Details

Time bar (total: 4.0s)

analyze535.0ms (13.3%)

Algorithm
search
egg-herbie
Rules
801×cube-prod_binary64
678×unswap-sqr_binary64
585×unpow3_binary64
360×sqr-pow_binary64
358×distribute-rgt-in_binary64
340×associate-/l*_binary64
280×distribute-lft-in_binary64
264×div-sub_binary64
185×*-commutative_binary64
179×associate-/r*_binary64
168×pow-sqr_binary64 associate-*l*_binary64
167×associate-*r*_binary64
150×cube-mult_binary64
144×cube-div_binary64
77×associate-/l/_binary64
73×associate-*l/_binary64
66×sub-neg_binary64
60×mul0-rgt_binary64
59×associate-*r/_binary64
56×mul0-lft_binary64
54×swap-sqr_binary64
49×associate-/r/_binary64
36×times-frac_binary64
28×+-commutative_binary64
25×*-rgt-identity_binary64
21×*-lft-identity_binary64 div0_binary64
15×/-rgt-identity_binary64
12×cube-unmult_binary64
*-inverses_binary64
--rgt-identity_binary64 remove-double-div_binary64
cancel-sign-sub-inv_binary64 associate--l-_binary64
neg-mul-1_binary64 neg-sub0_binary64 sub0-neg_binary64 +-rgt-identity_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 associate--r+_binary64 associate-+l-_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 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-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 unsub-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 +-lft-identity_binary64 +-inverses_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--r-_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05088
18576
214448
321936
424536
567936
6132436
7153636
8140436
9151136
10171336
11212636
12329136
13499036
14523236
033
133
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
23.4%51.5%25.1%7
24.2%50.7%25.1%8
24.6%50.3%25.1%9
36.9%25.5%37.6%10
37.2%25.3%37.6%11
37.3%25.1%37.6%12
43.5%12.7%43.8%13
43.6%12.6%43.8%14
Compiler

Compiled 29 to 21 computations (27.6% saved)

sample41.0ms (1%)

Algorithm
intervals
Results
28.0ms256×body128valid
2.0ms20×body128nan
Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify120.0ms (3%)

Algorithm
egg-herbie
Rules
662×cube-prod_binary64
617×distribute-rgt-in_binary64
522×pow-sqr_binary64
486×distribute-lft-in_binary64
453×associate-/l*_binary64
447×sqr-pow_binary64
380×div-sub_binary64
331×cube-div_binary64
275×unpow3_binary64
272×cube-mult_binary64
266×associate-*l*_binary64
242×times-frac_binary64
181×swap-sqr_binary64
129×*-commutative_binary64
108×associate-/l/_binary64
79×unswap-sqr_binary64
77×associate-*l/_binary64
64×associate-/r/_binary64
50×associate-*r/_binary64
48×sub-neg_binary64
44×associate-/r*_binary64
41×mul0-lft_binary64
32×mul0-rgt_binary64
24×associate-*r*_binary64
20×+-commutative_binary64
18×pow-plus_binary64 div0_binary64
11×remove-double-div_binary64
/-rgt-identity_binary64
unpow2_binary64
*-rgt-identity_binary64
cube-unmult_binary64
unpow1_binary64 rem-sqrt-square_binary64 *-lft-identity_binary64 *-inverses_binary64
--rgt-identity_binary64 lft-mult-inverse_binary64
unpow1/2_binary64 1-exp_binary64 neg-mul-1_binary64 neg-sub0_binary64 sub0-neg_binary64 +-rgt-identity_binary64 rgt-mult-inverse_binary64 cancel-sign-sub-inv_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-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 unsub-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 +-lft-identity_binary64 +-inverses_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--r-_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01922
13119
24912
3709
4789
51979
64529
78679
810259
916079
1018989
1129229
1239789
1342459
1443329
1549689

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Compiler

Compiled 40 to 32 computations (20% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite30.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×times-frac_binary64
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64
log-pow_binary64 associate-/r*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
1 → 31
Calls

1 calls:

3.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))
Compiler

Compiled 367 to 88 computations (76% saved)

series47.0ms (1.2%)

Error
0.3b
Counts
1 → 9
Calls

1 calls:

44.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))
Compiler

Compiled 153 to 145 computations (5.2% saved)

simplify93.0ms (2.3%)

Algorithm
egg-herbie
Rules
556×distribute-neg-in_binary64
438×div-sub_binary64
404×distribute-rgt-in_binary64
382×neg-mul-1_binary64
379×sub-neg_binary64
356×distribute-lft-in_binary64
354×neg-sub0_binary64
280×distribute-frac-neg_binary64
222×distribute-neg-frac_binary64
217×distribute-rgt-neg-out_binary64
188×associate-/l/_binary64
174×cancel-sign-sub-inv_binary64
167×remove-double-neg_binary64
156×times-frac_binary64
147×associate-/l*_binary64
121×sqr-pow_binary64
116×distribute-lft-neg-out_binary64
106×log-div_binary64
97×cube-div_binary64 associate-/r*_binary64
92×log-prod_binary64
91×cube-prod_binary64
86×associate-/r/_binary64
83×unsub-neg_binary64
79×+-lft-identity_binary64
67×associate-*l/_binary64
64×distribute-neg-out_binary64
61×div0_binary64
55×associate-*l*_binary64
54×associate-*r/_binary64
51×exp-prod_binary64
49×*-lft-identity_binary64
45×mul0-rgt_binary64
44×*-rgt-identity_binary64 mul0-lft_binary64
39×associate-*r*_binary64
36×unswap-sqr_binary64
31×/-rgt-identity_binary64
29×exp-sum_binary64
26×*-commutative_binary64
24×swap-sqr_binary64
23×cube-neg_binary64
21×unpow3_binary64
20×+-rgt-identity_binary64
19×cube-mult_binary64
18×associate--r+_binary64 associate-+r+_binary64
17×pow-sqr_binary64 distribute-rgt-neg-in_binary64 associate-+r-_binary64
16×distribute-lft-neg-in_binary64
15×+-commutative_binary64
14×exp-diff_binary64 sqr-neg_binary64 mul-1-neg_binary64
13×log-rec_binary64
12×associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+l+_binary64
10×rem-sqrt-square_binary64
associate--l+_binary64
cube-unmult_binary64
exp-neg_binary64 distribute-rgt-out_binary64
sub0-neg_binary64 distribute-rgt-out--_binary64
--rgt-identity_binary64 remove-double-div_binary64
unpow1/2_binary64 unpow-1_binary64 1-exp_binary64 exp-1-e_binary64 +-inverses_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_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 *-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-lft-out--_binary64
Counts
40 → 13
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
063610
1107572
2213572
3400572
41451572
53750572
64020572
74804572

prune8.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New10313
Fresh011
Picked011
Done000
Total10515
Error
0.2b
Counts
15 → 5
Compiler

Compiled 126 to 66 computations (47.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b
(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))

rewrite62.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
pow1/3_binary64
add-exp-log_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 73
Calls

4 calls:

6.0ms
(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 1601 to 235 computations (85.3% saved)

series135.0ms (3.3%)

Error
0.2b
Counts
4 → 24
Calls

4 calls:

38.0ms
(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
32.0ms
(cbrt.f64 (atan2.f64 im re))
31.0ms
(cbrt.f64 (atan2.f64 im re))
30.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 897 to 565 computations (37% saved)

simplify116.0ms (2.9%)

Algorithm
egg-herbie
Rules
584×log-prod_binary64
394×sqr-pow_binary64
327×*-commutative_binary64
311×distribute-lft-out_binary64
278×associate-*l*_binary64
266×associate-/r/_binary64
258×associate-/l/_binary64
188×exp-prod_binary64
172×associate-*r*_binary64
157×log-pow_binary64
151×distribute-rgt-out_binary64
145×cube-prod_binary64
126×pow-sqr_binary64
119×log-div_binary64
112×unswap-sqr_binary64
111×swap-sqr_binary64
104×associate-/l*_binary64
75×associate-+l+_binary64
69×associate-+r+_binary64
61×distribute-rgt-in_binary64
57×distribute-lft-in_binary64
54×times-frac_binary64
42×rem-sqrt-square_binary64
40×pow-plus_binary64 +-commutative_binary64
36×count-2_binary64
35×associate-*r/_binary64
31×*-rgt-identity_binary64 *-lft-identity_binary64
30×unpow3_binary64
25×cube-mult_binary64
24×associate-/r*_binary64
22×distribute-rgt1-in_binary64
12×cube-div_binary64
11×cube-unmult_binary64
10×distribute-lft1-in_binary64
unpow1/2_binary64
associate-*l/_binary64
unpow2_binary64
unpow1_binary64
unpow1/3_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64
log-rec_binary64 exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_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 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-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-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-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
97 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0511160
1821069
22591037
38701017
41628891
52483891
64799891
74826891

prune23.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New60464
Fresh033
Picked101
Done011
Total61869
Error
0.1b
Counts
69 → 8
Compiler

Compiled 597 to 205 computations (65.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b
(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))

rewrite71.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
18×cbrt-prod_binary64
11×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
unpow-prod-down_binary64
pow1_binary64 add-exp-log_binary64
pow1/3_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
pow-unpow_binary64
pow-pow_binary64
pow-to-exp_binary64 pow-exp_binary64 sqr-pow_binary64
Counts
4 → 57
Calls

4 calls:

4.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 1539 to 396 computations (74.3% saved)

series154.0ms (3.8%)

Error
0.1b
Counts
4 → 24
Calls

4 calls:

50.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
34.0ms
(cbrt.f64 (atan2.f64 im re))
34.0ms
(cbrt.f64 (atan2.f64 im re))
33.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 1131 to 731 computations (35.4% saved)

simplify64.0ms (1.6%)

Algorithm
egg-herbie
Rules
862×unswap-sqr_binary64
358×associate-*l*_binary64
276×distribute-rgt-in_binary64
272×distribute-lft-in_binary64
228×associate-*r*_binary64
183×log-prod_binary64
166×sqr-pow_binary64
137×associate-+l+_binary64 associate-+r+_binary64
78×associate-/l*_binary64
75×exp-prod_binary64
63×cube-prod_binary64
40×cube-unmult_binary64 associate-/l/_binary64
35×pow-sqr_binary64 distribute-rgt-out_binary64
34×*-commutative_binary64
31×pow-plus_binary64
26×count-2_binary64
25×associate-*r/_binary64
22×log-pow_binary64
21×associate-/r*_binary64
20×distribute-lft-out_binary64
16×associate-/r/_binary64
rem-sqrt-square_binary64 swap-sqr_binary64
unpow3_binary64 *-lft-identity_binary64 associate-*l/_binary64
times-frac_binary64 *-rgt-identity_binary64 distribute-rgt1-in_binary64
cube-mult_binary64 /-rgt-identity_binary64
unpow1/3_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-3cbrt-lft_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 log-div_binary64 pow-base-0_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_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-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-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 +-commutative_binary64
Counts
81 → 38
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
064941
1115875
2222875
3503875
41398875
54985875

prune18.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New37138
Fresh066
Picked101
Done011
Total38846
Error
0.1b
Counts
46 → 8
Compiler

Compiled 533 to 204 computations (61.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))
4.1b
(cbrt.f64 (atan2.f64 im re))

rewrite44.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
12×cbrt-prod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1/3_binary64 pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 44
Calls

4 calls:

1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
1.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 1436 to 288 computations (79.9% saved)

series140.0ms (3.5%)

Error
0.1b
Counts
4 → 24
Calls

4 calls:

36.0ms
(cbrt.f64 (atan2.f64 im re))
34.0ms
(cbrt.f64 (atan2.f64 im re))
34.0ms
(cbrt.f64 (atan2.f64 im re))
32.0ms
(cbrt.f64 (atan2.f64 im re))
Compiler

Compiled 1456 to 795 computations (45.4% saved)

simplify102.0ms (2.5%)

Algorithm
egg-herbie
Rules
813×associate-/r/_binary64
551×log-prod_binary64
409×associate-*l*_binary64
350×distribute-rgt-out_binary64
267×sqr-pow_binary64
254×associate-*r*_binary64
241×times-frac_binary64
222×distribute-lft-out_binary64
217×*-commutative_binary64
205×distribute-rgt-in_binary64
201×distribute-lft-in_binary64
166×unswap-sqr_binary64
162×associate-/l*_binary64
122×associate-/l/_binary64
118×distribute-rgt1-in_binary64
107×pow-sqr_binary64
106×+-commutative_binary64
91×associate-+l+_binary64
89×associate-+r+_binary64
80×exp-prod_binary64
69×log-pow_binary64
61×cube-prod_binary64
56×count-2_binary64
52×associate-/r*_binary64
49×associate-*r/_binary64
42×distribute-lft1-in_binary64
28×pow-plus_binary64
27×associate-*l/_binary64
19×unpow3_binary64
15×cube-mult_binary64 *-lft-identity_binary64
11×*-rgt-identity_binary64
cube-unmult_binary64
rem-sqrt-square_binary64
unpow2_binary64
/-rgt-identity_binary64
unpow1_binary64
unpow1/3_binary64 unpow1/2_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 swap-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-rec_binary64 log-div_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_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-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-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
68 → 32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019588
127560
254560
3110560
4336560
51522560
62771560
73674560
85131560

prune5.0ms (0.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New32032
Fresh066
Picked011
Done011
Total32840
Error
0.1b
Counts
40 → 8
Compiler

Compiled 167 to 51 computations (69.5% saved)

regimes761.0ms (18.9%)

Accuracy

Total 0.2b remaining (57.6%)

Threshold costs 0.2b (57.6%)

Compiler

Compiled 11218 to 6453 computations (42.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
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 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 *-commutative_binary64 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
179

end1.0ms (0%)

Compiler

Compiled 6 to 6 computations (0% saved)

sample1.4s (34.9%)

Algorithm
intervals
Results
805.0ms8000×body128valid
86.0ms966×body128nan
Compiler

Compiled 195 to 137 computations (29.7% saved)

Profiling

Loading profile data...