Details

Time bar (total: 11.6s)

analyze1.7s (14.8%)

Algorithm
search
egg-herbie
Rules
912×unswap-sqr_binary64
752×sqr-pow_binary64
360×cube-prod_binary64
336×unpow3_binary64
320×cube-mult_binary64
257×*-commutative_binary64
208×pow-sqr_binary64
200×associate-*l*_binary64
192×pow-plus_binary64
168×associate-*r*_binary64
120×rem-sqrt-square_binary64
40×unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-unmult_binary64
16×swap-sqr_binary64
associate-/l*_binary64
+-commutative_binary64
associate-/r/_binary64 associate-*l/_binary64 associate-*r/_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-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--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
039136
186136
2197136
3361136
4698136
5868136
61296136
72649136
82812136
93009136
103411136
114084136
124396136
134716136
144940136
154958136
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
25%62.4%12.6%8
31.2%56.2%12.6%9
34.3%53%12.6%10
42.9%44.5%12.6%11
46.8%40.6%12.6%12
47.8%39.6%12.6%13
52.6%34.8%12.6%14
Compiler

Compiled 22 to 20 computations (9.1% saved)

sample176.0ms (1.5%)

Algorithm
intervals
Results
47.0ms48×body1024valid
43.0ms48×body1024invalid
21.0ms165×body128valid
13.0ms23×body512valid
13.0msbody2048valid
12.0ms19×body512invalid
4.0ms12×body256invalid
3.0ms11×body256valid
2.0ms19×body128invalid
Compiler

Compiled 43 to 42 computations (2.3% saved)

simplify150.0ms (1.3%)

Algorithm
egg-herbie
Rules
1308×sqr-pow_binary64
632×pow-sqr_binary64
484×unswap-sqr_binary64
332×cube-prod_binary64
271×*-commutative_binary64
238×unpow3_binary64 cube-mult_binary64
186×associate-*l*_binary64
120×associate-*r*_binary64
84×pow-plus_binary64
42×rem-sqrt-square_binary64
14×unpow2_binary64 unpow1/2_binary64 unpow1_binary64
10×cube-unmult_binary64
swap-sqr_binary64
associate-/l*_binary64
1-exp_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-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--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
01634
13034
26434
311034
419934
543534
661534
7106834
8108334
9125534
10145634
11177834
12219834
13271234
14336034
15357234
16370234
17373434
18373834
19373834
20455734
21525234

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
18.9b
Counts
1 → 1
Compiler

Compiled 21 to 19 computations (9.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 PI.f64 (/.f64 angle 180))
0.3b
(*.f64 PI.f64 (/.f64 angle 180))
23.2b
(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
23.2b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite352.0ms (3%)

Algorithm
rewrite-expression-head
Error
18.1b
Rules
30×add-sqr-sqrt_binary64
26×associate-*r*_binary64
20×add-cube-cbrt_binary64 *-un-lft-identity_binary64 times-frac_binary64
14×add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
associate-*l*_binary64
add-log-exp_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
pow-prod-down_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 78
Calls

4 calls:

7.0ms
(*.f64 PI.f64 (/.f64 angle 180))
7.0ms
(*.f64 PI.f64 (/.f64 angle 180))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms
(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
Compiler

Compiled 2070 to 1467 computations (29.1% saved)

series56.0ms (0.5%)

Error
18.2b
Counts
4 → 15
Calls

4 calls:

13.0ms
(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
11.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
9.0ms
(*.f64 PI.f64 (/.f64 angle 180))
9.0ms
(*.f64 PI.f64 (/.f64 angle 180))
Compiler

Compiled 804 to 697 computations (13.3% saved)

simplify87.0ms (0.8%)

Algorithm
egg-herbie
Rules
480×associate-*l*_binary64
447×associate-*r*_binary64
390×associate-/l/_binary64
341×unswap-sqr_binary64
329×distribute-rgt-neg-in_binary64
312×associate-/r/_binary64
308×distribute-lft-neg-in_binary64
248×cancel-sign-sub-inv_binary64
180×neg-mul-1_binary64
169×associate-*r/_binary64
158×associate-*l/_binary64
157×associate-/l*_binary64
130×*-commutative_binary64
77×log-prod_binary64
61×cube-prod_binary64
54×times-frac_binary64
46×sqr-pow_binary64
43×log-div_binary64
42×associate-/r*_binary64
41×cube-div_binary64
40×*-rgt-identity_binary64
38×exp-prod_binary64 *-lft-identity_binary64
37×neg-sub0_binary64 sub-neg_binary64
35×distribute-rgt-out--_binary64
23×distribute-rgt-out_binary64
22×distribute-lft-out--_binary64
21×unpow3_binary64
17×distribute-lft-out_binary64
16×/-rgt-identity_binary64
15×swap-sqr_binary64
14×cube-unmult_binary64
13×cube-mult_binary64
12×+-commutative_binary64
11×pow-plus_binary64
associate-+l+_binary64 associate-+r+_binary64
associate-+l-_binary64
log-pow_binary64 pow-sqr_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-+r-_binary64
rem-sqrt-square_binary64 +-rgt-identity_binary64
unpow1/2_binary64 sub0-neg_binary64 distribute-lft-neg-out_binary64
log-rec_binary64 unsub-neg_binary64 count-2_binary64 associate--l+_binary64
unpow2_binary64 unpow1_binary64 remove-double-div_binary64 distribute-rgt1-in_binary64 associate--r+_binary64
exp-sum_binary64 1-exp_binary64 exp-1-e_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 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 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 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-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
93 → 55
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01131229
12431091
27371091
324631088
446521085
549531085

prune116.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New371855
Fresh000
Picked101
Done000
Total381856
Error
18.2b
Counts
56 → 18
Compiler

Compiled 1656 to 1208 computations (27.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
23.2b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
23.3b
(cos.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))

rewrite150.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
18.2b
Rules
add-sqr-sqrt_binary64
pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64 sqrt-prod_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
Counts
4 → 40
Calls

4 calls:

3.0ms
(cos.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1158 to 740 computations (36.1% saved)

series43.0ms (0.4%)

Error
18.2b
Counts
4 → 9
Calls

4 calls:

13.0ms
(cos.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))
11.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 592 to 487 computations (17.7% saved)

simplify74.0ms (0.6%)

Algorithm
egg-herbie
Rules
928×distribute-rgt-neg-in_binary64
873×distribute-lft-neg-in_binary64
567×cancel-sign-sub-inv_binary64
504×neg-mul-1_binary64
496×neg-sub0_binary64
360×unswap-sqr_binary64
278×associate-*r*_binary64
263×associate-*l*_binary64
107×sub-neg_binary64
77×*-commutative_binary64
55×distribute-neg-in_binary64 distribute-lft-neg-out_binary64
43×sqr-pow_binary64
40×distribute-rgt-out--_binary64
29×distribute-rgt-out_binary64
26×cube-prod_binary64 distribute-lft-out--_binary64
22×associate-/l*_binary64
20×pow-plus_binary64
17×unpow3_binary64
16×distribute-lft-out_binary64
13×cube-unmult_binary64 unsub-neg_binary64
12×associate-/r*_binary64 +-commutative_binary64
10×distribute-rgt-neg-out_binary64
swap-sqr_binary64 associate-/r/_binary64
cube-mult_binary64
associate-+l-_binary64 associate-+l+_binary64
log-pow_binary64 log-prod_binary64 pow-sqr_binary64 associate-/l/_binary64
rem-sqrt-square_binary64 +-rgt-identity_binary64 associate-*l/_binary64 associate-+r-_binary64
unpow2_binary64 unpow1_binary64 exp-prod_binary64 sub0-neg_binary64 associate-*r/_binary64
unpow1/2_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
1-exp_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-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
49 → 17
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
067607
1131483
2293483
31291479
42898476
54619473
65172473

prune73.0ms (0.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New15217
Fresh01717
Picked011
Done000
Total152035
Error
18.2b
Counts
35 → 20
Compiler

Compiled 1010 to 781 computations (22.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 1/180 (*.f64 angle PI.f64))
0.4b
(log.f64 (exp.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))))
22.9b
(cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
23.2b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite163.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
18.2b
Rules
10×pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 log-pow_binary64
exp-prod_binary64 log-prod_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
rem-log-exp_binary64 associate-*r*_binary64 *-commutative_binary64
Counts
4 → 47
Calls

4 calls:

5.0ms
(*.f64 1/180 (*.f64 angle PI.f64))
3.0ms
(log.f64 (exp.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))))
2.0ms
(cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
2.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
Compiler

Compiled 1269 to 900 computations (29.1% saved)

series88.0ms (0.8%)

Error
17.8b
Counts
4 → 17
Calls

4 calls:

22.0ms
(log.f64 (exp.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))))
14.0ms
(cos.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
11.0ms
(*.f64 1/180 (*.f64 angle PI.f64))
11.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
Compiler

Compiled 1028 to 885 computations (13.9% saved)

simplify77.0ms (0.7%)

Algorithm
egg-herbie
Rules
639×associate-*l*_binary64
574×cancel-sign-sub-inv_binary64
540×associate-*r*_binary64
412×unswap-sqr_binary64
380×distribute-rgt-neg-in_binary64
373×distribute-lft-neg-in_binary64
199×neg-mul-1_binary64
194×neg-sub0_binary64
162×*-commutative_binary64
116×sqr-pow_binary64
108×sub-neg_binary64
55×log-prod_binary64
48×exp-prod_binary64 cube-prod_binary64
38×distribute-rgt-out--_binary64
36×distribute-rgt-out_binary64
28×distribute-lft-out--_binary64
27×swap-sqr_binary64
24×unpow3_binary64 pow-sqr_binary64 associate-/l*_binary64
19×+-commutative_binary64
17×distribute-lft-out_binary64
16×cube-mult_binary64
15×associate-+l+_binary64
14×cube-unmult_binary64
13×unsub-neg_binary64
11×log-pow_binary64 pow-plus_binary64 associate-+r+_binary64
10×associate-/r*_binary64
associate-/l/_binary64 associate-/r/_binary64
associate-*r/_binary64
distribute-rgt-neg-out_binary64 associate-+l-_binary64
rem-log-exp_binary64
exp-sum_binary64 +-rgt-identity_binary64 distribute-lft-neg-out_binary64 count-2_binary64 associate-+r-_binary64
sub0-neg_binary64 associate-*l/_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-exp-log_binary64 rem-sqrt-square_binary64 times-frac_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate--l+_binary64 associate--r+_binary64
1-exp_binary64 exp-1-e_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 e-exp-1_binary64 exp-0_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_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-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
64 → 27
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0102932
1188814
2521814
32006808
43988808
55156808

prune90.0ms (0.8%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New24327
Fresh41418
Picked101
Done011
Total291847
Error
18.2b
Counts
47 → 18
Compiler

Compiled 1107 to 850 computations (23.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(cbrt.f64 (pow.f64 PI.f64 3/2))
1.0b
(sqrt.f64 PI.f64)
23.2b
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
23.3b
(cos.f64 (*.f64 (cbrt.f64 (pow.f64 PI.f64 3/2)) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))

rewrite138.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
18.1b
Rules
add-sqr-sqrt_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64 cbrt-prod_binary64
pow1_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
sqrt-prod_binary64 unpow-prod-down_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 pow1/3_binary64 sqr-pow_binary64
Counts
4 → 42
Calls

4 calls:

3.0ms
(cos.f64 (*.f64 (cbrt.f64 (pow.f64 PI.f64 3/2)) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))
2.0ms
(cbrt.f64 (pow.f64 PI.f64 3/2))
1.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1373 to 988 computations (28% saved)

series46.0ms (0.4%)

Error
18.2b
Counts
4 → 9
Calls

4 calls:

14.0ms
(cos.f64 (*.f64 (cbrt.f64 (pow.f64 PI.f64 3/2)) (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64))))
12.0ms
(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(cbrt.f64 (pow.f64 PI.f64 3/2))
Compiler

Compiled 612 to 517 computations (15.5% saved)

simplify93.0ms (0.8%)

Algorithm
egg-herbie
Rules
538×distribute-rgt-neg-in_binary64
530×distribute-lft-neg-in_binary64
524×unswap-sqr_binary64
385×associate-*r*_binary64
382×neg-mul-1_binary64
374×neg-sub0_binary64
361×associate-*l*_binary64
354×cancel-sign-sub-inv_binary64
332×sub-neg_binary64
303×distribute-rgt-in_binary64
132×sqr-pow_binary64
83×swap-sqr_binary64
82×*-commutative_binary64
61×unsub-neg_binary64 distribute-lft-neg-out_binary64
56×distribute-neg-in_binary64
50×distribute-rgt-out--_binary64
44×distribute-rgt-out_binary64
37×associate-/l*_binary64
35×pow-plus_binary64 cube-prod_binary64
32×pow-sqr_binary64
27×unpow3_binary64 distribute-lft-out_binary64
26×distribute-lft-out--_binary64
24×cube-unmult_binary64
12×associate-/r*_binary64 +-commutative_binary64
11×rem-sqrt-square_binary64 associate-/r/_binary64 associate-*l/_binary64
cube-mult_binary64
distribute-rgt-neg-out_binary64 associate-*r/_binary64
unpow2_binary64 pow-base-1_binary64 associate-+l-_binary64 associate-+l+_binary64
log-pow_binary64 log-prod_binary64 associate-/l/_binary64
+-rgt-identity_binary64 associate-+r-_binary64
unpow1_binary64 exp-prod_binary64 remove-double-neg_binary64 sub0-neg_binary64
unpow1/2_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
1-exp_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 sqr-abs_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 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
51 → 22
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
093719
1170653
2377653
31727649
44109544
54324541
65116541

prune59.0ms (0.5%)

Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New20222
Fresh11516
Picked011
Done011
Total211940
Error
18.1b
Counts
40 → 19
Compiler

Compiled 614 to 432 computations (29.6% saved)

regimes1.8s (15.7%)

Accuracy

Total 1.2b remaining (5.7%)

Threshold costs 0b (0%)

Compiler

Compiled 28385 to 24529 computations (13.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (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
02667
13367
23367

end2.0ms (0%)

Compiler

Compiled 39 to 34 computations (12.8% saved)

sample6.0s (51.3%)

Algorithm
intervals
Results
1.5s1618×body1024valid
1.2s1324×body1024invalid
636.0ms5020×body128valid
456.0ms758×body512valid
393.0ms648×body512invalid
288.0ms212×body2048valid
128.0ms389×body256valid
123.0ms333×body256invalid
83.0ms667×body128invalid
14.0msbody4096valid
Compiler

Compiled 612 to 535 computations (12.6% saved)

Profiling

Loading profile data...