Details

Time bar (total: 6.1s)

analyze1.4s (23.1%)

Algorithm
search
egg-herbie
Rules
736×times-frac_binary64
662×div-sub_binary64
597×associate-/l*_binary64
537×sub-neg_binary64
495×neg-mul-1_binary64
482×unsub-neg_binary64
468×neg-sub0_binary64
438×distribute-lft-neg-in_binary64
354×distribute-rgt-neg-in_binary64
352×cancel-sign-sub-inv_binary64
333×associate-/r*_binary64
324×distribute-neg-frac_binary64
320×distribute-frac-neg_binary64
275×distribute-rgt-in_binary64
214×distribute-lft-in_binary64
211×remove-double-neg_binary64
190×distribute-lft-neg-out_binary64
172×distribute-rgt-neg-out_binary64
159×+-commutative_binary64
154×distribute-neg-in_binary64
128×associate-*l*_binary64
110×*-commutative_binary64
91×associate-/r/_binary64
90×associate--r+_binary64
71×associate--r-_binary64
63×div0_binary64
60×*-rgt-identity_binary64 +-lft-identity_binary64
58×distribute-lft-out--_binary64
56×mul0-rgt_binary64 mul0-lft_binary64
53×associate-*r*_binary64
52×/-rgt-identity_binary64
48×distribute-lft-out_binary64 associate-+l-_binary64
44×sub0-neg_binary64 distribute-neg-out_binary64
42×*-lft-identity_binary64
34×associate--l-_binary64
30×associate-/l/_binary64
25×associate-+l+_binary64
18×associate-+r-_binary64 associate-+r+_binary64
16×mul-1-neg_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64
14×--rgt-identity_binary64
associate--l+_binary64
remove-double-div_binary64 cancel-sign-sub_binary64
1-exp_binary64 associate-*l/_binary64 swap-x-y swap-z-t
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 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_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 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 count-2_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042143
1106143
2218143
3354143
4829143
51159143
61545143
73951143
83323143
93857143
103957143
114139143
124203143
134800143
055
155
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
16.4%83.4%0.2%11
19.9%79.9%0.2%12
21.6%77.2%1.2%13
24.8%73.7%1.4%14
Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 10 to 10 computations (0% saved)

sample48.0ms (0.8%)

Algorithm
intervals
Results
9.0ms256×body128valid
3.0ms77×body128invalid
Compiler

Compiled 19 to 24 computations (-26.3% saved)

simplify42.0ms (0.7%)

Algorithm
egg-herbie
Rules
130×cancel-sign-sub-inv_binary64
113×distribute-rgt-in_binary64
103×associate-/l*_binary64
96×div-sub_binary64
90×distribute-lft-in_binary64
61×distribute-rgt-neg-in_binary64
59×unsub-neg_binary64
55×sub-neg_binary64 distribute-lft-neg-in_binary64
50×associate-/r*_binary64
47×associate-*r*_binary64
46×associate-/r/_binary64
36×neg-mul-1_binary64
34×distribute-neg-frac_binary64
33×distribute-lft-neg-out_binary64
30×neg-sub0_binary64
29×associate-*l*_binary64
26×distribute-neg-in_binary64 *-commutative_binary64
25×distribute-rgt-neg-out_binary64
24×mul0-rgt_binary64
23×mul0-lft_binary64
20×associate--r+_binary64 +-commutative_binary64
17×+-lft-identity_binary64
14×associate-/l/_binary64
12×*-lft-identity_binary64
10×div0_binary64 associate-+l-_binary64
remove-double-neg_binary64 sub0-neg_binary64
*-rgt-identity_binary64
associate-+l+_binary64
/-rgt-identity_binary64 associate--r-_binary64
--rgt-identity_binary64
+-rgt-identity_binary64 associate-*l/_binary64 associate-+r-_binary64 associate-+r+_binary64
1-exp_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 associate-*r/_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 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 mul-1-neg_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 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--l-_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12013
24013
36613
412913
518313
624313
738213
851913
962413
1060713
1163313
1262313
1362413
1455113

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
9.8b
Counts
1 → 1
Compiler

Compiled 9 to 9 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
9.3b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

rewrite65.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
9.6b
Rules
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
times-frac_binary64
add-exp-log_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
associate-/l*_binary64 associate-/r*_binary64
pow1_binary64 flip3--_binary64 associate-/l/_binary64 flip--_binary64
div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 div-sub_binary64 clear-num_binary64 div-inv_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
2 → 42
Calls

2 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
3.0ms
(-.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 786 to 148 computations (81.2% saved)

series115.0ms (1.9%)

Error
9.6b
Counts
2 → 51
Calls

2 calls:

70.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
39.0ms
(-.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 732 to 727 computations (0.7% saved)

simplify100.0ms (1.6%)

Algorithm
egg-herbie
Rules
633×distribute-rgt-in_binary64
566×distribute-lft-in_binary64
267×associate-*l*_binary64
209×associate-*r*_binary64
197×div-sub_binary64
175×associate-*l/_binary64
169×distribute-lft-neg-out_binary64
167×cancel-sign-sub-inv_binary64
163×distribute-rgt-neg-out_binary64
127×associate-*r/_binary64
110×exp-prod_binary64
109×*-commutative_binary64
108×distribute-rgt-neg-in_binary64
99×distribute-lft-neg-in_binary64
83×associate-/l*_binary64
72×associate-/l/_binary64
69×distribute-neg-frac_binary64
68×sub-neg_binary64
66×distribute-frac-neg_binary64
58×neg-sub0_binary64
53×sqr-pow_binary64
48×unsub-neg_binary64 associate-/r/_binary64
47×neg-mul-1_binary64
43×distribute-rgt-out_binary64
41×associate-/r*_binary64
31×cube-prod_binary64
29×swap-sqr_binary64
28×times-frac_binary64 unswap-sqr_binary64
24×distribute-lft-out_binary64
23×exp-sum_binary64
22×difference-of-squares_binary64
21×log-div_binary64 log-prod_binary64 +-commutative_binary64
20×unpow3_binary64
17×cube-div_binary64
16×exp-diff_binary64
14×distribute-neg-in_binary64
10×cube-mult_binary64 mul-1-neg_binary64 /-rgt-identity_binary64
*-lft-identity_binary64
mul0-rgt_binary64 mul0-lft_binary64
associate-+r-_binary64 associate-+r+_binary64
*-rgt-identity_binary64 +-rgt-identity_binary64 pow-sqr_binary64 associate-+l-_binary64 associate-+l+_binary64
cube-unmult_binary64 remove-double-neg_binary64
sqr-neg_binary64 sub0-neg_binary64
log-rec_binary64 cube-neg_binary64 div0_binary64 associate--r+_binary64
associate--r-_binary64 associate--l-_binary64
div-exp_binary64 1-exp_binary64 --rgt-identity_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 pow-base-0_binary64 unpow1/3_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 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--l+_binary64
Counts
93 → 62
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0891380
12371303
26831303
320871303
449211303
549461303

prune41.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New53962
Fresh000
Picked011
Done000
Total531063
Error
9.5b
Counts
63 → 10
Compiler

Compiled 798 to 227 computations (71.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 (*.f64 x y) (*.f64 t z))
0.6b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 t z))))
9.1b
(/.f64 a (-.f64 (*.f64 x y) (*.f64 t z)))

rewrite164.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
9.5b
Rules
90×times-frac_binary64
55×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
18×associate-/r*_binary64
16×add-exp-log_binary64
11×associate-/r/_binary64
10×add-cbrt-cube_binary64
div-exp_binary64
div-inv_binary64 flip3--_binary64 flip--_binary64 associate-/l*_binary64
add-log-exp_binary64
pow1_binary64 cbrt-undiv_binary64
frac-2neg_binary64 clear-num_binary64 1-exp_binary64 rec-exp_binary64
inv-pow_binary64 pow-flip_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
3 → 125
Calls

3 calls:

9.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 t z))))
5.0ms
(/.f64 a (-.f64 (*.f64 x y) (*.f64 t z)))
4.0ms
(-.f64 (*.f64 x y) (*.f64 t z))
Compiler

Compiled 2967 to 786 computations (73.5% saved)

series202.0ms (3.3%)

Error
9.5b
Counts
3 → 78
Calls

3 calls:

81.0ms
(/.f64 a (-.f64 (*.f64 x y) (*.f64 t z)))
70.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 t z))))
41.0ms
(-.f64 (*.f64 x y) (*.f64 t z))
Compiler

Compiled 1770 to 1620 computations (8.5% saved)

simplify164.0ms (2.7%)

Algorithm
egg-herbie
Rules
680×times-frac_binary64
545×associate-/l*_binary64
443×associate-/r*_binary64
324×associate-/r/_binary64
288×associate-/l/_binary64
185×div-sub_binary64
146×distribute-rgt-in_binary64
142×distribute-lft-in_binary64
95×cancel-sign-sub-inv_binary64
90×exp-prod_binary64
86×distribute-rgt-neg-in_binary64
79×distribute-lft-neg-in_binary64
77×*-commutative_binary64
73×associate-*l/_binary64
58×associate-*r*_binary64
54×associate-*l*_binary64
50×cube-prod_binary64
43×distribute-neg-frac_binary64
42×associate-*r/_binary64
38×sub-neg_binary64 sqr-pow_binary64 unswap-sqr_binary64
37×exp-sum_binary64
36×neg-sub0_binary64 *-rgt-identity_binary64
35×neg-mul-1_binary64
24×distribute-lft-neg-out_binary64
17×distribute-rgt-out_binary64 +-commutative_binary64
15×distribute-rgt-neg-out_binary64
14×log-div_binary64
13×log-prod_binary64
12×unpow3_binary64
10×exp-diff_binary64 distribute-neg-in_binary64
cube-div_binary64 *-lft-identity_binary64 associate-+r+_binary64
cube-unmult_binary64 cube-mult_binary64 distribute-lft-out_binary64
/-rgt-identity_binary64 swap-sqr_binary64
log-rec_binary64 mul-1-neg_binary64
unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 unpow1_binary64 rem-sqrt-square_binary64 unsub-neg_binary64 remove-double-div_binary64 associate--r+_binary64 associate-+r-_binary64
cube-neg_binary64 sqr-neg_binary64 div0_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64 associate--r-_binary64
exp-neg_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 pow-sqr_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 associate-+l+_binary64
div-exp_binary64 1-exp_binary64 exp-1-e_binary64 sub0-neg_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 log-pow_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_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 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate--l-_binary64 associate--l+_binary64 associate-+l-_binary64
Counts
203 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01814407
14374133
215404011
346734011
452454011

prune66.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1186124
Fresh268
Picked101
Done011
Total12113134
Error
9.4b
Counts
134 → 13
Compiler

Compiled 1418 to 454 computations (68% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 (*.f64 x y) (*.f64 t z))
9.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a) (*.f64 (-.f64 (*.f64 x y) (*.f64 t z)) (cbrt.f64 1)))

rewrite75.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
23×add-exp-log_binary64
16×add-cbrt-cube_binary64
11×prod-exp_binary64 cbrt-unprod_binary64
pow1_binary64 associate-*l*_binary64
associate-*l/_binary64
div-exp_binary64 add-log-exp_binary64 add-cube-cbrt_binary64 cbrt-undiv_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64 times-frac_binary64
frac-times_binary64 associate-*r/_binary64
div-inv_binary64 associate-*r*_binary64 *-commutative_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
2 → 47
Calls

2 calls:

14.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a) (*.f64 (-.f64 (*.f64 x y) (*.f64 t z)) (cbrt.f64 1)))
4.0ms
(-.f64 (*.f64 x y) (*.f64 t z))
Compiler

Compiled 1348 to 703 computations (47.8% saved)

series129.0ms (2.1%)

Error
9.4b
Counts
2 → 51
Calls

2 calls:

71.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a) (*.f64 (-.f64 (*.f64 x y) (*.f64 t z)) (cbrt.f64 1)))
49.0ms
(-.f64 (*.f64 x y) (*.f64 t z))
Compiler

Compiled 1097 to 1080 computations (1.5% saved)

simplify112.0ms (1.8%)

Algorithm
egg-herbie
Rules
753×div-sub_binary64
421×associate-*l/_binary64
353×distribute-rgt-in_binary64
352×distribute-lft-in_binary64
319×*-commutative_binary64
275×associate-/l*_binary64
214×associate-*r/_binary64
187×exp-prod_binary64
183×times-frac_binary64
151×associate-*l*_binary64
135×associate-*r*_binary64
117×cancel-sign-sub-inv_binary64
106×unsub-neg_binary64
100×associate-/r*_binary64
98×exp-sum_binary64
96×unswap-sqr_binary64
84×sqr-pow_binary64
79×neg-sub0_binary64
75×neg-mul-1_binary64
68×sub-neg_binary64
65×log-div_binary64
57×associate-/r/_binary64
50×log-prod_binary64
48×exp-diff_binary64
43×distribute-rgt-neg-in_binary64
38×swap-sqr_binary64
37×distribute-lft-neg-in_binary64
35×cube-div_binary64
34×*-rgt-identity_binary64
32×*-lft-identity_binary64 associate-/l/_binary64
29×associate-+l+_binary64
28×distribute-lft-neg-out_binary64 associate-+r+_binary64 +-commutative_binary64
23×cube-prod_binary64
22×unpow3_binary64 difference-of-squares_binary64
20×cube-mult_binary64 distribute-rgt-neg-out_binary64
18×associate-+l-_binary64
17×mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt-out_binary64
15×associate-+r-_binary64
11×cube-unmult_binary64
10×/-rgt-identity_binary64 pow-sqr_binary64
+-rgt-identity_binary64 distribute-lft-out_binary64
log-rec_binary64 exp-neg_binary64 sqr-neg_binary64 associate--r+_binary64
distribute-neg-frac_binary64 distribute-neg-in_binary64 associate--r-_binary64
cube-neg_binary64 mul-1-neg_binary64 sub0-neg_binary64
remove-double-neg_binary64 associate--l+_binary64
unpow1/2_binary64 div0_binary64
div-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_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 log-pow_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 --rgt-identity_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--l-_binary64
Counts
98 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01132141
13421346
211171328
335391328
445111328
559981328

prune38.0ms (0.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New61162
Fresh01111
Picked011
Done011
Total611475
Error
9.4b
Counts
75 → 14
Compiler

Compiled 785 to 392 computations (50.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) a))
10.4b
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
10.4b
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
10.4b
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))

rewrite121.0ms (2%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
30×cbrt-div_binary64
25×add-sqr-sqrt_binary64
22×associate-*r*_binary64
20×add-cube-cbrt_binary64 *-un-lft-identity_binary64 times-frac_binary64
19×cbrt-prod_binary64
16×add-exp-log_binary64 frac-times_binary64
15×flip3--_binary64 flip--_binary64
12×associate-*l/_binary64
10×add-cbrt-cube_binary64
pow1_binary64
prod-exp_binary64 cbrt-unprod_binary64
associate-*r/_binary64
add-log-exp_binary64
pow1/3_binary64 pow-prod-down_binary64 unswap-sqr_binary64
div-exp_binary64 cbrt-undiv_binary64
associate-*l*_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 100
Calls

4 calls:

23.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) a))
4.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
4.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
3.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
Compiler

Compiled 4380 to 441 computations (89.9% saved)

series389.0ms (6.3%)

Error
9.4b
Counts
4 → 84
Calls

4 calls:

91.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z))) a))
85.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
83.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
80.0ms
(cbrt.f64 (-.f64 (*.f64 x y) (*.f64 t z)))
Compiler

Compiled 6824 to 4140 computations (39.3% saved)

simplify184.0ms (3%)

Algorithm
egg-herbie
Rules
678×times-frac_binary64
221×associate-*l*_binary64
217×associate-*r*_binary64
176×*-commutative_binary64
165×distribute-lft-in_binary64
164×distribute-rgt-in_binary64
160×associate-/l*_binary64
155×associate-/l/_binary64
148×distribute-rgt-neg-in_binary64
145×distribute-lft-neg-in_binary64
125×cancel-sign-sub-inv_binary64
123×associate-*r/_binary64
99×exp-prod_binary64
76×distribute-neg-frac_binary64
72×sub-neg_binary64
66×sqr-pow_binary64
63×associate-/r*_binary64
59×exp-diff_binary64
53×neg-sub0_binary64
47×associate-*l/_binary64
45×neg-mul-1_binary64
40×exp-sum_binary64 unswap-sqr_binary64
30×log-prod_binary64 +-commutative_binary64
28×*-rgt-identity_binary64
27×exp-neg_binary64
24×*-lft-identity_binary64
20×log-div_binary64 distribute-lft-neg-out_binary64
19×div-sub_binary64 distribute-rgt-out_binary64
18×distribute-lft-out_binary64
16×unsub-neg_binary64
15×distribute-rgt-neg-out_binary64
12×unpow3_binary64 cube-prod_binary64 distribute-neg-out_binary64 associate-/r/_binary64
11×distribute-neg-in_binary64
10×unpow1/3_binary64
mul-1-neg_binary64 /-rgt-identity_binary64 pow-sqr_binary64
swap-sqr_binary64 associate--r-_binary64
cube-mult_binary64
pow-plus_binary64 exp-to-pow_binary64 cube-unmult_binary64 associate-+l+_binary64
log-pow_binary64 log-rec_binary64 remove-double-neg_binary64
associate-+r+_binary64
unpow1/2_binary64 difference-of-squares_binary64 associate-+r-_binary64
unpow2_binary64 unpow1_binary64 cube-div_binary64 distribute-lft-out--_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_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 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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-rgt-out--_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
184 → 172
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02575382
17015187
222085133
348175073
449895073

prune98.0ms (1.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New1711172
Fresh01111
Picked011
Done022
Total17115186
Error
9.4b
Counts
186 → 15
Compiler

Compiled 4501 to 801 computations (82.2% saved)

regimes1.3s (21.9%)

Accuracy

Total 0.5b remaining (6.4%)

Threshold costs 0.5b (6.4%)

Compiler

Compiled 20961 to 14202 computations (32.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
distribute-lft-neg-out_binary64 distribute-lft-neg-in_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 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_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11713
22713
33313
43713
53813
63813

end22.0ms (0.4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 45 to 45 computations (0% saved)

sample1.2s (18.8%)

Algorithm
intervals
Results
285.0ms8000×body128valid
113.0ms3076×body128invalid
Compiler

Compiled 311 to 252 computations (19% saved)

Profiling

Loading profile data...