Details

Time bar (total: 5.6s)

analyze27.0ms (0.5%)

Algorithm
search
egg-herbie
Rules
28×sub-neg_binary64
25×cancel-sign-sub-inv_binary64
18×distribute-rgt-in_binary64
16×neg-mul-1_binary64
15×associate--r+_binary64
14×unsub-neg_binary64
12×associate--r-_binary64
10×neg-sub0_binary64 distribute-lft-in_binary64
*-lft-identity_binary64 sub0-neg_binary64 distribute-neg-in_binary64 +-commutative_binary64
distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 associate-+l-_binary64
+-lft-identity_binary64 associate-+l+_binary64
distribute-rgt-neg-out_binary64 *-commutative_binary64
*-rgt-identity_binary64
--rgt-identity_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
1-exp_binary64 remove-double-neg_binary64 +-rgt-identity_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 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
11422
22222
33322
44222
56622
69922
711622
813922
914322
1013122
1111722
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample77.0ms (1.4%)

Algorithm
intervals
Results
33.0ms103×body1024valid
20.0ms39×body2048valid
8.0ms42×body512valid
3.0ms23×body256valid
3.0ms49×body128valid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify12.0ms (0.2%)

Algorithm
egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
neg-mul-1_binary64
associate--r+_binary64
unsub-neg_binary64
neg-sub0_binary64 associate--r-_binary64
distribute-neg-in_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-in_binary64 +-commutative_binary64
*-lft-identity_binary64 sub0-neg_binary64 associate-+l-_binary64
+-lft-identity_binary64 distribute-rgt-neg-out_binary64 associate-+l+_binary64 *-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 distribute-lft-neg-in_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--l-_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32111
42711
54211
66511
77811
89011
99211
108611
117211

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
34.6b
Counts
1 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.3b
(sin.f64 (+.f64 x eps))

rewrite41.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
21.1b
Rules
add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64
sin-sum_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
diff-sin_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate--l+_binary64
Counts
2 → 26
Calls

2 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 373 to 99 computations (73.5% saved)

series57.0ms (1%)

Error
11.3b
Counts
2 → 22
Calls

2 calls:

20.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
16.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 567 to 371 computations (34.6% saved)

simplify90.0ms (1.6%)

Algorithm
egg-herbie
Rules
539×unsub-neg_binary64
473×*-commutative_binary64
391×sub-neg_binary64
358×neg-mul-1_binary64
323×neg-sub0_binary64
279×distribute-rgt-neg-in_binary64
272×distribute-lft-neg-in_binary64
234×distribute-rgt-in_binary64
214×associate-*r*_binary64
200×distribute-lft-in_binary64
181×associate-*l*_binary64
158×cancel-sign-sub-inv_binary64
154×unswap-sqr_binary64
127×associate-+l-_binary64
105×distribute-neg-in_binary64
102×associate-+l+_binary64
91×+-commutative_binary64
88×associate-+r+_binary64
81×sqr-pow_binary64
75×associate--l+_binary64
66×distribute-neg-out_binary64
59×distribute-rgt-out_binary64
58×sub0-neg_binary64
56×associate-+r-_binary64
53×distribute-lft-neg-out_binary64
48×cancel-sign-sub_binary64
45×distribute-rgt-neg-out_binary64
44×distribute-rgt-out--_binary64
40×distribute-lft-out_binary64 associate--r+_binary64
38×mul0-rgt_binary64
37×mul0-lft_binary64
35×exp-sum_binary64 +-rgt-identity_binary64 distribute-lft-out--_binary64
33×exp-prod_binary64
28×div-sub_binary64
26×cube-unmult_binary64
25×pow-plus_binary64
24×cube-prod_binary64 difference-of-squares_binary64
21×times-frac_binary64
20×associate--l-_binary64
19×unpow3_binary64
17×exp-diff_binary64 pow-sqr_binary64
16×swap-sqr_binary64
--rgt-identity_binary64
fabs-mul_binary64 sqr-neg_binary64
mul-1-neg_binary64 distribute-rgt1-in_binary64
cube-mult_binary64 cube-neg_binary64 remove-double-neg_binary64 associate-/l*_binary64
sin-neg_binary64 rem-sqrt-square_binary64 distribute-frac-neg_binary64 associate--r-_binary64
unpow2_binary64 fabs-sqr_binary64 +-inverses_binary64 distribute-neg-frac_binary64
cos-neg_binary64 unpow1/2_binary64 unpow1_binary64 count-2_binary64
log-prod_binary64 div-exp_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 fabs-sub_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 distribute-lft1-in_binary64 associate-/r/_binary64 associate-/r*_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-fabs_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_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 associate-/l/_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
48 → 38
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
090739
1219716
2506683
31615675
43478675
54505675
64860675

prune34.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New35338
Fresh000
Picked101
Done000
Total36339
Error
0.2b
Counts
39 → 3
Compiler

Compiled 459 to 177 computations (61.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
0.1b
(*.f64 (cos.f64 eps) (sin.f64 x))
4.0b
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite101.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
15×add-sqr-sqrt_binary64
11×add-log-exp_binary64 *-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
associate-*l*_binary64 associate-*r*_binary64
cancel-sign-sub-inv_binary64
sum-log_binary64 diff-log_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate--l+_binary64 sin-cos-mult_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
4 → 66
Calls

4 calls:

10.0ms
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
7.0ms
(*.f64 (cos.f64 eps) (sin.f64 x))
5.0ms
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
5.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
Compiler

Compiled 1415 to 267 computations (81.1% saved)

series143.0ms (2.5%)

Error
0.2b
Counts
4 → 40
Calls

4 calls:

41.0ms
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
32.0ms
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
26.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
24.0ms
(*.f64 (cos.f64 eps) (sin.f64 x))
Compiler

Compiled 1460 to 900 computations (38.4% saved)

simplify117.0ms (2.1%)

Algorithm
egg-herbie
Rules
312×+-commutative_binary64
306×*-commutative_binary64
279×distribute-rgt-neg-in_binary64
255×cancel-sign-sub-inv_binary64
236×sub-neg_binary64 distribute-lft-neg-in_binary64
226×distribute-rgt-in_binary64
204×distribute-lft-in_binary64
200×neg-mul-1_binary64
175×neg-sub0_binary64
169×associate-+l-_binary64
164×times-frac_binary64
132×associate-*r*_binary64
128×distribute-rgt-out_binary64 associate-*l*_binary64
125×associate--l+_binary64
89×associate-+r-_binary64 associate-+l+_binary64
88×sqr-pow_binary64
86×unswap-sqr_binary64
76×distribute-rgt-out--_binary64
74×exp-prod_binary64
73×unsub-neg_binary64 associate--r+_binary64
69×associate-+r+_binary64
47×distribute-lft-neg-out_binary64
45×exp-sum_binary64
44×distribute-lft-out_binary64
32×cube-prod_binary64 distribute-rgt-neg-out_binary64
31×log-prod_binary64
30×+-rgt-identity_binary64 distribute-lft-out--_binary64
29×sub0-neg_binary64 associate-/l*_binary64
26×exp-diff_binary64
25×distribute-neg-in_binary64
24×associate--l-_binary64
22×swap-sqr_binary64
18×*-lft-identity_binary64
17×*-rgt-identity_binary64
15×unpow3_binary64
14×difference-of-squares_binary64 associate-/r*_binary64
12×pow-sqr_binary64
associate-/l/_binary64 associate-/r/_binary64
cube-unmult_binary64 rem-sqrt-square_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt1-in_binary64
associate-*r/_binary64
unpow1/2_binary64 cube-mult_binary64 sqr-neg_binary64 cancel-sign-sub_binary64 associate--r-_binary64
div-exp_binary64 div-sub_binary64 distribute-lft1-in_binary64
pow-plus_binary64
unpow2_binary64 unpow1_binary64 fabs-mul_binary64 count-2_binary64
sin-neg_binary64 log-pow_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 rem-3cbrt-lft_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 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 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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64
Counts
106 → 75
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01661937
14281875
212011781
327231775
444591775
549871775

prune65.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New66975
Fresh112
Picked101
Done000
Total681078
Error
0.1b
Counts
78 → 10
Compiler

Compiled 1487 to 526 computations (64.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)

rewrite85.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
11×*-un-lft-identity_binary64
10×add-log-exp_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 flip-+_binary64
sum-log_binary64 difference-of-sqr--1_binary64 distribute-lft-out_binary64 +-commutative_binary64 cbrt-prod_binary64
cbrt-div_binary64
pow1/3_binary64
Counts
4 → 52
Calls

4 calls:

6.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 2608 to 1096 computations (58% saved)

series150.0ms (2.7%)

Error
0.1b
Counts
4 → 21
Calls

4 calls:

99.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
12.0ms
(+.f64 (cos.f64 eps) -1)
11.0ms
(+.f64 (cos.f64 eps) -1)
10.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 2689 to 1465 computations (45.5% saved)

simplify107.0ms (1.9%)

Algorithm
egg-herbie
Rules
442×associate-*l*_binary64
441×unswap-sqr_binary64
400×associate-*r*_binary64
253×distribute-rgt-in_binary64
231×distribute-rgt-neg-out_binary64
226×distribute-lft-in_binary64
160×sub-neg_binary64
158×*-commutative_binary64
131×cancel-sign-sub-inv_binary64
113×unsub-neg_binary64
112×distribute-neg-in_binary64
89×times-frac_binary64
84×neg-sub0_binary64
77×distribute-rgt-neg-in_binary64 associate-/l*_binary64
71×neg-mul-1_binary64 sqr-pow_binary64
69×distribute-lft-neg-in_binary64
68×distribute-neg-frac_binary64
62×associate-/r*_binary64
61×cancel-sign-sub_binary64
47×log-prod_binary64
46×associate-+l+_binary64
43×+-commutative_binary64
39×associate--r+_binary64
37×associate-+r+_binary64
35×cube-prod_binary64
30×associate-/r/_binary64
28×associate--l+_binary64
24×distribute-lft-neg-out_binary64
21×associate-+l-_binary64 associate-+r-_binary64
20×exp-prod_binary64
19×associate-*l/_binary64
17×log-pow_binary64 associate-*r/_binary64
16×div-sub_binary64
15×+-rgt-identity_binary64 swap-sqr_binary64 distribute-rgt-out--_binary64
14×sub0-neg_binary64 distribute-frac-neg_binary64
13×cube-unmult_binary64 distribute-rgt-out_binary64
11×unpow3_binary64
distribute-neg-out_binary64
unpow1/3_binary64 exp-sum_binary64 rem-sqrt-square_binary64 distribute-lft-out--_binary64
pow-sqr_binary64
cube-mult_binary64 mul-1-neg_binary64 difference-of-squares_binary64
pow-plus_binary64 distribute-lft-out_binary64 associate--l-_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 *-rgt-identity_binary64 associate-/l/_binary64
cube-neg_binary64 sqr-neg_binary64 *-lft-identity_binary64 difference-of-sqr-1_binary64 associate--r-_binary64
exp-to-pow_binary64 exp-diff_binary64 rem-exp-log_binary64 remove-double-neg_binary64 --rgt-identity_binary64
sub-1-cos_binary64 prod-exp_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 fabs-mul_binary64 fabs-sqr_binary64 difference-of-sqr--1_binary64 distribute-rgt1-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 -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 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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-square-sqrt_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 distribute-lft1-in_binary64 count-2_binary64
Counts
73 → 55
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01151388
13141336
28521263
331791233
449741233
549751233

prune69.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New52355
Fresh189
Picked101
Done000
Total541165
Error
0.0b
Counts
65 → 11
Compiler

Compiled 2917 to 1289 computations (55.8% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

2.7b
(-.f64 (cos.f64 eps) 1)
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)
2.8b
(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))

rewrite125.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
18×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
10×add-log-exp_binary64
log-pow_binary64 add-cube-cbrt_binary64
exp-prod_binary64 log-prod_binary64
cancel-sign-sub-inv_binary64
pow1_binary64
difference-of-squares_binary64 exp-sum_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
difference-of-sqr-1_binary64 distribute-lft-out--_binary64 sub-neg_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 difference-of-sqr--1_binary64 distribute-lft-out_binary64 +-commutative_binary64
exp-diff_binary64 log-div_binary64 rem-log-exp_binary64 diff-log_binary64 flip3--_binary64 flip--_binary64
Counts
4 → 68
Calls

4 calls:

5.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
5.0ms
(-.f64 (cos.f64 eps) 1)
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 3158 to 1424 computations (54.9% saved)

series64.0ms (1.1%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

19.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
12.0ms
(+.f64 (cos.f64 eps) -1)
11.0ms
(+.f64 (cos.f64 eps) -1)
9.0ms
(-.f64 (cos.f64 eps) 1)
Compiler

Compiled 1788 to 990 computations (44.6% saved)

simplify112.0ms (2%)

Algorithm
egg-herbie
Rules
511×log-prod_binary64
274×associate--r+_binary64
249×associate-+l-_binary64
244×unsub-neg_binary64
223×associate--l+_binary64
205×times-frac_binary64
199×associate-*l*_binary64
179×distribute-rgt-out_binary64
166×cancel-sign-sub-inv_binary64
164×unswap-sqr_binary64
153×associate-*r*_binary64
150×associate--r-_binary64
134×distribute-rgt-neg-in_binary64
115×distribute-lft-neg-in_binary64
113×distribute-rgt-in_binary64
111×sub-neg_binary64
109×associate--l-_binary64
105×log-pow_binary64
94×distribute-neg-out_binary64
90×distribute-lft-in_binary64
89×log-div_binary64
85×distribute-neg-in_binary64
81×distribute-rgt-out--_binary64
77×distribute-rgt-neg-out_binary64
76×sqr-pow_binary64
74×exp-sum_binary64 distribute-lft-neg-out_binary64
67×neg-sub0_binary64 *-commutative_binary64
52×distribute-lft-out_binary64
49×exp-prod_binary64 associate-+r+_binary64
47×associate-+l+_binary64
41×neg-mul-1_binary64
40×associate-/l*_binary64
35×associate-+r-_binary64
34×exp-diff_binary64
33×rem-sqrt-square_binary64
32×distribute-lft-out--_binary64
31×+-commutative_binary64
29×distribute-rgt1-in_binary64
27×associate-*r/_binary64
24×cube-prod_binary64 pow-sqr_binary64 associate-/r*_binary64
23×associate-/l/_binary64
19×fabs-mul_binary64 *-rgt-identity_binary64
17×div-sub_binary64 *-lft-identity_binary64 distribute-lft1-in_binary64
14×log-rec_binary64 pow-plus_binary64 cube-unmult_binary64
13×mul0-rgt_binary64 mul0-lft_binary64 associate-*l/_binary64
12×rem-log-exp_binary64
11×fabs-sqr_binary64 remove-double-neg_binary64
10×rem-exp-log_binary64 +-rgt-identity_binary64 associate-/r/_binary64
unpow3_binary64 exp-sqrt_binary64 sub0-neg_binary64
distribute-frac-neg_binary64 count-2_binary64
exp-to-pow_binary64 mul-1-neg_binary64
cube-neg_binary64
unpow1/2_binary64 exp-neg_binary64 cube-div_binary64 difference-of-sqr-1_binary64
sqr-neg_binary64 --rgt-identity_binary64
div-exp_binary64 prod-exp_binary64 cube-mult_binary64 +-lft-identity_binary64 difference-of-sqr--1_binary64 swap-sqr_binary64 cancel-sign-sub_binary64
sub-1-cos_binary64 1-sub-cos_binary64 unpow2_binary64 unpow1_binary64 exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 /-rgt-identity_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 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-squares_binary64 distribute-neg-frac_binary64
Counts
83 → 61
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
091849
1151779
2286773
3604773
41725773
54231773
64712767
75129767

prune69.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New60161
Fresh01010
Picked101
Done000
Total611172
Error
0.0b
Counts
72 → 11
Compiler

Compiled 2332 to 1015 computations (56.5% saved)

regimes1.2s (21.7%)

Accuracy

Total 0.3b remaining (69.6%)

Threshold costs 0.3b (69.6%)

Compiler

Compiled 22806 to 13423 computations (41.1% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64 *-lft-identity_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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 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
01421
12121
22021

end1.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.8s (49.4%)

Algorithm
intervals
Results
1.0s3396×body1024valid
655.0ms1279×body2048valid
249.0ms1323×body512valid
88.0ms1356×body128valid
79.0ms643×body256valid
3.0msbody4096valid
Compiler

Compiled 478 to 289 computations (39.5% saved)

Profiling

Loading profile data...