Details

Time bar (total: 5.0s)

analyze40.0ms (0.8%)

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)

sample55.0ms (1.1%)

Algorithm
intervals
Results
19.0ms67×body1024valid
10.0ms143×body128valid
7.0ms34×body512valid
4.0ms256×pre128true
2.0ms12×body256valid
Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify14.0ms (0.3%)

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
0.2b
Counts
1 → 1
Compiler

Compiled 11 to 9 computations (18.2% saved)

localize8.0ms (0.2%)

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))

rewrite83.0ms (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))))
5.0ms
(*.f64 e (cos.f64 v))
4.0ms
(*.f64 e (sin.f64 v))
Compiler

Compiled 1015 to 368 computations (63.7% saved)

series103.0ms (2.1%)

Error
0.2b
Counts
3 → 27
Calls

3 calls:

45.0ms
(/.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 1223 to 892 computations (27.1% saved)

simplify87.0ms (1.7%)

Algorithm
egg-herbie
Rules
526×associate-/r*_binary64
400×associate-*l/_binary64
303×associate-/r/_binary64
290×associate-/l/_binary64
240×cancel-sign-sub-inv_binary64
147×associate-*r*_binary64
143×associate-*l*_binary64
135×associate-/l*_binary64
126×unswap-sqr_binary64
122×distribute-rgt-neg-in_binary64
104×distribute-lft-neg-in_binary64
88×sub-neg_binary64
84×*-commutative_binary64
82×times-frac_binary64
80×distribute-rgt-in_binary64
56×distribute-lft-in_binary64
52×+-commutative_binary64
47×log-div_binary64 log-prod_binary64
46×cube-prod_binary64 sqr-pow_binary64
43×cube-div_binary64
40×distribute-neg-frac_binary64 associate-*r/_binary64
37×neg-mul-1_binary64 neg-sub0_binary64
36×div-sub_binary64
34×associate--l+_binary64
33×associate-+r+_binary64
32×exp-prod_binary64 *-rgt-identity_binary64 associate-+l+_binary64
26×distribute-neg-in_binary64 distribute-rgt-out_binary64
23×*-lft-identity_binary64
22×associate--r+_binary64
19×unsub-neg_binary64 distribute-rgt-out--_binary64
18×distribute-lft-out--_binary64
16×unpow3_binary64 /-rgt-identity_binary64
14×distribute-lft-out_binary64
13×cube-mult_binary64 distribute-lft-neg-out_binary64
log-rec_binary64 swap-sqr_binary64
cube-unmult_binary64
log-pow_binary64 unpow1/2_binary64 rem-sqrt-square_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64
pow-sqr_binary64 distribute-rgt1-in_binary64
1-exp_binary64 exp-1-e_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 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_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
86 → 42
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01851642
14961489
219211464
347931464
449631464

prune52.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New34842
Fresh000
Picked101
Done000
Total35843
Error
0.0b
Counts
43 → 8
Compiler

Compiled 971 to 542 computations (44.2% saved)

localize8.0ms (0.2%)

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)))

rewrite152.0ms (3%)

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:

13.0ms
(*.f64 e (/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1)))
10.0ms
(/.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)

series132.0ms (2.7%)

Error
0.0b
Counts
3 → 30
Calls

3 calls:

44.0ms
(*.f64 e (/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1)))
41.0ms
(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1670 to 1217 computations (27.1% saved)

simplify86.0ms (1.7%)

Algorithm
egg-herbie
Rules
634×associate-/r*_binary64
339×cancel-sign-sub-inv_binary64
304×associate-/r/_binary64
187×associate-*r*_binary64
186×associate-*l*_binary64
175×associate-/l/_binary64
155×distribute-rgt-neg-in_binary64
138×associate-/l*_binary64
135×distribute-lft-neg-in_binary64
131×unswap-sqr_binary64
128×sub-neg_binary64
119×*-commutative_binary64
97×distribute-rgt-in_binary64
93×associate-*r/_binary64
90×times-frac_binary64
87×+-commutative_binary64
69×associate-*l/_binary64
66×distribute-lft-in_binary64 associate-+r+_binary64
63×distribute-neg-frac_binary64
58×associate-+l+_binary64
52×associate--l+_binary64
48×distribute-neg-in_binary64
46×sqr-pow_binary64
43×neg-mul-1_binary64 neg-sub0_binary64
37×distribute-rgt-out_binary64
36×associate--r+_binary64
34×*-rgt-identity_binary64 *-lft-identity_binary64
27×unsub-neg_binary64
24×distribute-rgt-out--_binary64
23×log-prod_binary64
22×distribute-lft-out_binary64
19×distribute-lft-out--_binary64
18×cube-prod_binary64
17×exp-prod_binary64
15×distribute-lft-neg-out_binary64
14×/-rgt-identity_binary64
log-div_binary64 swap-sqr_binary64
distribute-rgt1-in_binary64
unpow3_binary64 cube-mult_binary64 cube-div_binary64
cube-unmult_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64
log-pow_binary64 rem-sqrt-square_binary64 div-sub_binary64 pow-sqr_binary64 distribute-lft1-in_binary64
log-rec_binary64 1-exp_binary64 exp-1-e_binary64 difference-of-sqr-1_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 pow-plus_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 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-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--l-_binary64
Counts
111 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02422764
16542570
224522548
351562548

prune103.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh167
Picked101
Done000
Total78886
Error
0.0b
Counts
86 → 8
Compiler

Compiled 1882 to 971 computations (48.4% saved)

localize8.0ms (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)))

rewrite188.0ms (3.8%)

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:

8.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
7.0ms
(/.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)

series125.0ms (2.5%)

Error
0.0b
Counts
3 → 30
Calls

3 calls:

44.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
38.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
15.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1330 to 962 computations (27.7% saved)

simplify123.0ms (2.5%)

Algorithm
egg-herbie
Rules
690×associate-/r/_binary64
679×associate-/r*_binary64
315×cancel-sign-sub-inv_binary64
164×associate-/l*_binary64
157×associate-*r*_binary64
145×*-commutative_binary64
131×associate-*l*_binary64
125×distribute-rgt-neg-in_binary64
123×unswap-sqr_binary64
121×sub-neg_binary64
120×associate-*l/_binary64
118×distribute-rgt-in_binary64
115×associate-/l/_binary64
105×distribute-lft-neg-in_binary64
88×distribute-lft-in_binary64
85×times-frac_binary64
76×+-commutative_binary64
72×associate-*r/_binary64
55×associate-+l+_binary64
54×associate-+r+_binary64
51×*-rgt-identity_binary64
49×associate--l+_binary64
44×sqr-pow_binary64
43×neg-mul-1_binary64 neg-sub0_binary64
39×distribute-neg-frac_binary64
37×distribute-neg-in_binary64
35×/-rgt-identity_binary64
33×distribute-rgt-out_binary64
32×associate--r+_binary64
27×unsub-neg_binary64
22×distribute-rgt-out--_binary64
21×log-prod_binary64
20×log-div_binary64
19×*-lft-identity_binary64
18×distribute-lft-out_binary64
15×exp-prod_binary64
14×distribute-lft-out--_binary64
13×cube-prod_binary64 swap-sqr_binary64 distribute-lft-neg-out_binary64
10×cube-div_binary64
cube-unmult_binary64
log-rec_binary64 unpow3_binary64 cube-mult_binary64 div-sub_binary64 distribute-rgt1-in_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 remove-double-div_binary64
log-pow_binary64 rem-sqrt-square_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 pow-plus_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
147 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02984125
17433901
227163861
351963861

prune138.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1143117
Fresh257
Picked011
Done000
Total1169125
Error
0.0b
Counts
125 → 9
Compiler

Compiled 2624 to 1181 computations (55% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b
(*.f64 e (cos.f64 v))
0.2b
(*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e)))
0.3b
(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite321.0ms (6.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
22×add-exp-log_binary64 add-cbrt-cube_binary64
19×add-sqr-sqrt_binary64
13×pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
12×associate-*l*_binary64
10×associate-*r*_binary64
prod-exp_binary64 cbrt-unprod_binary64
sqrt-prod_binary64
pow-prod-down_binary64
add-log-exp_binary64
unswap-sqr_binary64 *-commutative_binary64 div-exp_binary64 cbrt-undiv_binary64 times-frac_binary64 associate-/r*_binary64
associate-/r/_binary64
frac-2neg_binary64 clear-num_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64 associate-/l*_binary64
Counts
4 → 86
Calls

4 calls:

10.0ms
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms
(*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms
(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1775 to 508 computations (71.4% saved)

series136.0ms (2.7%)

Error
0.0b
Counts
4 → 36
Calls

4 calls:

48.0ms
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
22.0ms
(*.f64 (sin.f64 v) (sqrt.f64 e))
19.0ms
(*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e)))
16.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 1751 to 1229 computations (29.8% saved)

simplify160.0ms (3.2%)

Algorithm
egg-herbie
Rules
366×associate-/r/_binary64
343×cancel-sign-sub-inv_binary64
269×associate-/l/_binary64
257×associate-*r*_binary64
235×associate-*l*_binary64
186×sub-neg_binary64
185×distribute-rgt-neg-in_binary64
159×distribute-lft-neg-in_binary64 associate-/l*_binary64
156×unswap-sqr_binary64
134×neg-mul-1_binary64 neg-sub0_binary64
125×*-commutative_binary64
117×times-frac_binary64
83×associate-/r*_binary64
80×distribute-rgt-in_binary64
72×log-prod_binary64
61×+-commutative_binary64
58×log-div_binary64
56×sqr-pow_binary64 distribute-lft-in_binary64
54×exp-prod_binary64 cube-prod_binary64
52×associate-*l/_binary64
50×associate-*r/_binary64
44×cube-div_binary64
43×associate--l+_binary64
40×unsub-neg_binary64
38×distribute-neg-frac_binary64
37×distribute-rgt-out_binary64
36×*-rgt-identity_binary64
35×unpow3_binary64 associate-+l+_binary64 associate-+r+_binary64
30×distribute-rgt-out--_binary64
29×div-sub_binary64
28×distribute-neg-in_binary64
26×associate--r+_binary64
25×*-lft-identity_binary64
23×distribute-lft-out--_binary64
20×distribute-lft-out_binary64
18×swap-sqr_binary64
17×cube-mult_binary64
16×/-rgt-identity_binary64 distribute-lft-neg-out_binary64
log-rec_binary64 cube-unmult_binary64
rem-sqrt-square_binary64
log-pow_binary64 unpow1/2_binary64 pow-plus_binary64
unpow2_binary64 unpow1_binary64 pow-sqr_binary64
distribute-rgt1-in_binary64
1-exp_binary64 exp-1-e_binary64 rem-square-sqrt_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 mul-1-neg_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_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
122 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332495
16311994
224271949
344901949
449581949
549991949
649551949

prune75.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New73376
Fresh347
Picked011
Done011
Total76985
Error
0.0b
Counts
85 → 9
Compiler

Compiled 1275 to 595 computations (53.3% saved)

regimes831.0ms (16.6%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Compiler

Compiled 11482 to 7845 computations (31.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_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 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
01436
12336
22536
32236

end1.0ms (0%)

Compiler

Compiled 23 to 13 computations (43.5% saved)

sample1.9s (39%)

Algorithm
intervals
Results
574.0ms1973×body1024valid
332.0ms4513×body128valid
219.0ms997×body512valid
164.0ms8000×pre128true
81.0ms513×body256valid
3.0msbody2048valid
Compiler

Compiled 221 to 158 computations (28.5% saved)

Profiling

Loading profile data...