Details

Time bar (total: 4.8s)

analyze43.0ms (0.9%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
12834
23634
34234
44434
54334
022
122
Search
TrueOtherFalseIter
0%25%75%0
0%25%75%1
12.5%12.5%75%2
12.5%12.5%75%3
18.7%6.2%75%4
21.8%3.1%75%5
23.4%1.6%75%6
23.4%1.6%75%7
24.2%0.8%75%8
24.2%0.8%75%9
24.6%0.4%75%10
24.6%0.4%75%11
24.8%0.2%75%12
24.8%0.2%75%13
24.9%0.1%75%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample58.0ms (1.2%)

Algorithm
intervals
Results
19.0ms66×body1024valid
9.0ms45×body512valid
9.0ms127×body128valid
5.0ms256×pre128true
2.0ms18×body256valid
Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify9.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
11717
22117
32417
42517
52417

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Compiler

Compiled 11 to 9 computations (18.2% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b
(*.f64 e (cos.f64 v))
0.1b
(*.f64 e (sin.f64 v))

rewrite77.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×add-sqr-sqrt_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1_binary64
associate-*l*_binary64 associate-*r*_binary64
prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 times-frac_binary64 associate-/r*_binary64
pow-prod-down_binary64 unswap-sqr_binary64 *-commutative_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-/r/_binary64
frac-2neg_binary64 clear-num_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64 associate-/l*_binary64
Counts
3 → 59
Calls

3 calls:

6.0ms
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
4.0ms
(*.f64 e (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1015 to 368 computations (63.7% saved)

series98.0ms (2%)

Error
0.1b
Counts
3 → 25
Calls

3 calls:

45.0ms
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
19.0ms
(*.f64 e (sin.f64 v))
18.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1050 to 763 computations (27.3% saved)

simplify81.0ms (1.7%)

Algorithm
egg-herbie
Rules
387×associate-/r*_binary64
340×associate-*l/_binary64
332×unswap-sqr_binary64
314×*-commutative_binary64
255×associate-/l/_binary64
243×associate-/r/_binary64
237×associate-*r/_binary64
191×sub-neg_binary64
171×cancel-sign-sub-inv_binary64
129×associate-*l*_binary64
125×associate-*r*_binary64
109×associate-/l*_binary64
103×distribute-rgt-neg-in_binary64
92×associate-+l+_binary64
89×distribute-lft-neg-in_binary64
80×sqr-pow_binary64
77×associate--l+_binary64
75×*-rgt-identity_binary64
74×neg-mul-1_binary64 neg-sub0_binary64
69×+-commutative_binary64
62×times-frac_binary64
59×*-lft-identity_binary64
58×distribute-rgt-in_binary64
55×associate-+r+_binary64
50×log-prod_binary64
49×cube-prod_binary64
43×log-div_binary64
40×cube-div_binary64 distribute-lft-in_binary64
37×div-sub_binary64
34×unsub-neg_binary64
33×exp-prod_binary64
30×distribute-neg-frac_binary64 associate-+l-_binary64
29×/-rgt-identity_binary64
25×associate-+r-_binary64
24×distribute-rgt-out_binary64
19×+-rgt-identity_binary64 associate--r+_binary64
17×distribute-rgt-out--_binary64 distribute-lft-out--_binary64
15×unpow3_binary64
13×difference-of-squares_binary64
12×cube-mult_binary64 distribute-lft-out_binary64
10×sub0-neg_binary64 pow-sqr_binary64 distribute-lft-neg-out_binary64
swap-sqr_binary64
log-rec_binary64
cube-unmult_binary64
distribute-neg-in_binary64 associate--l-_binary64
log-pow_binary64 unpow1/2_binary64 rem-sqrt-square_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64
div0_binary64 difference-of-sqr-1_binary64 distribute-rgt1-in_binary64
1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 +-inverses_binary64 remove-double-div_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 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 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-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 count-2_binary64 associate--r-_binary64
Counts
84 → 40
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01561394
14071241
214951222
341811222
450021222

prune45.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New33740
Fresh000
Picked101
Done000
Total34741
Error
0.0b
Counts
41 → 7
Compiler

Compiled 771 to 400 computations (48.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (*.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1)))
0.0b
(/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1))
0.1b
(*.f64 e (cos.f64 v))
0.1b
(*.f64 e (sin.f64 v))

rewrite164.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
34×add-exp-log_binary64
27×add-sqr-sqrt_binary64
23×add-cube-cbrt_binary64 *-un-lft-identity_binary64
22×add-cbrt-cube_binary64
21×associate-*r*_binary64
18×times-frac_binary64
14×pow1_binary64 prod-exp_binary64
cbrt-unprod_binary64
associate-*l*_binary64
div-exp_binary64
pow-prod-down_binary64
add-log-exp_binary64 associate-/r/_binary64
*-commutative_binary64 1-exp_binary64 rec-exp_binary64 cbrt-undiv_binary64 associate-/l*_binary64 associate-/r*_binary64
unswap-sqr_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64
inv-pow_binary64 pow-flip_binary64 frac-2neg_binary64 clear-num_binary64 un-div-inv_binary64 associate-*r/_binary64
Counts
4 → 109
Calls

4 calls:

11.0ms
(*.f64 (*.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1)))
6.0ms
(/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1))
4.0ms
(*.f64 e (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 2190 to 1013 computations (53.7% saved)

series127.0ms (2.6%)

Error
0.0b
Counts
4 → 34
Calls

4 calls:

45.0ms
(*.f64 (*.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1)))
22.0ms
(*.f64 e (sin.f64 v))
20.0ms
(/.f64 1 (+.f64 (*.f64 e (cos.f64 v)) 1))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1407 to 1033 computations (26.6% saved)

simplify132.0ms (2.7%)

Algorithm
egg-herbie
Rules
639×associate-/l*_binary64
318×cancel-sign-sub-inv_binary64
317×associate-/r*_binary64
255×associate-*l*_binary64
251×sub-neg_binary64
220×associate-*l/_binary64
207×associate-*r*_binary64
149×distribute-rgt-neg-in_binary64
140×associate-/r/_binary64
127×distribute-lft-neg-in_binary64
126×*-commutative_binary64
116×neg-mul-1_binary64
114×neg-sub0_binary64
104×unswap-sqr_binary64
100×sqr-pow_binary64
87×associate-/l/_binary64
71×div-sub_binary64
64×associate-*r/_binary64
63×distribute-rgt-in_binary64
57×*-lft-identity_binary64
54×*-rgt-identity_binary64
53×/-rgt-identity_binary64
48×exp-prod_binary64
44×log-div_binary64 +-commutative_binary64
42×log-prod_binary64 distribute-lft-in_binary64
41×cube-prod_binary64
40×times-frac_binary64
38×cube-div_binary64
34×distribute-rgt-out_binary64
30×distribute-rgt-out--_binary64
27×distribute-lft-out--_binary64
26×associate--l+_binary64
23×unsub-neg_binary64
22×associate-+l+_binary64
21×swap-sqr_binary64
20×unpow3_binary64 distribute-lft-out_binary64
19×distribute-neg-frac_binary64
17×cube-mult_binary64
15×pow-sqr_binary64 distribute-lft-neg-out_binary64
14×associate--r+_binary64 associate-+r+_binary64
12×rem-sqrt-square_binary64
log-rec_binary64 unpow1/2_binary64 associate-+r-_binary64
cube-unmult_binary64 distribute-neg-in_binary64
log-pow_binary64
pow-plus_binary64 +-rgt-identity_binary64
unpow2_binary64 unpow1_binary64 difference-of-squares_binary64 distribute-rgt1-in_binary64
remove-double-div_binary64 associate-+l-_binary64
1-exp_binary64 exp-1-e_binary64 sub0-neg_binary64 +-lft-identity_binary64 div0_binary64 difference-of-sqr-1_binary64 distribute-lft1-in_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 remove-double-neg_binary64 --rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 associate--r-_binary64 associate--l-_binary64
Counts
143 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02012489
15162213
218162188
344792188
448692188
550692188

prune62.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New70171
Fresh156
Picked101
Done000
Total72678
Error
0.0b
Counts
78 → 6
Compiler

Compiled 1044 to 533 computations (48.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 e e) (pow.f64 (cos.f64 v) 2))
0.1b
(*.f64 e (cos.f64 v))
0.1b
(*.f64 e (sin.f64 v))
0.3b
(pow.f64 (cos.f64 v) 2)

rewrite139.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
22×add-exp-log_binary64
18×add-sqr-sqrt_binary64
14×associate-*r*_binary64
13×add-cbrt-cube_binary64
12×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×prod-exp_binary64
pow1_binary64
unpow-prod-down_binary64 associate-*l*_binary64
unswap-sqr_binary64
cbrt-unprod_binary64
add-log-exp_binary64
pow-unpow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64 pow-prod-down_binary64 *-commutative_binary64
pow-pow_binary64 pow2_binary64
Counts
4 → 84
Calls

4 calls:

8.0ms
(*.f64 (*.f64 e e) (pow.f64 (cos.f64 v) 2))
6.0ms
(*.f64 e (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
2.0ms
(pow.f64 (cos.f64 v) 2)
Compiler

Compiled 2301 to 1105 computations (52% saved)

series87.0ms (1.8%)

Error
0.0b
Counts
4 → 23
Calls

4 calls:

24.0ms
(*.f64 (*.f64 e e) (pow.f64 (cos.f64 v) 2))
23.0ms
(*.f64 e (sin.f64 v))
20.0ms
(*.f64 e (cos.f64 v))
9.0ms
(pow.f64 (cos.f64 v) 2)
Compiler

Compiled 1300 to 955 computations (26.5% saved)

simplify119.0ms (2.5%)

Algorithm
egg-herbie
Rules
330×*-commutative_binary64
282×sqr-pow_binary64
268×associate-/l*_binary64
233×distribute-rgt-in_binary64
218×times-frac_binary64
205×associate-*l*_binary64
191×log-prod_binary64 associate-/l/_binary64
187×exp-prod_binary64
174×distribute-lft-in_binary64
150×associate-*r*_binary64
127×+-commutative_binary64
121×cube-prod_binary64 associate-/r*_binary64
112×associate-/r/_binary64
110×unswap-sqr_binary64
103×pow-sqr_binary64 distribute-rgt-neg-in_binary64
96×associate-+l+_binary64
84×distribute-lft-neg-in_binary64 associate-*r/_binary64
83×cancel-sign-sub-inv_binary64
66×associate-+r+_binary64
63×rem-sqrt-square_binary64
61×distribute-lft-out_binary64
51×log-pow_binary64
48×unpow3_binary64
35×sub-neg_binary64 distribute-rgt-out_binary64
34×associate-*l/_binary64
31×neg-mul-1_binary64
30×swap-sqr_binary64
29×neg-sub0_binary64
28×cube-mult_binary64
27×*-lft-identity_binary64
24×*-rgt-identity_binary64
20×pow-plus_binary64
19×distribute-neg-in_binary64
17×unpow1/2_binary64
16×associate--r+_binary64
12×cube-unmult_binary64 associate-+l-_binary64
11×count-2_binary64
10×distribute-lft-out--_binary64
distribute-lft-neg-out_binary64 associate-+r-_binary64
unpow2_binary64
unpow1_binary64 distribute-rgt-out--_binary64 associate--l+_binary64
distribute-rgt1-in_binary64
/-rgt-identity_binary64 +-rgt-identity_binary64 distribute-lft1-in_binary64
unsub-neg_binary64 sub0-neg_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-square-sqrt_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 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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 mul-1-neg_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 associate--r-_binary64 associate--l-_binary64
Counts
107 → 73
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01221162
1272958
2805931
31384928
42336901
54490901
64937901
74894901

prune60.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh055
Picked011
Done000
Total73679
Error
0.0b
Counts
79 → 6
Compiler

Compiled 1227 to 602 computations (50.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b
(*.f64 e (cos.f64 v))
0.1b
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
0.3b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))

rewrite165.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
84×times-frac_binary64
57×add-sqr-sqrt_binary64
55×add-cube-cbrt_binary64 *-un-lft-identity_binary64
16×associate-/r*_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
div-inv_binary64 associate-/l*_binary64
pow1_binary64
div-exp_binary64 cbrt-undiv_binary64
add-log-exp_binary64 associate-*l*_binary64 associate-*r*_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l/_binary64
associate-/r/_binary64 flip3-+_binary64 flip-+_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
3 → 117
Calls

3 calls:

9.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
6.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 2640 to 1096 computations (58.5% saved)

series115.0ms (2.4%)

Error
0.0b
Counts
3 → 28
Calls

3 calls:

45.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
36.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
15.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1144 to 822 computations (28.1% saved)

simplify148.0ms (3.1%)

Algorithm
egg-herbie
Rules
627×associate-/r/_binary64
541×associate-*l/_binary64
539×associate-/r*_binary64
221×cancel-sign-sub-inv_binary64
140×associate-/l*_binary64
132×associate-*r*_binary64
129×*-commutative_binary64
121×sub-neg_binary64
116×associate-*l*_binary64
114×associate-/l/_binary64
106×distribute-rgt-neg-in_binary64
96×neg-mul-1_binary64 neg-sub0_binary64
93×unswap-sqr_binary64
92×distribute-rgt-in_binary64
90×distribute-lft-neg-in_binary64
70×distribute-lft-in_binary64
65×times-frac_binary64
63×associate-*r/_binary64
49×*-rgt-identity_binary64
48×log-prod_binary64
46×log-div_binary64
44×+-commutative_binary64
43×cube-prod_binary64
40×sqr-pow_binary64
34×cube-div_binary64 /-rgt-identity_binary64
31×unsub-neg_binary64 associate--l+_binary64
29×exp-prod_binary64 distribute-neg-frac_binary64 distribute-rgt-out_binary64
22×associate-+l+_binary64
20×distribute-rgt-out--_binary64
18×*-lft-identity_binary64
15×div-sub_binary64 associate--r+_binary64 associate-+r+_binary64
14×distribute-lft-out--_binary64 distribute-lft-out_binary64
13×unpow3_binary64 swap-sqr_binary64
11×distribute-neg-in_binary64
10×cube-mult_binary64 distribute-lft-neg-out_binary64
cube-unmult_binary64
log-rec_binary64
unpow1/2_binary64
log-pow_binary64 rem-sqrt-square_binary64 distribute-rgt1-in_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64 remove-double-div_binary64
1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 div0_binary64 pow-sqr_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_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 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 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-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 count-2_binary64 associate--l-_binary64
Counts
145 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02613850
16333626
222123595
346613595
449553595

prune110.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1123115
Fresh314
Picked011
Done011
Total1156121
Error
0.0b
Counts
121 → 6
Compiler

Compiled 2262 to 933 computations (58.8% saved)

regimes1.0s (20.8%)

Accuracy

Total 0.1b remaining (74.1%)

Threshold costs 0.1b (74.1%)

Compiler

Compiled 10488 to 7444 computations (29% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64 sub-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 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01836
12636
22736
32536

end1.0ms (0%)

Compiler

Compiled 23 to 17 computations (26.1% saved)

sample1.9s (40%)

Algorithm
intervals
Results
611.0ms2037×body1024valid
326.0ms4467×body128valid
205.0ms992×body512valid
165.0ms8000×pre128true
75.0ms498×body256valid
4.0msbody2048valid
Compiler

Compiled 149 to 115 computations (22.8% saved)

Profiling

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