Details

Time bar (total: 20.9s)

analyze1.1s (5.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%96.7%3.3%9
16.4%74.9%8.7%10
17.6%71.8%10.7%11
26.3%59.5%14.2%12
30.7%45.7%23.5%13
31.7%43.5%24.7%14
Compiler

Compiled 30 to 25 computations (16.7% saved)

sample55.0ms (0.3%)

Algorithm
intervals
Results
22.0ms256×body128valid
12.0ms187×body128invalid
Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify150.0ms (0.7%)

Algorithm
egg-herbie
Rules
613×distribute-rgt-neg-in_binary64
464×div-sub_binary64
442×neg-mul-1_binary64
380×associate-*l*_binary64
365×associate-*r*_binary64
208×associate-/r*_binary64
147×sub-neg_binary64
145×distribute-neg-frac_binary64 associate-/l*_binary64
144×distribute-rgt-neg-out_binary64
143×cancel-sign-sub-inv_binary64
128×distribute-lft-neg-in_binary64
127×distribute-lft-neg-out_binary64
114×associate-/r/_binary64
110×*-commutative_binary64
109×distribute-neg-in_binary64
103×distribute-rgt-in_binary64
100×distribute-lft-in_binary64
91×neg-sub0_binary64
78×distribute-frac-neg_binary64 associate-/l/_binary64
49×unsub-neg_binary64
32×associate-*l/_binary64
24×div0_binary64 cancel-sign-sub_binary64 +-commutative_binary64
21×associate-+l-_binary64
18×remove-double-neg_binary64 associate-+r+_binary64
15×associate-+l+_binary64
14×times-frac_binary64 associate--l+_binary64
11×associate--r+_binary64
10×sub0-neg_binary64 associate-+r-_binary64
associate--r-_binary64
associate--l-_binary64
associate-*r/_binary64
+-rgt-identity_binary64
mul0-rgt_binary64 mul0-lft_binary64
1-exp_binary64 unswap-sqr_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 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 --rgt-identity_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 swap-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
Counts
1 → 3
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02343
15943
216337
359837
4263437
5474137
6499937

prune12.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New123
Fresh011
Picked000
Done000
Total134
Error
7.9b
Counts
4 → 3
Compiler

Compiled 158 to 115 computations (27.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 2 (*.f64 r r))
3.6b
(*.f64 (/.f64 (*.f64 r (*.f64 r (*.f64 w w))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
3.9b
(*.f64 r (*.f64 r (*.f64 w w)))
8.5b
(*.f64 r (*.f64 w w))

rewrite219.0ms (1%)

Algorithm
rewrite-expression-head
Error
0.9b
Rules
43×add-exp-log_binary64 add-cbrt-cube_binary64
21×prod-exp_binary64 cbrt-unprod_binary64
20×pow1_binary64
18×associate-*l*_binary64
17×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
10×pow-prod-down_binary64
times-frac_binary64
div-exp_binary64 cbrt-undiv_binary64
associate-*r*_binary64
add-log-exp_binary64
*-commutative_binary64 associate-/l*_binary64
unswap-sqr_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 associate-*r/_binary64 difference-of-squares_binary64 div-inv_binary64 associate-/r/_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 distribute-lft-out--_binary64 flip3--_binary64 flip--_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r*_binary64
Counts
4 → 103
Calls

4 calls:

16.0ms
(*.f64 (/.f64 (*.f64 r (*.f64 r (*.f64 w w))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
8.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
8.0ms
(*.f64 r (*.f64 w w))
5.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 3477 to 1878 computations (46% saved)

series490.0ms (2.3%)

Error
7.8b
Counts
4 → 30
Calls

4 calls:

270.0ms
(*.f64 (/.f64 (*.f64 r (*.f64 r (*.f64 w w))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
77.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
74.0ms
(*.f64 r (*.f64 w w))
26.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 2222 to 1793 computations (19.3% saved)

simplify169.0ms (0.8%)

Algorithm
egg-herbie
Rules
501×distribute-rgt-in_binary64
470×distribute-lft-in_binary64
298×associate-*l*_binary64
257×associate-*r*_binary64
155×*-commutative_binary64
130×associate-/l*_binary64
119×associate-*l/_binary64
108×times-frac_binary64
96×associate-*r/_binary64
94×log-prod_binary64
93×exp-prod_binary64
87×unswap-sqr_binary64
82×cancel-sign-sub-inv_binary64
76×associate-/r*_binary64
75×distribute-rgt-neg-in_binary64
63×sub-neg_binary64 distribute-lft-neg-in_binary64
62×distribute-rgt-out_binary64
54×log-div_binary64
49×distribute-lft-neg-out_binary64
46×distribute-rgt-neg-out_binary64
45×div-sub_binary64
42×sqr-pow_binary64
37×+-commutative_binary64
31×cube-prod_binary64
29×unpow3_binary64
28×swap-sqr_binary64
27×neg-mul-1_binary64 neg-sub0_binary64
24×distribute-neg-frac_binary64
23×distribute-lft-out_binary64
19×cube-div_binary64
17×*-lft-identity_binary64 associate-/r/_binary64
16×*-rgt-identity_binary64 distribute-neg-in_binary64
11×unsub-neg_binary64 associate--l+_binary64 associate-+l+_binary64 associate-+r+_binary64
cube-unmult_binary64
associate--r+_binary64
pow-plus_binary64 /-rgt-identity_binary64 pow-sqr_binary64
log-pow_binary64
distribute-rgt-out--_binary64 associate-+l-_binary64
unpow1/2_binary64 exp-sum_binary64
unpow2_binary64 unpow1_binary64 rem-sqrt-square_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64
log-rec_binary64 unpow-1_binary64 exp-diff_binary64 cube-mult_binary64 count-2_binary64 associate-+r-_binary64
1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 sqr-neg_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 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 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 rem-square-sqrt_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
133 → 205
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02182863
16332370
223822272
348412270
449902270
549992270
649382270

prune326.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New19510205
Fresh112
Picked101
Done000
Total19711208
Error
0.1b
Counts
208 → 11
Compiler

Compiled 7047 to 3805 computations (46% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
0.3b
(/.f64 2 (*.f64 r r))
0.4b
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
3.6b
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))

rewrite228.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
30×add-sqr-sqrt_binary64
25×add-exp-log_binary64 add-cbrt-cube_binary64
24×*-un-lft-identity_binary64
16×times-frac_binary64
15×add-cube-cbrt_binary64 associate-*l*_binary64
13×pow1_binary64
prod-exp_binary64 cbrt-unprod_binary64 associate-/r*_binary64
div-exp_binary64 cbrt-undiv_binary64 difference-of-squares_binary64 associate-*r*_binary64
add-log-exp_binary64 associate-/r/_binary64 associate-/l*_binary64
unswap-sqr_binary64 distribute-lft-out--_binary64 div-inv_binary64 swap-sqr_binary64
pow-prod-down_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 associate-*r/_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 pow2_binary64 pow-prod-up_binary64 pow-plus_binary64 sqr-abs_binary64 pow-sqr_binary64
Counts
4 → 115
Calls

4 calls:

13.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
7.0ms
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
4.0ms
(/.f64 2 (*.f64 r r))
4.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
Compiler

Compiled 4167 to 2094 computations (49.7% saved)

series705.0ms (3.4%)

Error
0.1b
Counts
4 → 45
Calls

4 calls:

338.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
221.0ms
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
59.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
27.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 3271 to 2344 computations (28.3% saved)

simplify109.0ms (0.5%)

Algorithm
egg-herbie
Rules
498×distribute-rgt-in_binary64
452×distribute-lft-in_binary64
228×associate-*l*_binary64
184×associate-*r*_binary64
136×unswap-sqr_binary64
133×cancel-sign-sub-inv_binary64 associate-/l*_binary64 associate-*l/_binary64
128×distribute-rgt-out_binary64
125×*-commutative_binary64
105×distribute-rgt-neg-in_binary64
94×associate-*r/_binary64
88×distribute-lft-neg-in_binary64
77×sub-neg_binary64 associate-/r*_binary64
75×times-frac_binary64
62×distribute-lft-out_binary64
56×div-sub_binary64 +-commutative_binary64
51×distribute-lft-neg-out_binary64
49×log-prod_binary64
48×distribute-neg-frac_binary64
46×exp-prod_binary64
45×distribute-rgt-neg-out_binary64
43×neg-sub0_binary64
42×neg-mul-1_binary64
40×log-div_binary64
39×sqr-pow_binary64
34×distribute-neg-in_binary64
33×associate-/l/_binary64 associate-+r+_binary64
32×cube-prod_binary64
30×swap-sqr_binary64
28×associate-/r/_binary64
26×*-rgt-identity_binary64 associate-+l+_binary64
22×unsub-neg_binary64
21×cube-div_binary64
20×*-lft-identity_binary64
14×associate--r+_binary64
12×/-rgt-identity_binary64
10×cube-unmult_binary64 distribute-rgt-out--_binary64
pow-sqr_binary64 distribute-rgt1-in_binary64
pow-plus_binary64
distribute-lft1-in_binary64
log-rec_binary64 exp-sum_binary64 rem-sqrt-square_binary64 distribute-frac-neg_binary64 associate-+r-_binary64
log-pow_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 associate-+l-_binary64
unpow3_binary64 exp-diff_binary64 cube-mult_binary64 +-rgt-identity_binary64 distribute-neg-out_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--l+_binary64
1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 remove-double-neg_binary64 div0_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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 associate--l-_binary64
Counts
160 → 224
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02333735
16603231
224943041
352253041

prune431.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2177224
Fresh4610
Picked101
Done000
Total22213235
Error
0.1b
Counts
235 → 13
Compiler

Compiled 8278 to 4668 computations (43.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 r (/.f64 2 r))
0.3b
(/.f64 1 (/.f64 r (/.f64 2 r)))
0.4b
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
3.6b
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))

rewrite872.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
478×times-frac_binary64
247×add-sqr-sqrt_binary64
241×*-un-lft-identity_binary64
238×add-cube-cbrt_binary64
57×associate-/r*_binary64
41×add-exp-log_binary64
29×add-cbrt-cube_binary64
23×div-inv_binary64
20×div-exp_binary64
15×associate-*l*_binary64
14×pow1_binary64
11×cbrt-undiv_binary64
associate-/r/_binary64
associate-*r*_binary64 associate-/l*_binary64
prod-exp_binary64 cbrt-unprod_binary64
add-log-exp_binary64
unswap-sqr_binary64 swap-sqr_binary64 1-exp_binary64 rec-exp_binary64
pow-prod-down_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 associate-*r/_binary64 difference-of-squares_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 distribute-lft-out--_binary64 flip3--_binary64 flip--_binary64 pow2_binary64 pow-prod-up_binary64 pow-plus_binary64 sqr-abs_binary64 pow-sqr_binary64 inv-pow_binary64 pow-flip_binary64
Counts
4 → 339
Calls

4 calls:

13.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
13.0ms
(/.f64 1 (/.f64 r (/.f64 2 r)))
6.0ms
(/.f64 r (/.f64 2 r))
4.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
Compiler

Compiled 13892 to 8003 computations (42.4% saved)

series498.0ms (2.4%)

Error
0.1b
Counts
4 → 30
Calls

4 calls:

338.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
55.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
30.0ms
(/.f64 1 (/.f64 r (/.f64 2 r)))
29.0ms
(/.f64 r (/.f64 2 r))
Compiler

Compiled 2304 to 1734 computations (24.7% saved)

simplify280.0ms (1.3%)

Algorithm
egg-herbie
Rules
419×associate-/r/_binary64
306×associate-*l/_binary64
301×associate-*l*_binary64
295×associate-*r/_binary64
290×*-commutative_binary64
269×associate-/l/_binary64
249×associate-*r*_binary64
238×associate-/l*_binary64
179×associate-/r*_binary64
156×unswap-sqr_binary64
136×times-frac_binary64
129×exp-prod_binary64
111×cube-prod_binary64
109×log-prod_binary64
101×distribute-rgt-in_binary64
96×distribute-lft-in_binary64
71×sub-neg_binary64
66×log-div_binary64
56×cube-div_binary64
54×*-rgt-identity_binary64
52×swap-sqr_binary64
43×+-commutative_binary64
41×sqr-pow_binary64
38×neg-mul-1_binary64
36×div-sub_binary64
35×neg-sub0_binary64
33×*-lft-identity_binary64
30×remove-double-div_binary64
29×unpow3_binary64
26×cancel-sign-sub-inv_binary64
24×cube-mult_binary64
22×associate-+r+_binary64
18×/-rgt-identity_binary64 distribute-rgt-neg-in_binary64
16×cube-unmult_binary64
14×associate-+l+_binary64
13×log-rec_binary64 pow-plus_binary64 distribute-lft-neg-in_binary64
12×unsub-neg_binary64 associate--r+_binary64
10×log-pow_binary64
exp-sum_binary64
distribute-neg-in_binary64
exp-diff_binary64 pow-sqr_binary64 associate-+r-_binary64
distribute-neg-frac_binary64
unpow1/2_binary64 rem-sqrt-square_binary64
distribute-rgt-out_binary64 distribute-lft-out_binary64 associate--r-_binary64
unpow2_binary64 unpow1_binary64 exp-sqrt_binary64 associate-+l-_binary64
rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 distribute-lft-neg-out_binary64 distribute-rgt1-in_binary64 distribute-rgt-out--_binary64 associate--l+_binary64
exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 +-rgt-identity_binary64 div0_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 --rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_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-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate--l-_binary64
Counts
369 → 1242
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04788733
111857555
241777179
347027097
449567097

prune4.3s (20.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New123841242
Fresh21012
Picked101
Done000
Total1241141255
Error
0.0b
Counts
1255 → 14
Compiler

Compiled 50100 to 28352 computations (43.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
0.2b
(/.f64 (/.f64 2 r) r)
0.4b
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
3.6b
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))

rewrite320.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
88×times-frac_binary64
70×add-sqr-sqrt_binary64
64×*-un-lft-identity_binary64
55×add-cube-cbrt_binary64
25×add-exp-log_binary64 add-cbrt-cube_binary64
15×associate-*l*_binary64
14×associate-/l*_binary64
13×pow1_binary64
associate-/r*_binary64
div-exp_binary64 cbrt-undiv_binary64 div-inv_binary64
prod-exp_binary64 cbrt-unprod_binary64 difference-of-squares_binary64 associate-*r*_binary64
add-log-exp_binary64 associate-/r/_binary64
unswap-sqr_binary64 distribute-lft-out--_binary64 swap-sqr_binary64
pow-prod-down_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 associate-*r/_binary64 flip3--_binary64 flip--_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 pow2_binary64 pow-prod-up_binary64 pow-plus_binary64 sqr-abs_binary64 pow-sqr_binary64 associate-/l/_binary64
Counts
4 → 164
Calls

4 calls:

13.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
7.0ms
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
6.0ms
(/.f64 (/.f64 2 r) r)
4.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
Compiler

Compiled 6042 to 3201 computations (47% saved)

series703.0ms (3.4%)

Error
0.0b
Counts
4 → 45
Calls

4 calls:

324.0ms
(*.f64 (/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v)) (+.f64 3/8 (*.f64 v -1/4)))
229.0ms
(/.f64 (*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r))) (-.f64 1 v))
58.0ms
(*.f64 (fabs.f64 (*.f64 w r)) (fabs.f64 (*.f64 w r)))
29.0ms
(/.f64 (/.f64 2 r) r)
Compiler

Compiled 3271 to 2385 computations (27.1% saved)

simplify170.0ms (0.8%)

Algorithm
egg-herbie
Rules
497×distribute-rgt-in_binary64
227×associate-*l*_binary64
186×associate-*r*_binary64
169×associate-/l/_binary64
158×associate-/l*_binary64 associate-*l/_binary64
142×*-commutative_binary64
133×cancel-sign-sub-inv_binary64
131×unswap-sqr_binary64
129×distribute-rgt-out_binary64
106×associate-/r*_binary64 associate-*r/_binary64
104×distribute-rgt-neg-in_binary64
100×log-prod_binary64
97×distribute-lft-in_binary64
89×times-frac_binary64
87×distribute-lft-neg-in_binary64
80×sub-neg_binary64
72×log-div_binary64
62×distribute-lft-out_binary64
57×+-commutative_binary64
56×div-sub_binary64
52×distribute-neg-frac_binary64
51×distribute-lft-neg-out_binary64
48×associate-/r/_binary64
46×exp-prod_binary64
45×distribute-rgt-neg-out_binary64
43×neg-sub0_binary64
42×neg-mul-1_binary64
39×sqr-pow_binary64
35×*-rgt-identity_binary64
34×cube-prod_binary64
33×swap-sqr_binary64 distribute-neg-in_binary64 associate-+r+_binary64
28×/-rgt-identity_binary64 *-lft-identity_binary64
27×associate-+l+_binary64
23×cube-div_binary64
22×unsub-neg_binary64
13×cube-unmult_binary64 associate--r+_binary64
10×log-pow_binary64 log-rec_binary64 distribute-rgt-out--_binary64
pow-sqr_binary64 distribute-rgt1-in_binary64
pow-plus_binary64
rem-sqrt-square_binary64 distribute-lft1-in_binary64
exp-sum_binary64 distribute-frac-neg_binary64 associate-+l-_binary64 associate-+r-_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 distribute-neg-out_binary64 associate--l+_binary64
unpow3_binary64 exp-diff_binary64 cube-mult_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 +-rgt-identity_binary64 distribute-lft-out--_binary64 count-2_binary64
1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 div0_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 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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64
Counts
209 → 316
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03264776
18654216
228663954
349403954
449623954

prune643.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3151316
Fresh11213
Picked101
Done000
Total31713330
Error
0.0b
Counts
330 → 13
Compiler

Compiled 11258 to 6301 computations (44% saved)

regimes2.8s (13.5%)

Accuracy

Total 0.3b remaining (96.7%)

Threshold costs 0.3b (96.7%)

Compiler

Compiled 43601 to 33525 computations (23.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
12×+-commutative_binary64
11×*-commutative_binary64
10×sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64
distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
unsub-neg_binary64 cancel-sign-sub-inv_binary64 distribute-neg-in_binary64
1-exp_binary64 distribute-neg-frac_binary64 distribute-lft-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 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: 0 (0.0ms)

IterNodesCost
02136
13536
24936
36336
48136
58936
69336
79436
89336

end0.0ms (0%)

sample6.2s (29.8%)

Algorithm
intervals
Results
552.0ms8000×body128valid
339.0ms4971×body128invalid
Compiler

Compiled 7019 to 5406 computations (23% saved)

Profiling

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