 3)
27.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
Compiler

Compiled 2855 to 2072 computations (27.4% saved)

simplify149.0ms (2.5%)

Algorithm
egg-herbie
Rules
766×associate-/r/_binary64
507×log-prod_binary64
476×unswap-sqr_binary64
271×associate-/l*_binary64
206×associate-*l*_binary64
196×associate-*r*_binary64
195×times-frac_binary64
162×log-div_binary64
129×exp-prod_binary64
105×associate-/r*_binary64
97×swap-sqr_binary64
90×cube-prod_binary64
89×sqr-pow_binary64
86×associate-/l/_binary64
76×distribute-rgt-neg-in_binary64
75×distribute-lft-neg-in_binary64
61×*-commutative_binary64
41×cube-div_binary64 cancel-sign-sub-inv_binary64
33×log-pow_binary64
32×associate-*l/_binary64
31×distribute-neg-frac_binary64
19×associate-*r/_binary64
18×*-rgt-identity_binary64
16×cube-unmult_binary64 sub-neg_binary64 pow-sqr_binary64
15×rem-sqrt-square_binary64
14×log-rec_binary64 fabs-mul_binary64 neg-mul-1_binary64 neg-sub0_binary64
12×*-lft-identity_binary64
11×distribute-rgt-in_binary64
distribute-lft-in_binary64
fabs-div_binary64 fabs-sqr_binary64 /-rgt-identity_binary64 +-commutative_binary64
pow-plus_binary64 unpow1_binary64 count-2_binary64
unpow2_binary64
unpow3_binary64 associate-+l+_binary64 associate-+r+_binary64
cube-mult_binary64
unpow1/2_binary64
rem-square-sqrt_binary64 mul-1-neg_binary64
1-exp_binary64 exp-1-e_binary64 rem-cbrt-cube_binary64 distribute-neg-in_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out_binary64 distribute-lft-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 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-cube-cbrt_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 unsub-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_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 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
219 → 174
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02433381
14293084
222952936
346132936
452722936

prune119.0ms (2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1740174
Fresh01111
Picked011
Done011
Total17413187
Error
0.7b
Counts
187 → 13
Compiler

Compiled 3512 to 2063 computations (41.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b
(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))
0.3b
(*.f64 a (*.f64 c c))
0.3b
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))

rewrite142.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
0.7b
Rules
32×add-exp-log_binary64
24×times-frac_binary64
18×*-un-lft-identity_binary64
17×add-cbrt-cube_binary64 add-sqr-sqrt_binary64
16×cancel-sign-sub-inv_binary64
14×add-cube-cbrt_binary64
12×prod-exp_binary64 associate-/r*_binary64
div-exp_binary64 unpow-prod-down_binary64 cube-prod_binary64
pow1_binary64
add-log-exp_binary64
cbrt-unprod_binary64
pow-to-exp_binary64 pow-exp_binary64 cbrt-undiv_binary64 unpow3_binary64 cube-mult_binary64 sqr-pow_binary64 pow-prod-down_binary64 associate-*l*_binary64
div-inv_binary64 diff-log_binary64 distribute-lft-out--_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64 neg-log_binary64 distribute-neg-frac_binary64 frac-sub_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-rgt-neg-in_binary64 neg-sub0_binary64 associate--l-_binary64
Counts
3 → 99
Calls

3 calls:

28.0ms
(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))
9.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
5.0ms
(*.f64 a (*.f64 c c))
Compiler

Compiled 1801 to 689 computations (61.7% saved)

series124.0ms (2.1%)

Error
0.7b
Counts
3 → 33
Calls

3 calls:

63.0ms
(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3)))
41.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
17.0ms
(*.f64 a (*.f64 c c))
Compiler

Compiled 791 to 685 computations (13.4% saved)

simplify108.0ms (1.8%)

Algorithm
egg-herbie
Rules
304×log-prod_binary64
282×distribute-rgt-neg-in_binary64
250×distribute-lft-neg-in_binary64
227×distribute-neg-frac_binary64
208×cancel-sign-sub-inv_binary64
191×times-frac_binary64
175×log-div_binary64
159×unswap-sqr_binary64
132×associate-/r*_binary64
129×distribute-rgt-in_binary64
125×distribute-lft-in_binary64
123×associate-/l*_binary64
122×associate-*r*_binary64
116×associate-*l*_binary64
105×distribute-lft-neg-out_binary64
99×distribute-rgt-neg-out_binary64
86×exp-prod_binary64
79×div-sub_binary64
78×*-commutative_binary64
77×associate-*l/_binary64
72×neg-sub0_binary64
69×associate-*r/_binary64
68×cube-prod_binary64
63×neg-mul-1_binary64
57×sub-neg_binary64
50×distribute-frac-neg_binary64
48×sqr-pow_binary64 swap-sqr_binary64
41×cube-div_binary64
34×associate-/l/_binary64
26×distribute-rgt-out_binary64
21×unsub-neg_binary64
20×associate-/r/_binary64
18×log-pow_binary64 +-commutative_binary64
17×*-rgt-identity_binary64
16×unpow3_binary64
15×distribute-neg-out_binary64
11×cube-mult_binary64
10×distribute-neg-in_binary64
pow-sqr_binary64
pow-plus_binary64 cube-unmult_binary64 rem-sqrt-square_binary64
exp-diff_binary64 distribute-lft-out_binary64 associate--l+_binary64
div0_binary64 distribute-rgt-out--_binary64
log-rec_binary64 exp-sum_binary64 difference-of-squares_binary64 distribute-rgt1-in_binary64 associate-+l+_binary64
remove-double-neg_binary64
exp-neg_binary64 cube-neg_binary64 sqr-neg_binary64 /-rgt-identity_binary64 +-rgt-identity_binary64 cancel-sign-sub_binary64 associate-+r-_binary64 associate-+r+_binary64
rec-exp_binary64 fabs-mul_binary64 fabs-sqr_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 associate-+l-_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 div-exp_binary64 prod-exp_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 *-lft-identity_binary64 sub0-neg_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 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 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_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 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
132 → 108
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01672147
14072040
219281978
344031978
449451978

prune42.0ms (0.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1053108
Fresh1910
Picked101
Done022
Total10714121
Error
0.7b
Counts
121 → 14
Compiler

Compiled 670 to 248 computations (63% saved)

regimes896.0ms (15.2%)

Accuracy

Total 4.4b remaining (86.4%)

Threshold costs 0b (0%)

Compiler

Compiled 14122 to 10120 computations (28.3% saved)

bsearch13.0ms (0.2%)

Steps
ItersRangePoint
1
0.08033017664957953
0.08771083636004132
0.08217534157719497
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify11.0ms (0.2%)

Algorithm
egg-herbie
Rules
31×*-commutative_binary64
29×+-commutative_binary64
25×sub-neg_binary64
23×neg-mul-1_binary64 neg-sub0_binary64
15×distribute-rgt-neg-in_binary64
14×distribute-lft-neg-in_binary64
unsub-neg_binary64 distribute-neg-in_binary64
distribute-neg-frac_binary64
cancel-sign-sub-inv_binary64
distribute-lft-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044114
174112
2104112
3139112
4179112
5208112
6231112
7243112
8249112
9251112
10248112

end2.0ms (0%)

Compiler

Compiled 75 to 51 computations (32% saved)

sample1.6s (26.9%)

Algorithm
intervals
Results
396.0ms7713×body128valid
265.0ms8783×pre128true
36.0ms783×body128nan
34.0ms287×body256valid
Compiler

Compiled 598 to 425 computations (28.9% saved)

Profiling

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