Details

Time bar (total: 10.7s)

analyze1.4s (12.9%)

Algorithm
search
egg-herbie
Rules
4016×associate-+l+_binary64
1230×+-commutative_binary64
282×associate-+r+_binary64
61×*-commutative_binary64
28×distribute-rgt-in_binary64 distribute-lft-in_binary64
sub-neg_binary64
swap-z-t swap-z-a
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 1-exp_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 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 count-2_binary64 associate-/l/_binary64 associate-/r/_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 swap-t-a
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0194928
1543928
21802928
31802928
41802928
52484928
62484928
72484928
86568928
088
188
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%74.7%25.3%8
0%74.7%25.3%9
0%65.4%34.6%10
0%51.4%48.6%11
0%51.4%48.6%12
0%51.4%48.6%13
0%51.4%48.6%14
Symmetry

(sort z t a)

Compiler

Compiled 22 to 21 computations (4.5% saved)

sample134.0ms (1.3%)

Algorithm
intervals
Results
28.0ms362×body128nan
22.0ms256×body128valid
3.0ms31×body128invalid
Compiler

Compiled 43 to 49 computations (-14% saved)

simplify60.0ms (0.6%)

Algorithm
egg-herbie
Rules
2664×associate-+l+_binary64
1041×associate-+r+_binary64
923×+-commutative_binary64
*-commutative_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64
sub-neg_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 1-exp_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 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 count-2_binary64 associate-/l/_binary64 associate-/r/_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
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02132
14032
29932
334232
498632
5120832
6120832
7120832
8120832
9226032
10226032
11222632
12222632
13197432
14195832

prune2.0ms (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 21 to 20 computations (4.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
0.0b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.2b
(*.f64 (-.f64 b 1/2) (log.f64 c))
0.2b
(*.f64 x (log.f64 y))

rewrite190.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
38×add-log-exp_binary64
25×sum-log_binary64
20×add-sqr-sqrt_binary64
18×log-prod_binary64
16×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
10×pow1_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64 associate-*r*_binary64
associate-*l/_binary64 associate-+r+_binary64
flip3-+_binary64 flip-+_binary64 frac-add_binary64
flip3--_binary64 flip--_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 log-pow_binary64 *-commutative_binary64 associate-+l+_binary64 +-commutative_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64
Counts
4 → 95
Calls

4 calls:

23.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
14.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
7.0ms
(*.f64 (-.f64 b 1/2) (log.f64 c))
5.0ms
(*.f64 x (log.f64 y))
Compiler

Compiled 3001 to 1007 computations (66.4% saved)

series697.0ms (6.5%)

Error
0.1b
Counts
4 → 95
Calls

4 calls:

319.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
263.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
37.0ms
(*.f64 (-.f64 b 1/2) (log.f64 c))
28.0ms
(*.f64 x (log.f64 y))
Compiler

Compiled 4034 to 3314 computations (17.8% saved)

simplify134.0ms (1.3%)

Algorithm
egg-herbie
Rules
925×associate--l+_binary64
280×associate-+l+_binary64
269×associate-+r+_binary64
261×cancel-sign-sub-inv_binary64
215×+-commutative_binary64
208×distribute-rgt-in_binary64
194×distribute-lft-in_binary64
188×sub-neg_binary64
179×associate-*l*_binary64
165×*-commutative_binary64
147×associate-*r*_binary64
130×distribute-lft-neg-out_binary64
115×distribute-rgt-neg-out_binary64
110×distribute-neg-in_binary64
87×unsub-neg_binary64 distribute-rgt-neg-in_binary64
64×exp-sum_binary64
57×distribute-lft-neg-in_binary64
54×neg-sub0_binary64
51×neg-mul-1_binary64
46×sqr-pow_binary64 distribute-rgt-out_binary64
36×exp-prod_binary64
35×associate--r-_binary64
31×prod-exp_binary64
30×associate--r+_binary64
28×associate--l-_binary64
26×*-lft-identity_binary64
25×*-rgt-identity_binary64
22×log-prod_binary64
20×cube-prod_binary64
19×exp-diff_binary64
17×distribute-rgt-out--_binary64
16×unswap-sqr_binary64
14×swap-sqr_binary64
11×unpow3_binary64
10×distribute-lft-out_binary64
cube-mult_binary64
exp-to-pow_binary64
associate-+r-_binary64
distribute-neg-out_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-+l-_binary64
log-div_binary64 cube-unmult_binary64 remove-double-neg_binary64 distribute-lft-out--_binary64
mul-1-neg_binary64 pow-sqr_binary64 difference-of-squares_binary64
log-rec_binary64 rem-exp-log_binary64 cube-neg_binary64 sqr-neg_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 count-2_binary64
1-exp_binary64 exp-1-e_binary64 div-sub_binary64 +-inverses_binary64 distribute-frac-neg_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 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_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 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-div_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 times-frac_binary64 /-rgt-identity_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_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 distribute-neg-frac_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64
Counts
190 → 154
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03304740
18994364
232774211
354594211

prune124.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1504154
Fresh000
Picked101
Done000
Total1514155
Error
0.0b
Counts
155 → 4
Compiler

Compiled 2585 to 946 computations (63.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(+.f64 (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c)))) (*.f64 (+.f64 -1/2 b) (log.f64 (cbrt.f64 c))))
0.2b
(*.f64 x (log.f64 y))
0.6b
(cbrt.f64 c)
0.6b
(cbrt.f64 c)

rewrite200.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
42×log-prod_binary64
33×distribute-rgt-in_binary64 distribute-lft-in_binary64
24×cbrt-prod_binary64 add-sqr-sqrt_binary64 associate-+l+_binary64
22×add-cube-cbrt_binary64 *-un-lft-identity_binary64
12×associate-+r+_binary64
associate-*l/_binary64
pow1_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
flip3-+_binary64 flip-+_binary64
associate-*r*_binary64 frac-add_binary64
associate-*l*_binary64
pow1/3_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 log-pow_binary64 *-commutative_binary64 sum-log_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
4 → 99
Calls

4 calls:

17.0ms
(+.f64 (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c)))) (*.f64 (+.f64 -1/2 b) (log.f64 (cbrt.f64 c))))
5.0ms
(*.f64 x (log.f64 y))
2.0ms
(cbrt.f64 c)
1.0ms
(cbrt.f64 c)
Compiler

Compiled 4074 to 1715 computations (57.9% saved)

series205.0ms (1.9%)

Error
0.0b
Counts
4 → 21
Calls

4 calls:

114.0ms
(+.f64 (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c)))) (*.f64 (+.f64 -1/2 b) (log.f64 (cbrt.f64 c))))
35.0ms
(*.f64 x (log.f64 y))
19.0ms
(cbrt.f64 c)
18.0ms
(cbrt.f64 c)
Compiler

Compiled 1700 to 1371 computations (19.4% saved)

simplify103.0ms (1%)

Algorithm
egg-herbie
Rules
266×associate-+l+_binary64
257×unsub-neg_binary64
241×associate-+r+_binary64
218×associate-*l*_binary64
215×+-commutative_binary64
212×associate-*r*_binary64
197×sub-neg_binary64
183×distribute-rgt-out_binary64
169×*-commutative_binary64
162×cancel-sign-sub-inv_binary64
140×neg-sub0_binary64
134×neg-mul-1_binary64
119×distribute-rgt-in_binary64
116×distribute-lft-out_binary64
114×log-prod_binary64 distribute-lft-in_binary64
113×distribute-rgt-neg-in_binary64
98×distribute-lft-neg-in_binary64
79×exp-prod_binary64
68×exp-sum_binary64 cube-prod_binary64
48×sqr-pow_binary64
44×associate--r+_binary64
43×distribute-rgt-out--_binary64
37×distribute-neg-in_binary64
36×swap-sqr_binary64
35×distribute-lft-neg-out_binary64
32×associate--l+_binary64
27×exp-to-pow_binary64
25×distribute-rgt-neg-out_binary64
24×distribute-lft-out--_binary64
21×log-div_binary64
19×associate-+r-_binary64
17×log-pow_binary64
16×exp-diff_binary64 associate-+l-_binary64
15×unpow3_binary64 div-sub_binary64
14×cube-mult_binary64 unswap-sqr_binary64 associate-/r*_binary64
13×distribute-rgt1-in_binary64
12×*-lft-identity_binary64
11×*-rgt-identity_binary64
cube-unmult_binary64
prod-exp_binary64 mul-1-neg_binary64 count-2_binary64
exp-lft-sqr_binary64 distribute-lft1-in_binary64 associate-/l*_binary64
log-rec_binary64
rem-sqrt-square_binary64 pow-sqr_binary64
unpow1/3_binary64 associate--r-_binary64
rec-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 sqr-neg_binary64 remove-double-neg_binary64 difference-of-squares_binary64
unpow1/2_binary64 pow-plus_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 +-inverses_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 unpow2_binary64 pow-base-1_binary64 unpow0_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 /-rgt-identity_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_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-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--l-_binary64
Counts
120 → 89
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02272083
15561835
218671614
341381606
449631606

prune142.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New88189
Fresh033
Picked011
Done000
Total88593
Error
0b
Counts
93 → 5
Compiler

Compiled 2715 to 1149 computations (57.7% saved)

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 c)
0.6b
(cbrt.f64 c)
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 c) (cbrt.f64 c)))
0.6b
(cbrt.f64 (cbrt.f64 c))

rewrite107.0ms (1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
16×cbrt-prod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1/3_binary64 pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 45
Calls

4 calls:

4.0ms
(cbrt.f64 (*.f64 (cbrt.f64 c) (cbrt.f64 c)))
2.0ms
(cbrt.f64 (cbrt.f64 c))
1.0ms
(cbrt.f64 c)
1.0ms
(cbrt.f64 c)
Compiler

Compiled 2099 to 768 computations (63.4% saved)

series107.0ms (1%)

Error
0b
Counts
4 → 12
Calls

4 calls:

27.0ms
(cbrt.f64 (*.f64 (cbrt.f64 c) (cbrt.f64 c)))
25.0ms
(cbrt.f64 (cbrt.f64 c))
21.0ms
(cbrt.f64 c)
19.0ms
(cbrt.f64 c)
Compiler

Compiled 1456 to 1117 computations (23.3% saved)

simplify57.0ms (0.5%)

Algorithm
egg-herbie
Rules
563×associate-+l+_binary64
542×distribute-rgt-in_binary64
535×distribute-lft-in_binary64
508×unswap-sqr_binary64
366×*-commutative_binary64
244×associate-*l*_binary64
207×log-prod_binary64
198×distribute-rgt-neg-in_binary64
196×distribute-lft-neg-in_binary64
193×associate-*r*_binary64
110×sqr-pow_binary64
69×swap-sqr_binary64
54×cancel-sign-sub-inv_binary64
35×pow-plus_binary64
32×cube-prod_binary64 neg-mul-1_binary64 neg-sub0_binary64
31×cube-unmult_binary64
28×distribute-rgt-out_binary64
26×log-pow_binary64 pow-sqr_binary64
21×count-2_binary64
15×exp-prod_binary64
13×rem-sqrt-square_binary64 sub-neg_binary64
12×*-rgt-identity_binary64 *-lft-identity_binary64
11×distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-lft-out_binary64
unpow3_binary64 associate-/l/_binary64 associate-*r/_binary64
unpow1/3_binary64 unpow2_binary64 associate-/l*_binary64
rem-3cbrt-lft_binary64
unpow1/2_binary64 unpow1_binary64 mul-1-neg_binary64 associate-/r/_binary64 associate-+r+_binary64
1-exp_binary64 cube-mult_binary64 rem-cbrt-cube_binary64 distribute-rgt1-in_binary64 associate-/r*_binary64 associate-+l-_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-rec_binary64 log-div_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 unsub-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
57 → 24
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
050474
188446
2224446
3976404
41846402
55168402

prune33.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New24024
Fresh033
Picked011
Done011
Total24529
Error
0b
Counts
29 → 5
Compiler

Compiled 770 to 381 computations (50.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
0.3b
(*.f64 x (log.f64 (cbrt.f64 y)))
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)

rewrite193.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
36×log-prod_binary64
30×distribute-rgt-in_binary64 distribute-lft-in_binary64
24×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64 *-un-lft-identity_binary64
12×pow1_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
pow1/3_binary64
log-pow_binary64 *-commutative_binary64
unswap-sqr_binary64
Counts
4 → 96
Calls

4 calls:

7.0ms
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
5.0ms
(*.f64 x (log.f64 (cbrt.f64 y)))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 3347 to 1412 computations (57.8% saved)

series168.0ms (1.6%)

Error
0b
Counts
4 → 18
Calls

4 calls:

60.0ms
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
57.0ms
(*.f64 x (log.f64 (cbrt.f64 y)))
20.0ms
(cbrt.f64 y)
18.0ms
(cbrt.f64 y)
Compiler

Compiled 1467 to 1232 computations (16% saved)

simplify100.0ms (0.9%)

Algorithm
egg-herbie
Rules
332×*-commutative_binary64
313×distribute-rgt-neg-out_binary64
232×log-prod_binary64
186×cancel-sign-sub-inv_binary64
181×associate-*l*_binary64
174×associate-*r*_binary64
169×unswap-sqr_binary64
144×sqr-pow_binary64
140×exp-prod_binary64
119×exp-sum_binary64
114×associate-+l+_binary64
102×swap-sqr_binary64
101×distribute-rgt-in_binary64
100×unsub-neg_binary64
98×distribute-lft-in_binary64
97×associate-+r+_binary64
96×cube-prod_binary64
94×count-2_binary64
84×distribute-neg-in_binary64
82×distribute-neg-out_binary64 distribute-rgt-out_binary64
69×log-div_binary64
64×sub-neg_binary64
50×exp-to-pow_binary64
48×neg-mul-1_binary64 neg-sub0_binary64
41×pow-sqr_binary64
40×associate-/r*_binary64
36×distribute-rgt-neg-in_binary64
35×distribute-lft-neg-in_binary64
32×*-lft-identity_binary64
30×log-pow_binary64 *-rgt-identity_binary64 associate--r+_binary64
27×associate-/l*_binary64
24×cube-div_binary64
23×distribute-neg-frac_binary64
19×+-commutative_binary64
16×exp-diff_binary64 cube-neg_binary64 sqr-neg_binary64 associate-/l/_binary64
15×distribute-frac-neg_binary64 distribute-lft-neg-out_binary64
14×rem-sqrt-square_binary64
13×exp-neg_binary64
10×log-rec_binary64 cube-unmult_binary64
unpow3_binary64 cube-mult_binary64 div-sub_binary64
unpow1/3_binary64
cancel-sign-sub_binary64 distribute-rgt1-in_binary64
exp-lft-sqr_binary64 associate-*r/_binary64
prod-exp_binary64
unpow1/2_binary64 distribute-lft-out_binary64
pow-plus_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 rem-log-exp_binary64
rem-exp-log_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 distribute-lft1-in_binary64 associate-/r/_binary64 associate-+r-_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 +-rgt-identity_binary64 remove-double-div_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 unpow2_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 e-exp-1_binary64 exp-0_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate-+l-_binary64
Counts
114 → 80
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01581683
12721435
28411421
315771421
426831413
550281413

prune78.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New80080
Fresh022
Picked011
Done022
Total80585
Error
0b
Counts
85 → 5
Compiler

Compiled 1376 to 625 computations (54.6% saved)

regimes3.5s (33.2%)

Accuracy

Total 0.1b remaining (72.4%)

Threshold costs 0.1b (72.4%)

Compiler

Compiled 54935 to 50215 computations (8.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03371
14671
24671

end15.0ms (0.1%)

Remove

(sort z t a)

Compiler

Compiled 132 to 102 computations (22.7% saved)

sample2.8s (26.3%)

Algorithm
intervals
Results
723.0ms9733×body128nan
686.0ms7997×body128valid
104.0ms1143×body128invalid
1.0msbody512valid
0.0msbody1024valid
Compiler

Compiled 264 to 233 computations (11.7% saved)

Profiling

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