Details

Time bar (total: 4.1s)

analyze467.0ms (11.5%)

Algorithm
search
egg-herbie
Rules
436×times-frac_binary64
374×div-sub_binary64
198×cancel-sign-sub-inv_binary64
185×sub-neg_binary64
167×associate-/l*_binary64
132×associate-/r*_binary64
118×distribute-rgt-in_binary64
107×associate-/r/_binary64
106×distribute-lft-in_binary64
82×distribute-neg-frac_binary64
80×distribute-rgt-neg-in_binary64
76×unsub-neg_binary64
59×distribute-lft-neg-in_binary64
48×associate-*r*_binary64
46×neg-mul-1_binary64
44×associate-/l/_binary64
37×distribute-rgt-neg-out_binary64
36×distribute-frac-neg_binary64
34×neg-sub0_binary64 associate-*l/_binary64
26×associate-*r/_binary64 associate-*l*_binary64 associate--r-_binary64 +-commutative_binary64
25×distribute-lft-neg-out_binary64 associate--r+_binary64
23×associate-+l-_binary64
21×*-commutative_binary64
18×associate-+r-_binary64
16×mul0-rgt_binary64 div0_binary64
13×sub0-neg_binary64
10×remove-double-neg_binary64 distribute-neg-in_binary64
/-rgt-identity_binary64
*-lft-identity_binary64 mul0-lft_binary64 associate-+r+_binary64
*-rgt-identity_binary64
distribute-neg-out_binary64 associate--l-_binary64
mul-1-neg_binary64 +-rgt-identity_binary64 associate-+l+_binary64
--rgt-identity_binary64
*-inverses_binary64 distribute-lft-out_binary64
1-exp_binary64 remove-double-div_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_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 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 +-lft-identity_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
12424
25024
39224
420724
530020
674020
788520
889220
989820
1088320
1188120
1288320
1388320
1478220
022
122
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
25%74.9%0.1%4
37.5%62.4%0.1%5
62.4%37.5%0.1%6
87.4%12.5%0.1%7
87.4%12.5%0.1%8
93.7%6.2%0.1%9
93.7%6.2%0.1%10
96.8%3.1%0.1%11
96.8%3.1%0.1%12
98.3%1.6%0.1%13
98.3%1.6%0.1%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample18.0ms (0.4%)

Algorithm
intervals
Results
7.0ms256×body128valid
Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify66.0ms (1.6%)

Algorithm
egg-herbie
Rules
457×times-frac_binary64
323×div-sub_binary64
147×sub-neg_binary64
141×cancel-sign-sub-inv_binary64
139×associate-/l*_binary64
107×associate-/r*_binary64
98×distribute-rgt-in_binary64
90×distribute-lft-in_binary64
87×unsub-neg_binary64
69×associate-/r/_binary64
50×distribute-neg-frac_binary64 distribute-rgt-neg-in_binary64
49×associate-/l/_binary64
34×distribute-frac-neg_binary64
32×neg-mul-1_binary64 associate-*l*_binary64
30×distribute-lft-neg-out_binary64
28×associate-*l/_binary64
26×distribute-lft-neg-in_binary64 associate-*r*_binary64
23×neg-sub0_binary64
20×distribute-rgt-neg-out_binary64 +-commutative_binary64
16×mul0-rgt_binary64 associate--r+_binary64 *-commutative_binary64
15×associate-+l-_binary64
12×div0_binary64 distribute-neg-in_binary64 associate-*r/_binary64 associate-+r-_binary64
11×sub0-neg_binary64
associate--r-_binary64 associate--l-_binary64
/-rgt-identity_binary64 *-lft-identity_binary64
remove-double-neg_binary64 mul0-lft_binary64 distribute-rgt-out--_binary64 associate-+r+_binary64
*-rgt-identity_binary64
distribute-neg-out_binary64
--rgt-identity_binary64
+-rgt-identity_binary64 associate-+l+_binary64
mul-1-neg_binary64 *-inverses_binary64 distribute-rgt-out_binary64 associate--l+_binary64
1-exp_binary64 remove-double-div_binary64 distribute-lft1-in_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 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 +-lft-identity_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 distribute-lft-out--_binary64 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0712
11812
23812
36612
414012
518712
653510
778910
896510
989310
1088610
1188510
1288710
1388710
1478210

prune14.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
0.0b
Counts
2 → 1
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(/.f64 (+.f64 f n) (-.f64 n f))

rewrite51.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
34×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
20×times-frac_binary64
12×add-cube-cbrt_binary64
distribute-lft-out_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64 associate-/r*_binary64
associate-/l*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l/_binary64 associate-/r/_binary64
pow1_binary64 div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64 flip3--_binary64 flip--_binary64
Counts
1 → 45
Calls

1 calls:

9.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 714 to 167 computations (76.6% saved)

series158.0ms (3.9%)

Error
0.0b
Counts
1 → 24
Calls

1 calls:

134.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 642 to 532 computations (17.1% saved)

simplify93.0ms (2.3%)

Algorithm
egg-herbie
Rules
506×cancel-sign-sub-inv_binary64
409×distribute-rgt-in_binary64
328×div-sub_binary64
177×distribute-rgt-neg-in_binary64
170×distribute-lft-neg-in_binary64
161×associate-/l*_binary64
160×distribute-neg-frac_binary64
155×times-frac_binary64
136×associate-/r*_binary64
130×associate-*l*_binary64
122×unswap-sqr_binary64
121×distribute-rgt-out_binary64
117×sub-neg_binary64
112×distribute-lft-in_binary64
109×associate-*r*_binary64
105×associate-*l/_binary64
81×*-commutative_binary64
74×associate-*r/_binary64
73×distribute-rgt-neg-out_binary64
72×neg-sub0_binary64 distribute-lft-out_binary64
71×unsub-neg_binary64
67×associate-+l+_binary64
63×neg-mul-1_binary64
61×distribute-neg-in_binary64
60×+-commutative_binary64
58×distribute-lft-neg-out_binary64
54×associate-/l/_binary64
52×associate-+r+_binary64
48×associate-/r/_binary64
33×cube-prod_binary64
28×sqr-pow_binary64 distribute-rgt-out--_binary64 associate--r+_binary64
24×associate-+l-_binary64
23×distribute-neg-out_binary64 distribute-lft-out--_binary64
22×distribute-frac-neg_binary64 associate-+r-_binary64
20×difference-of-squares_binary64
15×unpow3_binary64 cube-unmult_binary64
13×*-rgt-identity_binary64 sub0-neg_binary64 +-rgt-identity_binary64
12×cube-div_binary64 distribute-rgt1-in_binary64
11×log-prod_binary64
10×sqr-neg_binary64 /-rgt-identity_binary64
associate--l+_binary64
pow-plus_binary64 cube-mult_binary64
cube-neg_binary64 swap-sqr_binary64 distribute-lft1-in_binary64 associate--l-_binary64
*-lft-identity_binary64
log-div_binary64 rem-sqrt-square_binary64 mul0-rgt_binary64 mul0-lft_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 --rgt-identity_binary64 pow-sqr_binary64 associate--r-_binary64
1-exp_binary64 remove-double-neg_binary64 *-inverses_binary64 cancel-sign-sub_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 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 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 +-lft-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 count-2_binary64
Counts
69 → 34
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01061317
12631225
27571162
324501147
446801147
551351147

prune32.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New31334
Fresh000
Picked011
Done000
Total31435
Error
0b
Counts
35 → 4
Compiler

Compiled 445 to 196 computations (56% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
0.0b
(/.f64 (+.f64 f n) (-.f64 n f))
0.0b
(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

rewrite246.0ms (6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
150×*-un-lft-identity_binary64
100×times-frac_binary64
98×add-sqr-sqrt_binary64
58×cbrt-prod_binary64
56×add-cube-cbrt_binary64
52×unpow-prod-down_binary64 cube-prod_binary64
26×distribute-lft-out_binary64
21×difference-of-squares_binary64 distribute-lft-out--_binary64
10×associate-/r/_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
div-inv_binary64 flip3--_binary64 flip--_binary64 associate-/r*_binary64
pow1_binary64 associate-/l*_binary64
pow-unpow_binary64 add-log-exp_binary64
div-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64 cube-div_binary64 rem-cube-cbrt_binary64 cbrt-undiv_binary64 sqr-pow_binary64 associate-/l/_binary64
pow-pow_binary64 pow-to-exp_binary64 frac-2neg_binary64 clear-num_binary64 flip3-+_binary64 flip-+_binary64 pow1/3_binary64 cbrt-div_binary64 rem-cbrt-cube_binary64
Counts
3 → 185
Calls

3 calls:

11.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
10.0ms
(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
7.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 3934 to 1357 computations (65.5% saved)

series501.0ms (12.3%)

Error
0b
Counts
3 → 72
Calls

3 calls:

175.0ms
(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
126.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
123.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 2172 to 1837 computations (15.4% saved)

simplify157.0ms (3.9%)

Algorithm
egg-herbie
Rules
475×unswap-sqr_binary64
359×distribute-rgt-in_binary64
298×distribute-lft-in_binary64
149×sqr-pow_binary64
102×associate-*l/_binary64
99×associate-/l*_binary64
95×associate-*r/_binary64
87×log-prod_binary64
86×distribute-rgt-neg-in_binary64
85×distribute-lft-neg-in_binary64
84×cube-div_binary64
78×distribute-neg-in_binary64
71×times-frac_binary64
66×log-div_binary64
64×+-commutative_binary64
62×*-commutative_binary64
60×associate-*r*_binary64
58×exp-prod_binary64
55×sub-neg_binary64 distribute-neg-frac_binary64
53×neg-sub0_binary64
52×neg-mul-1_binary64
51×associate-/r*_binary64
49×unpow3_binary64 cube-prod_binary64
48×cube-mult_binary64
46×associate-+r+_binary64
44×associate-*l*_binary64
43×cancel-sign-sub-inv_binary64
36×associate-+l+_binary64
35×swap-sqr_binary64
32×rem-cbrt-cube_binary64 associate-/l/_binary64
30×unsub-neg_binary64
23×distribute-rgt-out_binary64
21×*-rgt-identity_binary64
19×associate--r+_binary64
15×rem-sqrt-square_binary64 associate-/r/_binary64
14×log-pow_binary64 distribute-lft-neg-out_binary64
13×pow-sqr_binary64
12×distribute-rgt-neg-out_binary64
11×div-sub_binary64
10×distribute-lft-out_binary64
pow-plus_binary64 *-lft-identity_binary64
cube-unmult_binary64
difference-of-squares_binary64
/-rgt-identity_binary64 distribute-rgt-out--_binary64 associate-+r-_binary64
unpow1/2_binary64 unpow1_binary64 rem-cube-cbrt_binary64 rem-square-sqrt_binary64 +-rgt-identity_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64
unpow2_binary64 distribute-lft1-in_binary64
1-exp_binary64 rem-3cbrt-lft_binary64 mul-1-neg_binary64 remove-double-neg_binary64 *-inverses_binary64 associate--r-_binary64 associate-+l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 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-neg_binary64 rem-3cbrt-rft_binary64 sqr-abs_binary64 sqr-neg_binary64 sub0-neg_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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--l-_binary64 associate--l+_binary64
Counts
257 → 189
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02435552
16705126
222144935
352004935

prune171.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1890189
Fresh022
Picked011
Done011
Total1894193
Error
0b
Counts
193 → 4
Compiler

Compiled 3076 to 1165 computations (62.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 1 (-.f64 n f))
0.2b
(*.f64 (/.f64 1 (-.f64 n f)) (+.f64 n f))

rewrite106.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
43×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
32×times-frac_binary64
22×add-cube-cbrt_binary64
21×associate-*l*_binary64
15×add-exp-log_binary64
add-cbrt-cube_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64
pow1_binary64 associate-/r*_binary64
div-exp_binary64 prod-exp_binary64 associate-/r/_binary64 associate-*r*_binary64
unswap-sqr_binary64 associate-/l*_binary64
1-exp_binary64 rec-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 associate-*r/_binary64 div-inv_binary64 flip3--_binary64 flip--_binary64
pow-prod-down_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 distribute-lft-out_binary64 *-commutative_binary64 inv-pow_binary64 pow-flip_binary64 frac-2neg_binary64 clear-num_binary64
Counts
2 → 91
Calls

2 calls:

13.0ms
(*.f64 (/.f64 1 (-.f64 n f)) (+.f64 n f))
5.0ms
(/.f64 1 (-.f64 n f))
Compiler

Compiled 1555 to 663 computations (57.4% saved)

series273.0ms (6.7%)

Error
0b
Counts
2 → 45
Calls

2 calls:

122.0ms
(*.f64 (/.f64 1 (-.f64 n f)) (+.f64 n f))
108.0ms
(/.f64 1 (-.f64 n f))
Compiler

Compiled 1410 to 1067 computations (24.3% saved)

simplify103.0ms (2.5%)

Algorithm
egg-herbie
Rules
572×times-frac_binary64
396×distribute-rgt-in_binary64
362×distribute-lft-in_binary64
310×associate-/l*_binary64
259×associate-*l/_binary64
257×div-sub_binary64
220×associate-/r*_binary64
177×associate-*r/_binary64
157×sub-neg_binary64
116×associate-+l+_binary64
82×associate-*l*_binary64 associate-*r*_binary64
81×neg-mul-1_binary64 *-commutative_binary64
80×neg-sub0_binary64
76×associate-/r/_binary64
65×unsub-neg_binary64
48×+-commutative_binary64
47×distribute-rgt-neg-in_binary64
42×distribute-lft-neg-in_binary64
38×distribute-neg-in_binary64
36×associate--r+_binary64
35×associate-+r+_binary64
34×cancel-sign-sub-inv_binary64
32×associate-+l-_binary64 associate-+r-_binary64
30×*-lft-identity_binary64 distribute-neg-frac_binary64
28×*-rgt-identity_binary64
27×exp-prod_binary64 cube-prod_binary64
26×associate-/l/_binary64
24×sqr-pow_binary64
17×distribute-rgt-out_binary64
16×cube-div_binary64 unswap-sqr_binary64
14×exp-sum_binary64
11×log-prod_binary64 distribute-lft-neg-out_binary64
10×associate--l+_binary64
log-div_binary64
cube-unmult_binary64 /-rgt-identity_binary64 distribute-rgt-neg-out_binary64
distribute-lft-out_binary64 associate--l-_binary64
unpow3_binary64 difference-of-squares_binary64 swap-sqr_binary64 distribute-rgt1-in_binary64 distribute-rgt-out--_binary64
+-rgt-identity_binary64
log-rec_binary64 unpow1/2_binary64 cube-mult_binary64 distribute-lft1-in_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64 exp-diff_binary64 rem-sqrt-square_binary64 distribute-neg-out_binary64 associate--r-_binary64
1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 sqr-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 +-lft-identity_binary64 *-inverses_binary64 rgt-mult-inverse_binary64 pow-sqr_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 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-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 --rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 +-inverses_binary64 lft-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-lft-out--_binary64
Counts
136 → 101
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01572164
14641987
213771895
341041895
449831895

prune78.0ms (1.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1010101
Fresh011
Picked011
Done022
Total1014105
Error
0b
Counts
105 → 4
Compiler

Compiled 1492 to 571 computations (61.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (/.f64 f n))
0.1b
(*.f64 (/.f64 f n) (+.f64 2 (*.f64 2 (/.f64 f n))))

rewrite97.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
28×add-sqr-sqrt_binary64
20×times-frac_binary64
18×add-cube-cbrt_binary64 *-un-lft-identity_binary64
16×associate-*l*_binary64 associate-*r*_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
associate-*r/_binary64
pow-prod-down_binary64 div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 flip3-+_binary64 frac-times_binary64 flip-+_binary64 div-inv_binary64 *-commutative_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64
Counts
2 → 70
Calls

2 calls:

8.0ms
(*.f64 (/.f64 f n) (+.f64 2 (*.f64 2 (/.f64 f n))))
7.0ms
(*.f64 2 (/.f64 f n))
Compiler

Compiled 1516 to 820 computations (45.9% saved)

series391.0ms (9.6%)

Error
0b
Counts
2 → 18
Calls

2 calls:

283.0ms
(*.f64 (/.f64 f n) (+.f64 2 (*.f64 2 (/.f64 f n))))
94.0ms
(*.f64 2 (/.f64 f n))
Compiler

Compiled 648 to 510 computations (21.3% saved)

simplify84.0ms (2.1%)

Algorithm
egg-herbie
Rules
651×associate-*l/_binary64
575×associate-*r/_binary64
369×associate-/l*_binary64
288×distribute-rgt-in_binary64
275×distribute-lft-in_binary64
252×times-frac_binary64
177×associate-/r*_binary64
124×associate-*l*_binary64
113×associate-*r*_binary64
104×*-commutative_binary64
72×associate-/l/_binary64
59×exp-prod_binary64
57×associate-/r/_binary64
52×log-prod_binary64
41×distribute-rgt-out_binary64
39×log-div_binary64
37×cube-div_binary64
33×distribute-lft-out_binary64
31×distribute-rgt-neg-in_binary64
27×cancel-sign-sub-inv_binary64
25×sqr-pow_binary64
24×distribute-lft-neg-in_binary64
23×distribute-rgt1-in_binary64
22×distribute-neg-frac_binary64
21×unswap-sqr_binary64
20×sub-neg_binary64
18×cube-prod_binary64
17×swap-sqr_binary64
15×*-rgt-identity_binary64 +-commutative_binary64
11×unpow3_binary64
10×neg-mul-1_binary64 neg-sub0_binary64 *-lft-identity_binary64
pow-plus_binary64 distribute-rgt-out--_binary64
prod-exp_binary64
exp-sum_binary64 cube-mult_binary64 distribute-lft-neg-out_binary64
exp-lft-sqr_binary64 cube-unmult_binary64
log-pow_binary64 log-rec_binary64 /-rgt-identity_binary64 distribute-rgt-neg-out_binary64
unpow1/2_binary64 distribute-lft-out--_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
unpow2_binary64 unpow1_binary64 rem-sqrt-square_binary64 pow-sqr_binary64
1-exp_binary64 exp-1-e_binary64 div-sub_binary64 distribute-neg-in_binary64 distribute-lft1-in_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-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_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 unsub-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_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
88 → 54
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01371429
14261297
212711294
347841294
449631294

prune53.0ms (1.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New54054
Fresh000
Picked011
Done033
Total54458
Error
0b
Counts
58 → 4
Compiler

Compiled 999 to 517 computations (48.2% saved)

regimes133.0ms (3.3%)

Accuracy

Total 0.0b remaining (95.5%)

Threshold costs 0.0b (95.5%)

Compiler

Compiled 930 to 666 computations (28.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 *-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 unsub-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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
1910
21410
31610
41710
51710

end0.0ms (0%)

sample746.0ms (18.3%)

Algorithm
intervals
Results
202.0ms8000×body128valid
Compiler

Compiled 307 to 213 computations (30.6% saved)

Profiling

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