Details

Time bar (total: 2.2s)

analyze24.0ms (1.1%)

Algorithm
search
egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
neg-mul-1_binary64
associate--r+_binary64
unsub-neg_binary64
neg-sub0_binary64
distribute-neg-in_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-in_binary64 associate--r-_binary64 +-commutative_binary64
*-lft-identity_binary64 sub0-neg_binary64 associate-+l-_binary64
+-lft-identity_binary64 distribute-rgt-neg-out_binary64 associate-+l+_binary64 *-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 distribute-lft-neg-in_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 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 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-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 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_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 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32211
42811
54311
66511
77711
88911
99111
108511
117111
011
111
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample30.0ms (1.3%)

Algorithm
intervals
Results
13.0ms72×body2048valid
4.0ms135×body128valid
3.0ms25×body1024valid
2.0ms18×body512valid
0.0msbody256valid
Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify13.0ms (0.6%)

Algorithm
egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
neg-mul-1_binary64
associate--r+_binary64
unsub-neg_binary64
neg-sub0_binary64
distribute-neg-in_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-in_binary64 associate--r-_binary64 +-commutative_binary64
*-lft-identity_binary64 sub0-neg_binary64 associate-+l-_binary64
+-lft-identity_binary64 distribute-rgt-neg-out_binary64 associate-+l+_binary64 *-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 distribute-lft-neg-in_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 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 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-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 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_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 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--l-_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32211
42811
54311
66511
77711
88911
99111
108511
117111

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
13.0b
Counts
1 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(atan.f64 (+.f64 N 1))
1.0b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite39.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
12.1b
Rules
add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
diff-atan_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
Counts
2 → 24
Calls

2 calls:

4.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms
(atan.f64 (+.f64 N 1))
Compiler

Compiled 339 to 221 computations (34.8% saved)

series13.0ms (0.6%)

Error
13.0b
Counts
2 → 6
Calls

2 calls:

7.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms
(atan.f64 (+.f64 N 1))
Compiler

Compiled 91 to 78 computations (14.3% saved)

simplify93.0ms (4.2%)

Algorithm
egg-herbie
Rules
632×unsub-neg_binary64
532×neg-sub0_binary64
514×neg-mul-1_binary64
430×associate-*l*_binary64
371×distribute-rgt-neg-in_binary64
350×associate-*r*_binary64
322×*-commutative_binary64
320×distribute-rgt-neg-out_binary64
305×distribute-lft-neg-out_binary64
255×unswap-sqr_binary64
223×distribute-rgt-in_binary64
193×distribute-lft-in_binary64
168×distribute-neg-in_binary64
144×distribute-rgt-out_binary64
135×cancel-sign-sub-inv_binary64
128×sub-neg_binary64
104×sqr-pow_binary64
101×+-commutative_binary64
86×times-frac_binary64
84×remove-double-neg_binary64
73×distribute-lft-out_binary64
58×exp-prod_binary64
56×distribute-lft-neg-in_binary64
51×cancel-sign-sub_binary64
49×div-sub_binary64
46×difference-of-squares_binary64
37×associate-+l-_binary64
35×exp-sum_binary64 distribute-neg-out_binary64
33×associate-+r+_binary64
32×pow-sqr_binary64
30×associate-+l+_binary64
28×mul0-rgt_binary64 mul0-lft_binary64
26×exp-diff_binary64 swap-sqr_binary64 associate--r+_binary64
25×cube-prod_binary64
24×pow-plus_binary64 sub0-neg_binary64
21×cube-unmult_binary64
17×distribute-rgt-out--_binary64
16×associate-+r-_binary64
14×sqr-neg_binary64 associate-/l*_binary64
11×+-rgt-identity_binary64
10×unpow3_binary64 distribute-frac-neg_binary64 associate--l+_binary64
log-prod_binary64
mul-1-neg_binary64
cube-neg_binary64 --rgt-identity_binary64 associate-/r*_binary64
unpow2_binary64 exp-neg_binary64 distribute-rgt1-in_binary64
rem-sqrt-square_binary64
cube-mult_binary64 *-lft-identity_binary64
+-lft-identity_binary64
unpow1_binary64 div-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 *-rgt-identity_binary64 +-inverses_binary64 distribute-lft-out--_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 pow-base-0_binary64 unpow1/3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 div0_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-neg-frac_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
30 → 8
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049423
1101400
2185391
3553391
41681391
52674391
64338391
74998391

prune6.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New718
Fresh000
Picked101
Done000
Total819
Error
0.4b
Counts
9 → 1
Compiler

Compiled 85 to 61 computations (28.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 N (+.f64 N 1))
0.4b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite48.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*r*_binary64
associate-*l*_binary64
add-log-exp_binary64 associate-*r/_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 *-commutative_binary64
Counts
2 → 30
Calls

2 calls:

6.0ms
(*.f64 N (+.f64 N 1))
0.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 435 to 334 computations (23.2% saved)

series21.0ms (0.9%)

Error
0.4b
Counts
2 → 9
Calls

2 calls:

10.0ms
(*.f64 N (+.f64 N 1))
6.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 157 to 140 computations (10.8% saved)

simplify90.0ms (4.1%)

Algorithm
egg-herbie
Rules
658×distribute-rgt-in_binary64
525×distribute-lft-in_binary64
475×unswap-sqr_binary64
213×associate-+l+_binary64
199×associate-+r+_binary64
192×associate-*r/_binary64
168×associate-*l/_binary64
156×associate-*l*_binary64
149×*-commutative_binary64
130×sqr-pow_binary64
129×distribute-rgt-out_binary64
116×associate-*r*_binary64
82×associate-/l*_binary64
79×exp-prod_binary64
76×difference-of-squares_binary64
62×associate-/l/_binary64
55×cancel-sign-sub-inv_binary64
48×distribute-lft-out_binary64
46×associate-/r/_binary64
44×*-rgt-identity_binary64 distribute-lft1-in_binary64
43×log-div_binary64 cube-div_binary64 pow-sqr_binary64
41×associate-/r*_binary64
37×rem-sqrt-square_binary64 distribute-rgt1-in_binary64
34×log-prod_binary64
31×*-lft-identity_binary64
29×sub-neg_binary64
27×cube-prod_binary64
23×pow-plus_binary64 distribute-rgt-neg-in_binary64
20×distribute-lft-neg-in_binary64
19×unpow3_binary64
18×distribute-rgt-out--_binary64
17×+-commutative_binary64
14×exp-sqrt_binary64 cube-unmult_binary64 unsub-neg_binary64
10×cube-mult_binary64 swap-sqr_binary64
exp-sum_binary64
unpow1/2_binary64
neg-sub0_binary64 difference-of-sqr--1_binary64
difference-of-sqr-1_binary64 associate-+l-_binary64
log-pow_binary64 mul-1-neg_binary64 count-2_binary64 associate-+r-_binary64
sub0-neg_binary64 +-rgt-identity_binary64
log-rec_binary64 unpow2_binary64 times-frac_binary64 distribute-neg-frac_binary64
exp-lft-sqr_binary64 exp-diff_binary64 neg-mul-1_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
unpow1_binary64 prod-exp_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-cbrt_binary64 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 /-rgt-identity_binary64 remove-double-neg_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
39 → 33
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
055455
1129395
2316394
3747392
42538392
53430392
64786392
74927392

prune35.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New27633
Fresh000
Picked101
Done000
Total28634
Error
0.4b
Counts
34 → 6
Compiler

Compiled 442 to 280 computations (36.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 N (+.f64 1 (*.f64 N N)))
0.4b
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

rewrite34.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
add-log-exp_binary64
*-un-lft-identity_binary64
sum-log_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
2 → 21
Calls

2 calls:

5.0ms
(+.f64 N (+.f64 1 (*.f64 N N)))
1.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
Compiler

Compiled 349 to 208 computations (40.4% saved)

series27.0ms (1.2%)

Error
0.4b
Counts
2 → 12
Calls

2 calls:

13.0ms
(+.f64 N (+.f64 1 (*.f64 N N)))
9.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
Compiler

Compiled 169 to 151 computations (10.7% saved)

simplify85.0ms (3.9%)

Algorithm
egg-herbie
Rules
532×associate-+l-_binary64
419×associate-+r-_binary64
306×sub-neg_binary64
264×distribute-rgt-out_binary64
240×distribute-rgt-in_binary64
206×distribute-lft-in_binary64
181×+-commutative_binary64
176×associate--r-_binary64
154×distribute-rgt-out--_binary64
148×cancel-sign-sub-inv_binary64 associate--l-_binary64
137×distribute-rgt-neg-in_binary64
132×*-commutative_binary64
122×neg-mul-1_binary64
105×associate--l+_binary64
99×distribute-lft-neg-in_binary64
96×distribute-neg-in_binary64
94×unswap-sqr_binary64
86×exp-prod_binary64
83×unsub-neg_binary64
75×associate--r+_binary64
70×distribute-lft-out--_binary64
65×associate-*l*_binary64
62×sqr-pow_binary64
59×associate-*r*_binary64
54×associate-+l+_binary64
46×difference-of-squares_binary64 associate-+r+_binary64
41×neg-sub0_binary64 distribute-lft-out_binary64
34×sub0-neg_binary64 distribute-rgt1-in_binary64
28×swap-sqr_binary64
27×exp-sum_binary64 cancel-sign-sub_binary64
26×div-sub_binary64
25×+-rgt-identity_binary64 distribute-lft-neg-out_binary64
23×cube-prod_binary64
21×exp-diff_binary64
18×distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64 associate-/l*_binary64
14×pow-plus_binary64 cube-unmult_binary64 times-frac_binary64 *-rgt-identity_binary64 associate-/l/_binary64
13×*-lft-identity_binary64 pow-sqr_binary64
11×distribute-neg-out_binary64 associate-*r/_binary64
10×associate-/r/_binary64
associate-/r*_binary64
unpow3_binary64 unpow1/2_binary64 rem-sqrt-square_binary64 remove-double-neg_binary64
prod-exp_binary64 cube-div_binary64 sqr-neg_binary64
+-inverses_binary64
difference-of-sqr-1_binary64 associate-*l/_binary64
log-prod_binary64 cube-mult_binary64
unpow2_binary64 unpow1_binary64 exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 mul-1-neg_binary64 difference-of-sqr--1_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 log-rec_binary64 log-div_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 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 /-rgt-identity_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64
Counts
33 → 18
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045477
1113429
2309429
31098420
42051420
54764420
64965420

prune17.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New18018
Fresh055
Picked011
Done000
Total18624
Error
0.4b
Counts
24 → 6
Compiler

Compiled 209 to 134 computations (35.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N)))) (cbrt.f64 (+.f64 N (*.f64 N N))))))
17.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
17.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))
17.2b
(cbrt.f64 (+.f64 N (*.f64 N N)))

rewrite88.0ms (4%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
15×cbrt-prod_binary64
10×*-un-lft-identity_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64
cbrt-div_binary64
pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1/3_binary64 flip3-+_binary64 flip-+_binary64 distribute-rgt1-in_binary64 distribute-rgt-out_binary64
Counts
4 → 52
Calls

4 calls:

3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
3.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
0.0ms
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N)))) (cbrt.f64 (+.f64 N (*.f64 N N))))))
Compiler

Compiled 1735 to 426 computations (75.4% saved)

series105.0ms (4.7%)

Error
0.4b
Counts
4 → 33
Calls

4 calls:

24.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
22.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
22.0ms
(cbrt.f64 (+.f64 N (*.f64 N N)))
6.0ms
(atan2.f64 1 (+.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 N (*.f64 N N))) (cbrt.f64 (+.f64 N (*.f64 N N)))) (cbrt.f64 (+.f64 N (*.f64 N N))))))
Compiler

Compiled 2016 to 1328 computations (34.1% saved)

simplify118.0ms (5.3%)

Algorithm
egg-herbie
Rules
692×associate-*l*_binary64
556×associate-*r*_binary64
351×neg-mul-1_binary64
324×distribute-rgt-neg-in_binary64
304×distribute-lft-neg-in_binary64
192×difference-of-squares_binary64
191×distribute-rgt-out--_binary64
161×*-commutative_binary64
145×cancel-sign-sub-inv_binary64
139×unswap-sqr_binary64
131×sub-neg_binary64
107×distribute-lft-neg-out_binary64
96×unsub-neg_binary64
92×distribute-rgt-neg-out_binary64
90×distribute-rgt-out_binary64
88×swap-sqr_binary64
86×distribute-rgt-in_binary64
84×cube-prod_binary64 sqr-pow_binary64
74×distribute-lft-in_binary64
66×neg-sub0_binary64
61×+-commutative_binary64
59×associate-/r*_binary64
57×associate-+l+_binary64
50×distribute-neg-in_binary64
49×distribute-lft-out_binary64
42×associate-+l-_binary64
36×pow-plus_binary64 distribute-rgt1-in_binary64 associate-+r+_binary64
33×unpow3_binary64
31×cube-unmult_binary64
25×associate-+r-_binary64
24×distribute-lft1-in_binary64
23×sub0-neg_binary64
21×associate--l+_binary64
19×cube-mult_binary64 +-rgt-identity_binary64
14×distribute-lft-out--_binary64 associate--r+_binary64
10×*-rgt-identity_binary64 *-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-neg-out_binary64
associate-/l/_binary64
unpow1/3_binary64 pow-sqr_binary64
cancel-sign-sub_binary64
mul-1-neg_binary64 difference-of-sqr--1_binary64
log-prod_binary64 unpow2_binary64 exp-prod_binary64 cube-neg_binary64 rem-sqrt-square_binary64 +-lft-identity_binary64 difference-of-sqr-1_binary64
unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 remove-double-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 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 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 /-rgt-identity_binary64 --rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 count-2_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
85 → 50
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0791422
11791386
23741386
39431386
429761386
548301386
650661386

prune54.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New50050
Fresh044
Picked011
Done011
Total50656
Error
0.4b
Counts
56 → 6
Compiler

Compiled 1044 to 481 computations (53.9% saved)

regimes147.0ms (6.6%)

Accuracy

Total 0.0b remaining (9.9%)

Threshold costs 0.0b (9.9%)

Compiler

Compiled 1775 to 1368 computations (22.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_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 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 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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11213
21113

end1.0ms (0%)

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.1s (49.5%)

Algorithm
intervals
Results
385.0ms2100×body2048valid
141.0ms4145×body128valid
124.0ms973×body1024valid
48.0ms518×body512valid
17.0ms264×body256valid
Compiler

Compiled 128 to 99 computations (22.7% saved)

Profiling

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