Details

Time bar (total: 4.6s)

analyze43.0ms (1%)

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)

sample57.0ms (1.2%)

Algorithm
intervals
Results
22.0ms76×body1024valid
10.0ms140×body128valid
6.0ms28×body512valid
4.0ms256×pre128true
2.0ms12×body256valid
Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify10.0ms (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))

rewrite79.0ms (1.7%)

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)

series85.0ms (1.9%)

Error
0.1b
Counts
3 → 23
Calls

3 calls:

33.0ms
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
21.0ms
(*.f64 e (sin.f64 v))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 772 to 551 computations (28.6% saved)

simplify115.0ms (2.5%)

Algorithm
egg-herbie
Rules
298×cancel-sign-sub-inv_binary64
288×associate-*l/_binary64
271×associate-/r*_binary64
267×*-commutative_binary64
251×unswap-sqr_binary64
223×associate-/l/_binary64
218×distribute-rgt-in_binary64
210×distribute-rgt-neg-in_binary64
195×associate-/r/_binary64
191×associate-*r/_binary64
181×distribute-lft-neg-in_binary64
136×sub-neg_binary64
118×associate-*l*_binary64
108×associate-*r*_binary64
95×distribute-rgt-out_binary64
88×associate-/l*_binary64
71×sqr-pow_binary64
63×*-rgt-identity_binary64 distribute-neg-frac_binary64
61×neg-mul-1_binary64 neg-sub0_binary64
60×log-prod_binary64
53×log-div_binary64 *-lft-identity_binary64 distribute-lft-out_binary64
52×cube-prod_binary64
51×distribute-rgt-out--_binary64
50×cube-div_binary64
46×times-frac_binary64
42×exp-prod_binary64
38×distribute-lft-out--_binary64
35×div-sub_binary64 +-commutative_binary64
29×swap-sqr_binary64
28×associate-+l+_binary64
25×/-rgt-identity_binary64 associate-+r+_binary64
24×distribute-lft-in_binary64
23×unpow3_binary64
22×associate-+l-_binary64
21×associate--l+_binary64
18×cube-mult_binary64
17×associate-+r-_binary64
14×unsub-neg_binary64
13×difference-of-squares_binary64
12×+-rgt-identity_binary64
11×log-rec_binary64 distribute-rgt1-in_binary64
cube-unmult_binary64 pow-sqr_binary64 distribute-lft-neg-out_binary64
log-pow_binary64 distribute-neg-in_binary64 distribute-lft1-in_binary64
sub0-neg_binary64 associate--r+_binary64
unpow1/2_binary64 associate--l-_binary64
distribute-frac-neg_binary64
rem-sqrt-square_binary64 distribute-neg-out_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64
div0_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64
exp-sum_binary64 1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 +-inverses_binary64 remove-double-div_binary64 distribute-rgt-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 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 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 count-2_binary64 associate--r-_binary64
Counts
82 → 38
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01331248
13381095
212001079
331631070
449441070
549911070
649541070

prune43.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New31738
Fresh000
Picked101
Done000
Total32739
Error
0.0b
Counts
39 → 7
Compiler

Compiled 656 to 315 computations (52% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite117.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
28×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64 *-un-lft-identity_binary64
19×times-frac_binary64
18×associate-*r*_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
associate-*l*_binary64
associate-/r/_binary64
prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 associate-/l*_binary64 associate-/r*_binary64
pow-prod-down_binary64 div-exp_binary64 cbrt-undiv_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64 *-commutative_binary64
associate-*r/_binary64 frac-2neg_binary64 clear-num_binary64
Counts
3 → 81
Calls

3 calls:

10.0ms
(*.f64 e (/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1)))
6.0ms
(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1618 to 677 computations (58.2% saved)

series100.0ms (2.2%)

Error
0.0b
Counts
3 → 26
Calls

3 calls:

35.0ms
(*.f64 e (/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1)))
29.0ms
(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 988 to 681 computations (31.1% saved)

simplify148.0ms (3.3%)

Algorithm
egg-herbie
Rules
537×times-frac_binary64
469×associate-/l*_binary64
260×associate-*r/_binary64
241×cancel-sign-sub-inv_binary64
238×associate-*l/_binary64
236×associate-/r*_binary64
170×sub-neg_binary64
165×associate-*l*_binary64
140×associate-*r*_binary64
133×neg-mul-1_binary64
128×distribute-rgt-neg-in_binary64
122×neg-sub0_binary64
115×associate-/r/_binary64
112×distribute-lft-neg-in_binary64
105×associate-/l/_binary64
90×div-sub_binary64
84×*-commutative_binary64
77×unswap-sqr_binary64
69×sqr-pow_binary64
68×log-prod_binary64
67×cube-prod_binary64
61×*-lft-identity_binary64
55×log-div_binary64
54×exp-prod_binary64
52×/-rgt-identity_binary64 *-rgt-identity_binary64
47×cube-div_binary64 distribute-rgt-in_binary64
37×distribute-rgt-out_binary64
34×associate-+l+_binary64
29×associate-+l-_binary64 +-commutative_binary64
28×distribute-lft-in_binary64 associate--l+_binary64
26×unsub-neg_binary64 associate-+r-_binary64
24×distribute-rgt-out--_binary64
23×unpow3_binary64
22×distribute-lft-out_binary64
21×distribute-neg-frac_binary64
20×cube-mult_binary64
19×distribute-lft-out--_binary64
17×+-rgt-identity_binary64
16×associate--r+_binary64
11×distribute-lft-neg-out_binary64
10×log-rec_binary64 sub0-neg_binary64 swap-sqr_binary64
pow-sqr_binary64
log-pow_binary64
rem-sqrt-square_binary64
unpow1/2_binary64 cube-unmult_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64 remove-double-div_binary64
exp-sum_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft1-in_binary64 associate--l-_binary64
1-exp_binary64 exp-1-e_binary64 difference-of-sqr-1_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 mul-1-neg_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 count-2_binary64 associate--r-_binary64 associate-+r+_binary64
Counts
107 → 74
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01682148
14231954
213941932
343901932
446971932
549971932
649461932

prune77.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New72274
Fresh156
Picked011
Done000
Total73881
Error
0.0b
Counts
81 → 8
Compiler

Compiled 1426 to 635 computations (55.5% 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))
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))

rewrite171.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
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:

8.0ms
(/.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)

series103.0ms (2.3%)

Error
0.0b
Counts
3 → 26
Calls

3 calls:

37.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
35.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 846 to 594 computations (29.8% saved)

simplify141.0ms (3.1%)

Algorithm
egg-herbie
Rules
576×associate-/r/_binary64
483×associate-*l/_binary64
422×associate-/r*_binary64
392×*-commutative_binary64
340×cancel-sign-sub-inv_binary64
268×associate-*r/_binary64
249×unswap-sqr_binary64
140×sub-neg_binary64
121×associate-/l*_binary64
113×associate-/l/_binary64
108×associate-*r*_binary64
102×associate-*l*_binary64
78×distribute-rgt-neg-in_binary64
76×*-rgt-identity_binary64
72×distribute-rgt-in_binary64
67×sqr-pow_binary64
66×distribute-lft-neg-in_binary64
59×neg-mul-1_binary64 neg-sub0_binary64
54×distribute-lft-in_binary64
53×+-commutative_binary64
50×log-prod_binary64
49×times-frac_binary64
45×*-lft-identity_binary64
43×cube-prod_binary64
42×log-div_binary64
40×/-rgt-identity_binary64 associate-+l+_binary64
39×associate-+r+_binary64
33×exp-prod_binary64 unsub-neg_binary64 swap-sqr_binary64
31×cube-div_binary64
26×associate--l+_binary64
24×associate-+l-_binary64
23×distribute-rgt-out_binary64 associate-+r-_binary64
20×distribute-rgt-out--_binary64
17×distribute-neg-frac_binary64
16×+-rgt-identity_binary64
15×difference-of-squares_binary64
14×div-sub_binary64 distribute-lft-out--_binary64
11×associate--r+_binary64
10×unpow3_binary64 distribute-lft-out_binary64
sub0-neg_binary64 pow-sqr_binary64
cube-unmult_binary64 cube-mult_binary64 distribute-neg-in_binary64 distribute-lft-neg-out_binary64
log-rec_binary64
unpow1/2_binary64
log-pow_binary64 rem-sqrt-square_binary64 remove-double-div_binary64 distribute-rgt1-in_binary64 associate--l-_binary64
unpow2_binary64 unpow1_binary64 mul0-rgt_binary64 mul0-lft_binary64
pow-plus_binary64 associate--r-_binary64
1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 --rgt-identity_binary64 div0_binary64 +-inverses_binary64 difference-of-sqr--1_binary64 distribute-rgt-neg-out_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 +-lft-identity_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 count-2_binary64
Counts
143 → 113
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02323686
15483462
218263434
340293434
450503434

prune120.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1112113
Fresh246
Picked011
Done011
Total1138121
Error
0b
Counts
121 → 8
Compiler

Compiled 2283 to 941 computations (58.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 e (cos.f64 v))
0.1b
(*.f64 e (sin.f64 v))
0.2b
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v)))
0.7b
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))

rewrite173.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
36×times-frac_binary64
34×add-exp-log_binary64
30×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64 *-un-lft-identity_binary64
22×add-cbrt-cube_binary64
14×div-exp_binary64
pow1_binary64
associate-/r*_binary64
cbrt-undiv_binary64
prod-exp_binary64 div-inv_binary64 associate-/l*_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 cbrt-unprod_binary64
1-exp_binary64 rec-exp_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l/_binary64 pow-prod-down_binary64 unswap-sqr_binary64 *-commutative_binary64
inv-pow_binary64 pow-flip_binary64 associate-/r/_binary64 flip3-+_binary64 flip-+_binary64
Counts
4 → 115
Calls

4 calls:

9.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
8.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v)))
4.0ms
(*.f64 e (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 2409 to 1105 computations (54.1% saved)

series133.0ms (2.9%)

Error
0b
Counts
4 → 33
Calls

4 calls:

41.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v)))
35.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
21.0ms
(*.f64 e (sin.f64 v))
17.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1126 to 830 computations (26.3% saved)

simplify148.0ms (3.2%)

Algorithm
egg-herbie
Rules
662×associate-/l*_binary64
544×associate-/r*_binary64
399×associate-/r/_binary64
280×associate-/l/_binary64
228×sub-neg_binary64
152×associate-*r*_binary64
144×cancel-sign-sub-inv_binary64 associate-*l*_binary64
138×div-sub_binary64
110×distribute-rgt-in_binary64
94×neg-mul-1_binary64 *-commutative_binary64
93×distribute-rgt-neg-in_binary64
90×neg-sub0_binary64
85×distribute-lft-in_binary64
84×sqr-pow_binary64
81×distribute-lft-neg-in_binary64
79×log-div_binary64
74×unswap-sqr_binary64
73×*-rgt-identity_binary64
72×/-rgt-identity_binary64
68×cube-div_binary64
67×associate-*l/_binary64
56×log-prod_binary64 exp-prod_binary64 times-frac_binary64
54×cube-prod_binary64 *-lft-identity_binary64
48×associate-*r/_binary64
45×unsub-neg_binary64
32×distribute-rgt-out_binary64
31×+-commutative_binary64
26×remove-double-div_binary64
24×distribute-lft-out_binary64
23×unpow3_binary64 distribute-neg-frac_binary64 distribute-rgt-out--_binary64
21×cube-mult_binary64 swap-sqr_binary64
20×distribute-lft-out--_binary64
17×log-rec_binary64
15×distribute-neg-in_binary64
13×associate--l+_binary64 associate-+r+_binary64
12×rem-sqrt-square_binary64 pow-sqr_binary64
10×associate--r+_binary64
unpow1/2_binary64 cube-unmult_binary64 distribute-lft-neg-out_binary64
associate-+l+_binary64
log-pow_binary64
distribute-rgt1-in_binary64
pow-plus_binary64 div0_binary64 associate--r-_binary64 associate-+r-_binary64
unpow2_binary64 unpow1_binary64
exp-sum_binary64 sub0-neg_binary64 +-lft-identity_binary64
1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-+l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-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 mul-1-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 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 associate--l-_binary64
Counts
148 → 97
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01993103
14862686
217072644
344572644
447042644
549952644

prune78.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh055
Picked011
Done022
Total978105
Error
0b
Counts
105 → 8
Compiler

Compiled 1318 to 626 computations (52.5% saved)

regimes629.0ms (13.8%)

Accuracy

Total 0.1b remaining (75.7%)

Threshold costs 0.1b (75.7%)

Compiler

Compiled 8367 to 5770 computations (31% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_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 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 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
11721
21621

end1.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.9s (42.4%)

Algorithm
intervals
Results
586.0ms1993×body1024valid
341.0ms4527×body128valid
217.0ms985×body512valid
142.0ms8000×pre128true
76.0ms492×body256valid
2.0msbody2048valid
Compiler

Compiled 184 to 138 computations (25% saved)

Profiling

Loading profile data...