Details

Time bar (total: 4.2s)

analyze279.0ms (6.7%)

Algorithm
search
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 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 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 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-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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 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--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%50%0%3
62.5%37.5%0%4
68.7%31.2%0%5
71.8%28.1%0%6
73.4%26.5%0%7
74.2%25.8%0%8
74.6%25.4%0%9
74.8%25.2%0%10
74.9%25.1%0%11
74.9%25%0%12
74.9%25%0%13
75%25%0%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample65.0ms (1.6%)

Algorithm
intervals
Results
28.0ms81×body1024valid
12.0ms38×body2048valid
9.0ms40×body512valid
3.0ms73×body128valid
3.0ms23×body256valid
0.0msbody4096valid
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify9.0ms (0.2%)

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 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 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 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-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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 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--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
52.0b
Counts
1 → 1
Compiler

Compiled 9 to 7 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.4b
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.3b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite88.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
51.9b
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 log-prod_binary64
add-cbrt-cube_binary64 flip3-+_binary64 flip-+_binary64 sqrt-prod_binary64
sqrt-div_binary64 log-div_binary64 distribute-lft-out_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 log-pow_binary64 rem-log-exp_binary64 sum-log_binary64 +-commutative_binary64
Counts
3 → 42
Calls

3 calls:

6.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 703 to 424 computations (39.7% saved)

series84.0ms (2%)

Error
0b
Counts
3 → 28
Calls

3 calls:

22.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
17.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
15.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 818 to 706 computations (13.7% saved)

simplify108.0ms (2.6%)

Algorithm
egg-herbie
Rules
414×sub-neg_binary64
354×unsub-neg_binary64
245×distribute-rgt-in_binary64
220×cancel-sign-sub-inv_binary64
219×times-frac_binary64
190×distribute-lft-in_binary64
169×neg-mul-1_binary64
155×neg-sub0_binary64
154×associate--r-_binary64
148×div-sub_binary64
140×associate-*r/_binary64
135×associate-/r*_binary64
132×associate-*l/_binary64 associate-*l*_binary64
120×associate-*r*_binary64
116×associate-/l/_binary64
110×associate-+l+_binary64
107×unswap-sqr_binary64 +-commutative_binary64
94×distribute-neg-frac_binary64 distribute-rgt-neg-in_binary64
81×associate--l+_binary64 associate-+r+_binary64
77×distribute-rgt-out_binary64
74×associate-/l*_binary64
71×distribute-lft-neg-in_binary64
69×associate-+l-_binary64
60×*-commutative_binary64
57×associate-+r-_binary64
54×sqr-pow_binary64
42×*-rgt-identity_binary64
39×distribute-rgt-out--_binary64
38×*-lft-identity_binary64 distribute-neg-in_binary64
36×cube-prod_binary64
34×--rgt-identity_binary64
29×+-rgt-identity_binary64
27×log-prod_binary64
26×sub0-neg_binary64
25×distribute-lft-out_binary64
24×associate--r+_binary64
20×pow-plus_binary64
19×unpow3_binary64 exp-prod_binary64
18×remove-double-neg_binary64
17×distribute-rgt1-in_binary64
13×cube-unmult_binary64 difference-of-sqr--1_binary64 difference-of-squares_binary64
12×log-div_binary64 distribute-lft-neg-out_binary64
10×distribute-lft-out--_binary64
cube-mult_binary64
cube-div_binary64 rem-sqrt-square_binary64 remove-double-div_binary64 pow-sqr_binary64 associate--l-_binary64
mul-1-neg_binary64 mul0-lft_binary64
exp-sum_binary64 mul0-rgt_binary64 distribute-lft1-in_binary64
log-pow_binary64 prod-exp_binary64 cube-neg_binary64 count-2_binary64
unpow1/2_binary64 exp-diff_binary64 sqr-neg_binary64 div0_binary64 +-inverses_binary64 difference-of-sqr-1_binary64 distribute-rgt-neg-out_binary64
log-rec_binary64 unpow2_binary64 +-lft-identity_binary64 swap-sqr_binary64 associate-/r/_binary64
unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 rem-square-sqrt_binary64 /-rgt-identity_binary64 distribute-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64
Counts
70 → 54
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01351157
13291080
27541050
321231044
443041044
546631044
648801044

prune45.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New51354
Fresh000
Picked011
Done000
Total51455
Error
0b
Counts
55 → 4
Compiler

Compiled 761 to 505 computations (33.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.2b
(*.f64 (pow.f64 x 3) 1/6)

rewrite41.0ms (1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
13×add-sqr-sqrt_binary64
12×associate-*l*_binary64
add-exp-log_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 unpow-prod-down_binary64 unswap-sqr_binary64 cube-prod_binary64
prod-exp_binary64 associate-*r*_binary64
pow1_binary64 sqr-pow_binary64
pow-to-exp_binary64 pow-exp_binary64 cbrt-unprod_binary64 unpow3_binary64 cube-mult_binary64 *-commutative_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64
Counts
2 → 43
Calls

2 calls:

6.0ms
(*.f64 (pow.f64 x 3) 1/6)
3.0ms
(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
Compiler

Compiled 518 to 396 computations (23.6% saved)

series25.0ms (0.6%)

Error
0b
Counts
2 → 9
Calls

2 calls:

14.0ms
(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
9.0ms
(*.f64 (pow.f64 x 3) 1/6)
Compiler

Compiled 108 to 93 computations (13.9% saved)

simplify119.0ms (2.8%)

Algorithm
egg-herbie
Rules
640×unswap-sqr_binary64
326×distribute-rgt-neg-in_binary64
309×distribute-lft-neg-in_binary64
280×log-prod_binary64
225×distribute-rgt-in_binary64
211×*-commutative_binary64
187×distribute-lft-in_binary64
181×associate-+l+_binary64
171×exp-prod_binary64
161×cancel-sign-sub-inv_binary64
112×sqr-pow_binary64
104×swap-sqr_binary64
97×associate-*l*_binary64
91×cube-prod_binary64
81×associate-*r*_binary64
58×neg-mul-1_binary64 neg-sub0_binary64
57×distribute-rgt-out_binary64
42×associate-/l*_binary64
37×log-pow_binary64
34×sub-neg_binary64
30×distribute-lft-out_binary64
23×pow-sqr_binary64
21×unpow3_binary64 unsub-neg_binary64
20×difference-of-squares_binary64
19×distribute-rgt-out--_binary64
17×distribute-lft-neg-out_binary64
15×pow-plus_binary64
14×associate-+r+_binary64 +-commutative_binary64
13×cube-mult_binary64 distribute-rgt-neg-out_binary64
exp-sum_binary64 times-frac_binary64
count-2_binary64
cube-unmult_binary64 *-rgt-identity_binary64 *-lft-identity_binary64
distribute-rgt1-in_binary64 associate-/r*_binary64 associate-+l-_binary64
rem-sqrt-square_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-out--_binary64 associate-+r-_binary64
exp-diff_binary64
sub0-neg_binary64 +-rgt-identity_binary64 distribute-neg-in_binary64 associate--r+_binary64
unpow1/2_binary64 div-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 rem-square-sqrt_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 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_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 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
52 → 38
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
078577
1158556
2619553
31458553
44828553
54995553
64978553
74926553

prune20.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New38038
Fresh022
Picked011
Done011
Total38442
Error
0b
Counts
42 → 4
Compiler

Compiled 377 to 280 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 x (+.f64 x (/.f64 1/2 x)))

rewrite20.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-log-exp_binary64 *-un-lft-identity_binary64
sum-log_binary64 distribute-lft-out_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
1 → 15
Calls

1 calls:

8.0ms
(+.f64 x (+.f64 x (/.f64 1/2 x)))
Compiler

Compiled 209 to 138 computations (34% saved)

series14.0ms (0.3%)

Error
0b
Counts
1 → 6
Calls

1 calls:

12.0ms
(+.f64 x (+.f64 x (/.f64 1/2 x)))
Compiler

Compiled 90 to 81 computations (10% saved)

simplify73.0ms (1.7%)

Algorithm
egg-herbie
Rules
555×sub-neg_binary64
325×times-frac_binary64
298×unsub-neg_binary64
257×associate-*l*_binary64
234×distribute-neg-in_binary64
225×associate-/l*_binary64
192×distribute-rgt-out_binary64
191×distribute-rgt-in_binary64
179×associate-*r*_binary64
167×distribute-lft-out_binary64 distribute-lft-in_binary64
156×associate--l+_binary64
153×associate--r+_binary64
145×+-commutative_binary64
142×div-sub_binary64
139×neg-mul-1_binary64
133×neg-sub0_binary64
128×associate-+l-_binary64
96×distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 associate-+r-_binary64
77×exp-prod_binary64 associate-+l+_binary64
76×cancel-sign-sub-inv_binary64
70×associate-*l/_binary64
65×associate-*r/_binary64
64×exp-sum_binary64
60×associate-+r+_binary64
49×*-commutative_binary64
48×exp-diff_binary64
46×cube-prod_binary64
43×distribute-rgt-out--_binary64
40×unswap-sqr_binary64 cancel-sign-sub_binary64
38×log-prod_binary64
37×associate-/l/_binary64
36×distribute-neg-frac_binary64 distribute-lft-neg-out_binary64
31×distribute-rgt-neg-out_binary64
26×sqr-pow_binary64
25×sub0-neg_binary64
23×associate--r-_binary64 associate--l-_binary64
19×+-rgt-identity_binary64
15×*-rgt-identity_binary64
14×*-lft-identity_binary64
10×cube-div_binary64
distribute-rgt1-in_binary64 distribute-lft-out--_binary64
log-div_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 associate-/r/_binary64
cube-unmult_binary64
remove-double-neg_binary64 +-inverses_binary64 swap-sqr_binary64
unpow3_binary64 pow-plus_binary64 +-lft-identity_binary64 difference-of-squares_binary64
prod-exp_binary64 sqr-neg_binary64 pow-sqr_binary64 count-2_binary64
unpow1/2_binary64 div-exp_binary64 cube-mult_binary64 cube-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64
unpow1_binary64 exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 --rgt-identity_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 distribute-frac-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 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_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-sqrt-square_binary64 rem-square-sqrt_binary64 div0_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 associate-/r*_binary64
Counts
21 → 16
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037283
1100253
2284241
3967235
42257235
54243235
64969235

prune7.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New16016
Fresh011
Picked011
Done022
Total16420
Error
0b
Counts
20 → 4
Compiler

Compiled 150 to 96 computations (36% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1/8 (pow.f64 x 3))
0.2b
(/.f64 1/16 (pow.f64 x 5))
11.9b
(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.3b
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite264.0ms (6.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
75×*-un-lft-identity_binary64
73×add-sqr-sqrt_binary64 times-frac_binary64
47×add-cube-cbrt_binary64
26×unpow-prod-down_binary64
19×associate-/r*_binary64
15×add-exp-log_binary64
14×cube-prod_binary64
11×log-prod_binary64
10×difference-of-squares_binary64 sqr-pow_binary64
add-log-exp_binary64
add-cbrt-cube_binary64
frac-sub_binary64 distribute-lft-out_binary64 distribute-lft-out--_binary64 div-exp_binary64 associate-/l*_binary64
pow1_binary64 cancel-sign-sub-inv_binary64 log-div_binary64
unpow3_binary64 cube-mult_binary64
diff-log_binary64 frac-add_binary64 flip3-+_binary64 flip-+_binary64 flip3--_binary64 flip--_binary64 pow-to-exp_binary64 pow-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
sum-log_binary64 sub-neg_binary64 associate--r+_binary64 log-pow_binary64 rem-log-exp_binary64
Counts
4 → 164
Calls

4 calls:

44.0ms
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
37.0ms
(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
5.0ms
(/.f64 1/8 (pow.f64 x 3))
5.0ms
(/.f64 1/16 (pow.f64 x 5))
Compiler

Compiled 3876 to 3168 computations (18.3% saved)

series64.0ms (1.5%)

Error
0b
Counts
4 → 18
Calls

4 calls:

21.0ms
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
16.0ms
(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
11.0ms
(/.f64 1/16 (pow.f64 x 5))
10.0ms
(/.f64 1/8 (pow.f64 x 3))
Compiler

Compiled 577 to 517 computations (10.4% saved)

simplify161.0ms (3.9%)

Algorithm
egg-herbie
Rules
496×log-prod_binary64
344×cancel-sign-sub-inv_binary64
320×unswap-sqr_binary64
256×distribute-rgt-in_binary64
198×distribute-rgt-neg-in_binary64
185×distribute-lft-neg-in_binary64
164×associate-/r*_binary64
159×associate-*r*_binary64
155×associate-*l*_binary64
96×log-div_binary64
77×sub-neg_binary64
72×distribute-rgt-out_binary64
67×cube-prod_binary64 sqr-pow_binary64
60×distribute-lft-out_binary64 *-commutative_binary64
56×distribute-neg-frac_binary64
53×associate-/l*_binary64
48×swap-sqr_binary64
44×+-commutative_binary64
43×exp-prod_binary64
42×associate-*l/_binary64 associate-*r/_binary64
41×times-frac_binary64 neg-mul-1_binary64
39×neg-sub0_binary64 distribute-neg-in_binary64
38×log-pow_binary64
36×cube-div_binary64 distribute-lft-in_binary64
33×distribute-lft-neg-out_binary64
32×associate-/l/_binary64
19×unpow3_binary64 distribute-rgt-neg-out_binary64
15×distribute-rgt-out--_binary64 associate-+l+_binary64 associate-+r+_binary64
13×associate-/r/_binary64
12×cube-mult_binary64 *-rgt-identity_binary64
11×pow-plus_binary64 cube-unmult_binary64 distribute-lft-out--_binary64 associate--r+_binary64
10×pow-sqr_binary64 associate--l+_binary64 associate-+r-_binary64
log-rec_binary64 rem-sqrt-square_binary64
exp-sum_binary64
unsub-neg_binary64
difference-of-squares_binary64
exp-diff_binary64 /-rgt-identity_binary64 +-rgt-identity_binary64
prod-exp_binary64 associate-+l-_binary64
div-exp_binary64
unpow1/2_binary64 rem-cbrt-cube_binary64 rem-square-sqrt_binary64 *-lft-identity_binary64 distribute-lft1-in_binary64
unpow2_binary64 unpow1_binary64 1-exp_binary64 rem-exp-log_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 count-2_binary64 associate--l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 associate--r-_binary64
Counts
182 → 121
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03053953
16183726
221573684
346323684
451683684

prune78.0ms (1.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1210121
Fresh000
Picked011
Done033
Total1214125
Error
0b
Counts
125 → 4
Compiler

Compiled 1989 to 1588 computations (20.2% saved)

regimes360.0ms (8.6%)

Accuracy

Total 0.2b remaining (83%)

Threshold costs 0.2b (83%)

Compiler

Compiled 2817 to 2163 computations (23.2% saved)

bsearch39.0ms (0.9%)

Steps
ItersRangePoint
11
8.997640312572469e-20
4.376922728436213
0.9528134754376202
9
-1414.8128857466409
-1.537821804780756e-05
-1.0021102368281627
Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03367
14967
26667
39267
410667
511267
611467
710967

end2.0ms (0%)

Compiler

Compiled 45 to 36 computations (20% saved)

sample2.2s (52.2%)

Algorithm
intervals
Results
904.0ms2476×body1024valid
399.0ms1228×body2048valid
259.0ms1249×body512valid
112.0ms2389×body128valid
69.0ms623×body256valid
15.0ms35×body4096valid
Compiler

Compiled 122 to 101 computations (17.2% saved)

Profiling

Loading profile data...