Details

Time bar (total: 2.0s)

analyze26.0ms (1.3%)

Algorithm
search
egg-herbie
Rules
*-commutative_binary64
associate-*l*_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 1-exp_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--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
069
1109
2119
3119
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample12.0ms (0.6%)

Algorithm
intervals
Results
5.0ms256×body128valid
Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify8.0ms (0.4%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*l*_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 1-exp_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--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 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1109
2119
3119

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
27.9b
Counts
2 → 1
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

26.9b
(sqrt.f64 (*.f64 (*.f64 2 x) x))

rewrite15.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
13.7b
Rules
pow1_binary64
pow-prod-down_binary64 sqrt-pow1_binary64
pow1/2_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
Counts
1 → 12
Calls

1 calls:

3.0ms
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Compiler

Compiled 114 to 85 computations (25.4% saved)

series11.0ms (0.5%)

Error
0.2b
Counts
1 → 3
Calls

1 calls:

7.0ms
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Compiler

Compiled 38 to 37 computations (2.6% saved)

simplify159.0ms (7.9%)

Algorithm
egg-herbie
Rules
1268×sqr-pow_binary64
651×pow-sqr_binary64
362×unswap-sqr_binary64
265×cube-prod_binary64
201×unpow3_binary64
198×cube-mult_binary64
169×associate-*l*_binary64
151×*-commutative_binary64
103×associate-*r*_binary64
48×pow-plus_binary64
23×distribute-rgt-in_binary64
17×rem-sqrt-square_binary64
cube-unmult_binary64 sub-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-in_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 +-commutative_binary64
unsub-neg_binary64
neg-sub0_binary64 sub0-neg_binary64 --rgt-identity_binary64 associate--r+_binary64 associate-+l-_binary64
mul-1-neg_binary64 distribute-rgt-neg-in_binary64
1-exp_binary64 rem-square-sqrt_binary64 neg-mul-1_binary64 distribute-lft-neg-in_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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 times-frac_binary64 div-sub_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-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 difference-of-squares_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-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--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Counts
15 → 10
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022129
134123
261123
377123
485123
5106123
6127123
7185123
8396123
9700123
10702123
11832123
12986123
131203123
141501123
151874123
162317123
172840123
183060123
193130123
203140123
213142123
223142123
233711123
244352123
254798123

prune12.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6410
Fresh000
Picked011
Done000
Total6511
Error
0.2b
Counts
11 → 5
Compiler

Compiled 118 to 93 computations (21.2% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))

rewrite123.0ms (6.1%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
158×pow1_binary64
154×sqrt-pow1_binary64
82×pow-prod-down_binary64
33×sqrt-prod_binary64
28×add-sqr-sqrt_binary64
24×pow1/2_binary64
21×pow-prod-up_binary64
13×add-cube-cbrt_binary64 *-un-lft-identity_binary64 pow-sqr_binary64
swap-sqr_binary64
associate-*l*_binary64 associate-*r*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 unswap-sqr_binary64
rem-sqrt-square_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 sqrt-unprod_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 *-commutative_binary64
Counts
4 → 131
Calls

4 calls:

15.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))))
4.0ms
(sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
Compiler

Compiled 1739 to 1328 computations (23.6% saved)

series37.0ms (1.9%)

Error
0.2b
Counts
4 → 12
Calls

4 calls:

9.0ms
(sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
8.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
8.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
7.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))))
Compiler

Compiled 369 to 318 computations (13.8% saved)

simplify119.0ms (5.9%)

Algorithm
egg-herbie
Rules
518×associate-*l/_binary64
418×*-commutative_binary64
383×associate-*r/_binary64
330×associate-*l*_binary64
278×log-div_binary64
260×associate-/l*_binary64
232×associate-+l+_binary64
226×associate-*r*_binary64
203×sqr-pow_binary64
184×associate-/l/_binary64
155×swap-sqr_binary64
132×associate-/r/_binary64
123×associate-+r+_binary64
111×distribute-rgt-in_binary64
99×distribute-lft-in_binary64
92×log-prod_binary64
90×associate-/r*_binary64
89×unswap-sqr_binary64
86×exp-prod_binary64
75×pow-sqr_binary64
74×cube-prod_binary64
36×rem-sqrt-square_binary64
30×times-frac_binary64
29×pow-plus_binary64
22×log-pow_binary64
20×distribute-rgt-out_binary64
17×*-rgt-identity_binary64 *-lft-identity_binary64
15×unpow3_binary64 cube-div_binary64 distribute-lft-out_binary64
11×cube-unmult_binary64
10×cube-mult_binary64 count-2_binary64
log-rec_binary64
rem-square-sqrt_binary64 +-commutative_binary64
unpow2_binary64 unpow1/2_binary64
sub-neg_binary64 distribute-rgt1-in_binary64
unpow1_binary64 unsub-neg_binary64 distribute-lft1-in_binary64
neg-sub0_binary64 distribute-rgt-neg-in_binary64
mul-1-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-neg-in_binary64
exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 neg-mul-1_binary64 sub0-neg_binary64 --rgt-identity_binary64 cancel-sign-sub-inv_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-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 /-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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
143 → 107
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0711408
11091306
23111286
38661203
413371173
519111173
646471173
749761173

prune36.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh123
Picked101
Done011
Total1066112
Error
0.2b
Counts
112 → 6
Compiler

Compiled 634 to 494 computations (22.1% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3)
19.1b
(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))

rewrite91.0ms (4.5%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
24×pow1_binary64
22×sqrt-prod_binary64
20×cbrt-prod_binary64
14×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 sqrt-pow1_binary64 *-un-lft-identity_binary64 unpow-prod-down_binary64 cube-prod_binary64
pow-prod-down_binary64
pow-pow_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
pow1/2_binary64 add-log-exp_binary64
pow-unpow_binary64
unpow3_binary64 cube-mult_binary64 sqr-pow_binary64
pow1/3_binary64 rem-cbrt-cube_binary64 pow-to-exp_binary64 pow-exp_binary64 rem-cube-cbrt_binary64 sqrt-pow2_binary64
Counts
4 → 91
Calls

4 calls:

6.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3)
4.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
Compiler

Compiled 1697 to 1348 computations (20.6% saved)

series46.0ms (2.3%)

Error
0.2b
Counts
4 → 12
Calls

4 calls:

14.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3)
10.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
10.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
8.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2)))) 3))
Compiler

Compiled 530 to 467 computations (11.9% saved)

simplify116.0ms (5.7%)

Algorithm
egg-herbie
Rules
803×associate-*l*_binary64
662×associate-*r*_binary64
505×log-prod_binary64
424×unswap-sqr_binary64
326×exp-prod_binary64
269×cube-prod_binary64
149×sqr-pow_binary64
120×swap-sqr_binary64
95×*-commutative_binary64
86×associate-/l*_binary64
67×associate-+l+_binary64
61×distribute-rgt-in_binary64
55×log-pow_binary64 distribute-lft-in_binary64
45×pow-sqr_binary64
44×rem-sqrt-square_binary64
35×pow-plus_binary64
29×cube-unmult_binary64
25×unpow3_binary64
16×count-2_binary64
14×cube-mult_binary64
13×distribute-rgt-out_binary64
11×associate-/l/_binary64
10×associate-+r+_binary64
rem-cbrt-cube_binary64
rem-square-sqrt_binary64 distribute-lft-out_binary64
associate-*r/_binary64
*-rgt-identity_binary64 *-lft-identity_binary64
neg-sub0_binary64 sub-neg_binary64 associate-*l/_binary64
mul-1-neg_binary64 distribute-rgt-neg-in_binary64 associate-/r/_binary64
unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 neg-mul-1_binary64 distribute-lft-neg-in_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 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 unsub-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate-/r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
103 → 71
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0911433
11721408
24781372
328931366
449141366
548791366

prune30.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New71071
Fresh044
Picked011
Done011
Total71677
Error
0.2b
Counts
77 → 6
Compiler

Compiled 601 to 474 computations (21.1% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))
26.9b
(sqrt.f64 (*.f64 x (*.f64 x 2)))

rewrite61.0ms (3%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
22×pow1_binary64
pow-prod-down_binary64 sqrt-pow1_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-prod_binary64 cbrt-prod_binary64
pow1/2_binary64
pow1/3_binary64
Counts
4 → 48
Calls

4 calls:

4.0ms
(cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
4.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
3.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
Compiler

Compiled 1217 to 927 computations (23.8% saved)

series64.0ms (3.2%)

Error
0.2b
Counts
4 → 12
Calls

4 calls:

21.0ms
(cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 x 2))))
11.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
10.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
10.0ms
(sqrt.f64 (*.f64 x (*.f64 x 2)))
Compiler

Compiled 792 to 652 computations (17.7% saved)

simplify101.0ms (5%)

Algorithm
egg-herbie
Rules
680×div-sub_binary64
488×times-frac_binary64
439×exp-sum_binary64
300×associate-*l*_binary64
212×exp-diff_binary64
205×associate-*r*_binary64
197×associate--r-_binary64
194×distribute-rgt-in_binary64
171×distribute-lft-in_binary64
162×exp-prod_binary64
129×log-prod_binary64
123×associate-+r-_binary64
118×*-commutative_binary64
111×rec-exp_binary64
102×prod-exp_binary64
86×associate-+l-_binary64
78×sub-neg_binary64
73×log-div_binary64
72×div-exp_binary64
68×sqr-pow_binary64
63×associate-+l+_binary64
58×unsub-neg_binary64 unswap-sqr_binary64
51×distribute-neg-in_binary64 associate--l+_binary64
39×associate--l-_binary64
36×associate--r+_binary64 +-commutative_binary64
35×associate-+r+_binary64
34×log-pow_binary64
30×associate-*r/_binary64
29×pow-plus_binary64
26×cancel-sign-sub-inv_binary64
25×pow-sqr_binary64
24×exp-to-pow_binary64
22×associate-/r*_binary64 associate-*l/_binary64
19×neg-sub0_binary64
18×associate-/l/_binary64
17×neg-mul-1_binary64
15×cube-unmult_binary64 associate-/l*_binary64
14×unpow1/3_binary64
13×associate-/r/_binary64
11×unpow3_binary64 exp-neg_binary64
10×distribute-rgt-neg-out_binary64
distribute-rgt-neg-in_binary64
sub0-neg_binary64 distribute-lft-neg-out_binary64
log-rec_binary64 --rgt-identity_binary64
rem-exp-log_binary64 rem-sqrt-square_binary64
cube-prod_binary64 distribute-neg-frac_binary64 distribute-neg-out_binary64
distribute-frac-neg_binary64 distribute-lft-neg-in_binary64
*-rgt-identity_binary64 *-lft-identity_binary64 swap-sqr_binary64 count-2_binary64
unpow2_binary64 mul-1-neg_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64
log-E_binary64 unpow1_binary64 unpow-1_binary64 1-exp_binary64 exp-1-e_binary64 rem-log-exp_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 distribute-rgt1-in_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 pow-base-0_binary64 unpow1/2_binary64 pow-base-1_binary64 unpow0_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 e-exp-1_binary64 exp-0_binary64 cube-mult_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 /-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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-lft-out--_binary64
Counts
60 → 24
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
049629
185611
2163604
3386590
4974549
52664549
64315547
74929547
84831547

prune16.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New24024
Fresh033
Picked011
Done022
Total24630
Error
0.2b
Counts
30 → 6
Compiler

Compiled 438 to 339 computations (22.6% saved)

regimes351.0ms (17.4%)

Accuracy

Total 0.2b remaining (48.4%)

Threshold costs 0.2b (48.4%)

Compiler

Compiled 3021 to 2503 computations (17.1% saved)

bsearch15.0ms (0.8%)

Steps
ItersRangePoint
10
-5.152681537499351e-300
4.271833802488331e-307
3.34772934547096e-310
Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
neg-sub0_binary64 sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
mul-1-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 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 /-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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
12025
22825
33325
43825
54025
64025

end1.0ms (0%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample527.0ms (26.2%)

Algorithm
intervals
Results
188.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 95 to 85 computations (10.5% saved)

Profiling

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