Details

Time bar (total: 6.1s)

analyze27.0ms (0.4%)

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 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)

sample71.0ms (1.2%)

Algorithm
intervals
Results
31.0ms114×body1024valid
16.0ms34×body2048valid
10.0ms52×body512valid
2.0ms41×body128valid
2.0ms15×body256valid
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 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
38.3b
Counts
1 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.2b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.9b
(sin.f64 (+.f64 x eps))

rewrite36.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
22.5b
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:

6.0ms
(-.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)

series61.0ms (1%)

Error
13.9b
Counts
2 → 23
Calls

2 calls:

20.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
19.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 598 to 389 computations (34.9% saved)

simplify94.0ms (1.5%)

Algorithm
egg-herbie
Rules
408×unsub-neg_binary64
279×distribute-rgt-neg-in_binary64
272×distribute-lft-neg-in_binary64
271×neg-mul-1_binary64
257×neg-sub0_binary64
242×associate-*r*_binary64
234×distribute-rgt-in_binary64
212×associate-*l*_binary64
205×cancel-sign-sub-inv_binary64
200×distribute-lft-in_binary64
186×sub-neg_binary64
149×associate-+l-_binary64
125×associate-+l+_binary64
108×+-commutative_binary64
103×associate-+r+_binary64
94×associate--l+_binary64
87×*-commutative_binary64
86×unswap-sqr_binary64
78×distribute-rgt-out_binary64
77×distribute-lft-out--_binary64
71×distribute-rgt-out--_binary64
65×associate-+r-_binary64
56×distribute-lft-out_binary64
53×distribute-lft-neg-out_binary64
47×associate--r+_binary64
45×distribute-rgt-neg-out_binary64
43×sqr-pow_binary64
28×exp-prod_binary64
23×unpow3_binary64 exp-sum_binary64 associate--l-_binary64
21×+-rgt-identity_binary64
20×pow-plus_binary64
19×cube-unmult_binary64 cube-prod_binary64 sub0-neg_binary64
17×exp-diff_binary64
14×div-sub_binary64
12×difference-of-squares_binary64
10×swap-sqr_binary64
cube-mult_binary64 distribute-neg-in_binary64
mul0-rgt_binary64 mul0-lft_binary64
sqr-neg_binary64 times-frac_binary64 distribute-rgt1-in_binary64
cancel-sign-sub_binary64 associate-/l*_binary64 associate--r-_binary64
rem-sqrt-square_binary64 pow-sqr_binary64
rec-exp_binary64 mul-1-neg_binary64
sin-neg_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-neg_binary64 +-inverses_binary64 distribute-neg-frac_binary64 count-2_binary64
cos-neg_binary64 log-prod_binary64 div-exp_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 --rgt-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 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 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 associate-/l/_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
49 → 39
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
098787
1237764
2555726
31795713
44233713
54952713
64922713

prune35.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New35439
Fresh000
Picked101
Done000
Total36440
Error
0.3b
Counts
40 → 4
Compiler

Compiled 502 to 208 computations (58.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
2.9b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))

rewrite107.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
14×add-sqr-sqrt_binary64
11×add-log-exp_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
cancel-sign-sub-inv_binary64 associate-*l*_binary64 associate-*r*_binary64
sin-cos-mult_binary64 associate-+r+_binary64
diff-log_binary64 sum-log_binary64 flip3--_binary64 frac-add_binary64 flip--_binary64 sub-neg_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
flip3-+_binary64 flip-+_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
4 → 71
Calls

4 calls:

9.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
5.0ms
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
4.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
4.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
Compiler

Compiled 1577 to 285 computations (81.9% saved)

series146.0ms (2.4%)

Error
0.3b
Counts
4 → 44
Calls

4 calls:

39.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
29.0ms
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
27.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
26.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
Compiler

Compiled 1637 to 1003 computations (38.7% saved)

simplify128.0ms (2.1%)

Algorithm
egg-herbie
Rules
405×distribute-rgt-in_binary64 *-commutative_binary64
398×cancel-sign-sub-inv_binary64
387×distribute-lft-in_binary64
344×sub-neg_binary64
327×times-frac_binary64
177×unswap-sqr_binary64
159×associate-*l*_binary64
157×unsub-neg_binary64
156×associate-*r*_binary64
155×associate-+l+_binary64
150×distribute-rgt-neg-in_binary64
143×associate-+r+_binary64
126×distribute-lft-neg-in_binary64
112×neg-mul-1_binary64
110×neg-sub0_binary64
99×sqr-pow_binary64
87×exp-prod_binary64
74×associate-+l-_binary64
71×associate--l+_binary64
69×+-commutative_binary64
65×associate-+r-_binary64
58×cube-prod_binary64
57×log-prod_binary64
49×distribute-rgt-out_binary64
48×associate--r+_binary64
41×exp-sum_binary64 +-rgt-identity_binary64
36×sub0-neg_binary64
33×distribute-rgt-out--_binary64
28×*-lft-identity_binary64
26×distribute-lft-neg-out_binary64
23×exp-diff_binary64 *-rgt-identity_binary64 distribute-lft-out_binary64
22×difference-of-squares_binary64
20×unpow3_binary64 distribute-neg-in_binary64
16×distribute-rgt-neg-out_binary64
13×mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-out--_binary64
12×cube-unmult_binary64 rem-sqrt-square_binary64 pow-sqr_binary64 swap-sqr_binary64
cube-mult_binary64 cube-neg_binary64
unpow1/2_binary64 pow-plus_binary64 remove-double-neg_binary64
sqr-neg_binary64 distribute-rgt1-in_binary64
associate-/l*_binary64
div-exp_binary64
sin-neg_binary64 unpow2_binary64 unpow1_binary64 prod-exp_binary64 associate--r-_binary64 associate--l-_binary64
log-pow_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 div-sub_binary64 --rgt-identity_binary64 associate-/r*_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 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 sqr-abs_binary64 mul-1-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 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64
Counts
115 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02032197
15372115
215792007
339412007
447762007
553722007

prune67.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New601171
Fresh123
Picked101
Done000
Total621375
Error
0.2b
Counts
75 → 13
Compiler

Compiled 1536 to 575 computations (62.6% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
2.5b
(+.f64 (cos.f64 eps) -1)
2.5b
(+.f64 (cos.f64 eps) -1)
2.5b
(+.f64 (cos.f64 eps) -1)

rewrite105.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
11×*-un-lft-identity_binary64
10×add-log-exp_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64 flip3-+_binary64 flip-+_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 cbrt-div_binary64
sum-log_binary64 difference-of-sqr--1_binary64 distribute-lft-out_binary64 +-commutative_binary64 cbrt-prod_binary64
associate-*r/_binary64 sin-cos-mult_binary64 frac-add_binary64
pow1/3_binary64
Counts
4 → 54
Calls

4 calls:

5.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.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 2763 to 1173 computations (57.5% saved)

series187.0ms (3.1%)

Error
0.2b
Counts
4 → 29
Calls

4 calls:

112.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
15.0ms
(+.f64 (cos.f64 eps) -1)
13.0ms
(+.f64 (cos.f64 eps) -1)
13.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 3747 to 2094 computations (44.1% saved)

simplify122.0ms (2%)

Algorithm
egg-herbie
Rules
458×times-frac_binary64
371×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
297×associate-/l*_binary64
261×cancel-sign-sub-inv_binary64
142×associate-*r*_binary64
130×unswap-sqr_binary64 distribute-rgt-neg-in_binary64
119×distribute-lft-neg-in_binary64
112×associate-*l*_binary64
105×*-commutative_binary64
99×sub-neg_binary64
78×distribute-neg-in_binary64
63×sqr-pow_binary64 associate-/r/_binary64
59×+-commutative_binary64
51×neg-sub0_binary64
49×neg-mul-1_binary64
36×distribute-lft-neg-out_binary64
29×associate-+l+_binary64
27×unsub-neg_binary64
26×distribute-rgt-out_binary64 associate--r+_binary64 associate-+r+_binary64
25×distribute-neg-frac_binary64
22×distribute-rgt-neg-out_binary64 associate-/l/_binary64
21×log-prod_binary64
20×distribute-rgt-out--_binary64 associate--l+_binary64
19×exp-prod_binary64
18×associate-/r*_binary64
15×unpow3_binary64
13×log-pow_binary64
11×cube-prod_binary64
10×associate-*r/_binary64
unpow1/3_binary64 distribute-lft-out--_binary64
pow-plus_binary64 associate-*l/_binary64
cube-mult_binary64 distribute-lft-out_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 mul-1-neg_binary64 swap-sqr_binary64
exp-sum_binary64
cube-unmult_binary64
exp-to-pow_binary64 exp-diff_binary64 rem-sqrt-square_binary64 *-rgt-identity_binary64 pow-sqr_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 associate-+l-_binary64 associate-+r-_binary64
sub-1-cos_binary64 prod-exp_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 *-lft-identity_binary64 remove-double-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-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 rem-exp-log_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 rem-square-sqrt_binary64 div-sub_binary64 /-rgt-identity_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
83 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862025
15241965
216341861
349471835
449871835
549471835

prune107.0ms (1.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New56965
Fresh4812
Picked101
Done000
Total611778
Error
0.1b
Counts
78 → 17
Compiler

Compiled 3895 to 1794 computations (53.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.5b
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
2.5b
(+.f64 (cos.f64 eps) -1)
2.5b
(+.f64 (cos.f64 eps) -1)

rewrite126.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
10×*-un-lft-identity_binary64
add-log-exp_binary64 add-sqr-sqrt_binary64 cbrt-div_binary64
add-cube-cbrt_binary64 flip3-+_binary64 flip-+_binary64 cbrt-prod_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-*r/_binary64 sin-cos-mult_binary64 frac-add_binary64
sum-log_binary64 difference-of-sqr--1_binary64 distribute-lft-out_binary64 +-commutative_binary64 pow1/3_binary64
Counts
4 → 56
Calls

4 calls:

7.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
5.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 3426 to 1526 computations (55.5% saved)

series307.0ms (5%)

Error
0.1b
Counts
4 → 34
Calls

4 calls:

115.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
114.0ms
(cbrt.f64 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
16.0ms
(+.f64 (cos.f64 eps) -1)
15.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 5330 to 3058 computations (42.6% saved)

simplify147.0ms (2.4%)

Algorithm
egg-herbie
Rules
458×times-frac_binary64
371×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
297×associate-/l*_binary64
261×cancel-sign-sub-inv_binary64
142×associate-*r*_binary64
130×unswap-sqr_binary64 distribute-rgt-neg-in_binary64
119×distribute-lft-neg-in_binary64
112×associate-*l*_binary64
105×*-commutative_binary64
99×sub-neg_binary64
78×distribute-neg-in_binary64
63×sqr-pow_binary64 associate-/r/_binary64
59×+-commutative_binary64
51×neg-sub0_binary64
49×neg-mul-1_binary64
36×distribute-lft-neg-out_binary64
29×associate-+l+_binary64
27×unsub-neg_binary64
26×distribute-rgt-out_binary64 associate--r+_binary64 associate-+r+_binary64
25×distribute-neg-frac_binary64
22×distribute-rgt-neg-out_binary64 associate-/l/_binary64
21×log-prod_binary64
20×distribute-rgt-out--_binary64 associate--l+_binary64
19×exp-prod_binary64
18×associate-/r*_binary64
15×unpow3_binary64
13×log-pow_binary64
11×cube-prod_binary64
10×associate-*r/_binary64
unpow1/3_binary64 distribute-lft-out--_binary64
pow-plus_binary64 associate-*l/_binary64
cube-mult_binary64 distribute-lft-out_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 mul-1-neg_binary64 swap-sqr_binary64
exp-sum_binary64
cube-unmult_binary64
exp-to-pow_binary64 exp-diff_binary64 rem-sqrt-square_binary64 *-rgt-identity_binary64 pow-sqr_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 associate-+l-_binary64 associate-+r-_binary64
sub-1-cos_binary64 prod-exp_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 *-lft-identity_binary64 remove-double-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-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 rem-exp-log_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 rem-square-sqrt_binary64 div-sub_binary64 /-rgt-identity_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
90 → 74
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01863074
15243010
216342810
349472758
449872758
549472758

prune108.0ms (1.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New71374
Fresh31316
Picked011
Done000
Total741791
Error
0.1b
Counts
91 → 17
Compiler

Compiled 4182 to 1879 computations (55.1% saved)

regimes1.0s (17.1%)

Accuracy

Total 0.3b remaining (73%)

Threshold costs 0.3b (73%)

Compiler

Compiled 18835 to 11085 computations (41.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11621
21621

end1.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample3.0s (49.2%)

Algorithm
intervals
Results
1.1s3525×body1024valid
634.0ms1203×body2048valid
264.0ms1379×body512valid
89.0ms1265×body128valid
84.0ms626×body256valid
2.0msbody4096valid
Compiler

Compiled 761 to 467 computations (38.6% saved)

Profiling

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