Details

Time bar (total: 2.7s)

analyze430.0ms (15.7%)

Algorithm
search
egg-herbie
Rules
100×distribute-rgt-in_binary64
78×associate-+l+_binary64
66×associate-+r+_binary64
64×distribute-lft-in_binary64
47×+-commutative_binary64
24×*-rgt-identity_binary64
18×distribute-rgt-out_binary64 associate-*l*_binary64 associate-*r*_binary64
16×*-commutative_binary64
15×*-lft-identity_binary64
1-exp_binary64 swap-x-y
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 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-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--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
14340
210340
317440
430240
530240
627840
726440
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
21.8%78%0.1%7
26.5%73.3%0.1%8
36.7%63.2%0.1%9
41.3%49.9%8.7%10
47.2%43.3%9.5%11
54.4%35.5%10.1%12
57.9%27.4%14.7%13
61.7%23.2%15.1%14
Symmetry

(sort x y)

Compiler

Compiled 8 to 8 computations (0% saved)

sample22.0ms (0.8%)

Algorithm
intervals
Results
6.0ms256×body128valid
0.0ms12×body128invalid
Compiler

Compiled 15 to 18 computations (-20% saved)

simplify12.0ms (0.4%)

Algorithm
egg-herbie
Rules
33×distribute-rgt-in_binary64
26×associate-+l+_binary64
22×associate-+r+_binary64
21×distribute-lft-in_binary64
16×+-commutative_binary64
11×*-rgt-identity_binary64
distribute-rgt-out_binary64 associate-*l*_binary64 associate-*r*_binary64
*-lft-identity_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 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-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--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
0810
11910
24310
37210
411610
511810
611010
710410

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.0b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite38.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
*-un-lft-identity_binary64
flip3-+_binary64 flip-+_binary64
add-sqr-sqrt_binary64
frac-times_binary64 associate-*l*_binary64 associate-*r*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64
associate-*l/_binary64 associate-*r/_binary64 distribute-lft-out_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 *-commutative_binary64
Counts
1 → 30
Calls

1 calls:

9.0ms
(*.f64 (+.f64 x y) (+.f64 z 1))
Compiler

Compiled 456 to 237 computations (48% saved)

series38.0ms (1.4%)

Error
0.0b
Counts
1 → 18
Calls

1 calls:

31.0ms
(*.f64 (+.f64 x y) (+.f64 z 1))
Compiler

Compiled 292 to 216 computations (26% saved)

simplify93.0ms (3.4%)

Algorithm
egg-herbie
Rules
803×distribute-rgt-in_binary64
766×distribute-lft-in_binary64
258×unsub-neg_binary64
250×cancel-sign-sub-inv_binary64
230×sub-neg_binary64
224×neg-mul-1_binary64
216×neg-sub0_binary64
211×*-commutative_binary64
161×associate-+r+_binary64
117×associate-+l+_binary64
104×unswap-sqr_binary64
87×sqr-pow_binary64
79×exp-sum_binary64
78×distribute-rgt-out_binary64
77×associate-*l*_binary64
72×*-rgt-identity_binary64
70×distribute-lft-neg-out_binary64
64×associate-+l-_binary64
63×associate-*r*_binary64
62×*-lft-identity_binary64 distribute-rgt-neg-out_binary64
53×exp-prod_binary64
50×associate-+r-_binary64
43×rem-sqrt-square_binary64
40×sub0-neg_binary64
34×distribute-rgt-neg-in_binary64
33×+-commutative_binary64
29×+-rgt-identity_binary64 distribute-neg-in_binary64
25×associate--r+_binary64
23×distribute-lft-neg-in_binary64
20×remove-double-neg_binary64
19×mul-1-neg_binary64
16×pow-sqr_binary64 distribute-neg-out_binary64
14×swap-sqr_binary64
12×cube-prod_binary64
10×distribute-rgt1-in_binary64
unpow1/2_binary64 distribute-lft1-in_binary64
div-sub_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64
log-prod_binary64 exp-diff_binary64
sqr-neg_binary64 distribute-lft-out_binary64
unpow3_binary64 cube-unmult_binary64 cube-mult_binary64
associate-/l/_binary64 associate-/l*_binary64 associate-*r/_binary64 associate--l+_binary64
pow-plus_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 difference-of-sqr-1_binary64 count-2_binary64 associate-/r/_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 log-pow_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_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 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft-out--_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
48 → 42
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
083700
1270622
2854622
33032622
43711622
54802622
64982622

prune27.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New39342
Fresh000
Picked011
Done000
Total39443
Error
0b
Counts
43 → 4
Compiler

Compiled 417 to 219 computations (47.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 z (+.f64 y x))
0.0b
(+.f64 (*.f64 z (+.f64 y x)) (+.f64 y x))

rewrite51.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
add-sqr-sqrt_binary64 flip3-+_binary64 associate-*r/_binary64 flip-+_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 frac-add_binary64 associate-*r*_binary64
sum-log_binary64 associate-*l*_binary64
distribute-rgt-out_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 associate-+l+_binary64 distribute-lft-in_binary64
distribute-lft1-in_binary64 associate-+r+_binary64 +-commutative_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
2 → 45
Calls

2 calls:

9.0ms
(+.f64 (*.f64 z (+.f64 y x)) (+.f64 y x))
6.0ms
(*.f64 z (+.f64 y x))
Compiler

Compiled 782 to 185 computations (76.3% saved)

series72.0ms (2.6%)

Error
0b
Counts
2 → 33
Calls

2 calls:

35.0ms
(+.f64 (*.f64 z (+.f64 y x)) (+.f64 y x))
27.0ms
(*.f64 z (+.f64 y x))
Compiler

Compiled 564 to 395 computations (30% saved)

simplify87.0ms (3.2%)

Algorithm
egg-herbie
Rules
413×associate--l+_binary64
365×associate-+l+_binary64
338×*-commutative_binary64
333×associate-+r+_binary64
319×distribute-rgt-out_binary64
304×associate--r+_binary64
243×cancel-sign-sub-inv_binary64
154×sub-neg_binary64
148×distribute-rgt-in_binary64
139×distribute-lft-in_binary64
127×unsub-neg_binary64
122×associate-*l*_binary64
120×neg-mul-1_binary64
116×+-commutative_binary64
104×associate-*r*_binary64
92×distribute-rgt-neg-in_binary64 distribute-rgt-out--_binary64
78×distribute-neg-in_binary64
73×distribute-lft-neg-in_binary64
66×exp-sum_binary64
59×distribute-lft-out_binary64
53×neg-sub0_binary64 sqr-pow_binary64
39×exp-prod_binary64
35×distribute-lft-neg-out_binary64
30×associate--r-_binary64
26×associate--l-_binary64
24×distribute-rgt1-in_binary64
23×distribute-rgt-neg-out_binary64
21×associate-+r-_binary64
20×unswap-sqr_binary64
19×distribute-lft1-in_binary64
17×+-rgt-identity_binary64
15×cube-prod_binary64 *-lft-identity_binary64 associate-+l-_binary64
14×log-prod_binary64 swap-sqr_binary64
10×*-rgt-identity_binary64
distribute-lft-out--_binary64
div-sub_binary64 sub0-neg_binary64
pow-plus_binary64
unpow3_binary64 unpow1/2_binary64
prod-exp_binary64 cube-mult_binary64 pow-sqr_binary64 difference-of-squares_binary64
exp-diff_binary64
sqr-neg_binary64 rem-sqrt-square_binary64 distribute-neg-out_binary64 associate-/l*_binary64
unpow2_binary64 1-exp_binary64 exp-1-e_binary64 cube-unmult_binary64 difference-of-sqr--1_binary64 count-2_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 log-pow_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_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 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64
Counts
78 → 56
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0107995
1322926
21227902
32782902
44897902
54774902

prune28.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh022
Picked011
Done011
Total56460
Error
0b
Counts
60 → 4
Compiler

Compiled 559 to 196 computations (64.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 x (*.f64 z x))

rewrite11.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-log-exp_binary64
*-un-lft-identity_binary64
sum-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 distribute-rgt1-in_binary64 distribute-rgt-out_binary64 +-commutative_binary64
Counts
1 → 13
Calls

1 calls:

3.0ms
(+.f64 x (*.f64 z x))
Compiler

Compiled 146 to 46 computations (68.5% saved)

series20.0ms (0.7%)

Error
0b
Counts
1 → 9
Calls

1 calls:

16.0ms
(+.f64 x (*.f64 z x))
Compiler

Compiled 81 to 85 computations (-4.9% saved)

simplify75.0ms (2.8%)

Algorithm
egg-herbie
Rules
505×distribute-rgt-out_binary64
255×times-frac_binary64
245×associate-*l/_binary64
243×distribute-lft-neg-out_binary64
231×distribute-rgt-in_binary64
225×*-commutative_binary64
214×unswap-sqr_binary64
213×associate-*l*_binary64
201×sub-neg_binary64
190×distribute-rgt-out--_binary64
174×distribute-lft-in_binary64
160×associate-*r*_binary64
156×+-commutative_binary64
155×distribute-rgt-neg-out_binary64
146×unsub-neg_binary64
145×cancel-sign-sub_binary64
141×distribute-rgt-neg-in_binary64
112×cancel-sign-sub-inv_binary64
93×distribute-rgt1-in_binary64
92×distribute-lft-neg-in_binary64
80×associate-+l+_binary64
79×sqr-pow_binary64
73×associate-+l-_binary64 associate-+r+_binary64
62×distribute-lft-out--_binary64
56×associate--r+_binary64
53×neg-mul-1_binary64
51×distribute-neg-in_binary64
47×distribute-neg-out_binary64
44×exp-prod_binary64
41×rem-sqrt-square_binary64 neg-sub0_binary64 distribute-lft1-in_binary64
40×cube-prod_binary64 sub0-neg_binary64
37×associate-+r-_binary64
34×distribute-lft-out_binary64 associate-/l/_binary64
32×associate-/l*_binary64
31×*-rgt-identity_binary64
28×cube-div_binary64
25×pow-sqr_binary64
24×log-prod_binary64
23×log-div_binary64 *-lft-identity_binary64
18×associate--l+_binary64
15×exp-diff_binary64 +-rgt-identity_binary64 associate-/r/_binary64
14×exp-sum_binary64
11×cube-unmult_binary64 cube-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 associate--r-_binary64
10×unpow3_binary64 swap-sqr_binary64
pow-plus_binary64 exp-sqrt_binary64 +-lft-identity_binary64
remove-double-neg_binary64 associate-/r*_binary64 associate-*r/_binary64
exp-neg_binary64 cube-mult_binary64 sqr-neg_binary64 div-sub_binary64
unpow1/2_binary64 associate--l-_binary64
exp-lft-sqr_binary64
difference-of-squares_binary64 distribute-frac-neg_binary64
log-rec_binary64 unpow2_binary64 prod-exp_binary64 distribute-neg-frac_binary64
1-exp_binary64 exp-1-e_binary64 --rgt-identity_binary64 difference-of-sqr-1_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 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-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 mul-1-neg_binary64 /-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64
Counts
22 → 12
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032213
195195
2270192
3794192
41605192
52512192
64529192
75126192

prune6.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New12012
Fresh011
Picked011
Done022
Total12416
Error
0b
Counts
16 → 4
Compiler

Compiled 117 to 77 computations (34.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 z 1) (-.f64 x y))
2.0b
(-.f64 (*.f64 x x) (*.f64 y y))
5.0b
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
28.8b
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))

rewrite152.0ms (5.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
25×flip3--_binary64 flip--_binary64
21×add-sqr-sqrt_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
16×*-un-lft-identity_binary64 frac-times_binary64
13×associate-*l*_binary64
10×add-cube-cbrt_binary64
cancel-sign-sub-inv_binary64 associate-*r*_binary64
pow1_binary64 associate-/l/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-/r/_binary64
difference-of-squares_binary64
prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
sub-neg_binary64
div-exp_binary64 cbrt-undiv_binary64
pow-prod-down_binary64 unswap-sqr_binary64 difference-of-sqr-1_binary64 *-commutative_binary64 distribute-lft-out--_binary64
frac-2neg_binary64 times-frac_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64 diff-log_binary64
Counts
4 → 124
Calls

4 calls:

18.0ms
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))
12.0ms
(*.f64 (-.f64 z 1) (-.f64 x y))
11.0ms
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
4.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 4053 to 1508 computations (62.8% saved)

series315.0ms (11.5%)

Error
0b
Counts
4 → 66
Calls

4 calls:

146.0ms
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))
76.0ms
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
38.0ms
(*.f64 (-.f64 z 1) (-.f64 x y))
28.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 3792 to 2749 computations (27.5% saved)

simplify142.0ms (5.2%)

Algorithm
egg-herbie
Rules
338×associate-*l*_binary64
327×times-frac_binary64
306×associate-*r*_binary64
237×div-sub_binary64
235×associate-/l*_binary64
228×distribute-rgt-in_binary64
219×distribute-lft-in_binary64
194×sub-neg_binary64
183×*-commutative_binary64
159×associate-/r*_binary64
79×+-commutative_binary64
65×unsub-neg_binary64
60×exp-prod_binary64
58×neg-sub0_binary64
54×neg-mul-1_binary64
50×log-prod_binary64
46×associate--l+_binary64 associate--r+_binary64
39×log-div_binary64
37×cube-prod_binary64
32×associate-+l+_binary64
30×associate-/r/_binary64
26×sqr-pow_binary64
25×distribute-rgt-neg-in_binary64 associate-*l/_binary64
24×associate-+r+_binary64
23×distribute-neg-in_binary64
22×exp-sum_binary64
21×associate-*r/_binary64
20×cancel-sign-sub-inv_binary64 distribute-lft-neg-in_binary64
13×swap-sqr_binary64
11×pow-plus_binary64
10×exp-diff_binary64
cube-unmult_binary64 cube-div_binary64 distribute-lft-neg-out_binary64
distribute-rgt-neg-out_binary64
difference-of-squares_binary64
unpow3_binary64 cube-mult_binary64 unswap-sqr_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 *-rgt-identity_binary64 distribute-rgt-out_binary64
log-rec_binary64
*-inverses_binary64 pow-sqr_binary64 difference-of-sqr--1_binary64 associate-/l/_binary64
log-pow_binary64 difference-of-sqr-1_binary64 distribute-rgt1-in_binary64 associate-+r-_binary64
div-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 *-lft-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 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 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-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 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64
Counts
190 → 163
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02914936
18314327
240174327
350944327

prune81.0ms (3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1630163
Fresh000
Picked011
Done033
Total1634167
Error
0b
Counts
167 → 4
Compiler

Compiled 2785 to 1164 computations (58.2% saved)

regimes406.0ms (14.8%)

Accuracy

Total 0.0b remaining (60.9%)

Threshold costs 0.0b (60.9%)

Compiler

Compiled 4155 to 3354 computations (19.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.2%)

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
0916
11416
21416

end6.0ms (0.2%)

Remove

(sort x y)

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample590.0ms (21.6%)

Algorithm
intervals
Results
211.0ms8000×body128valid
14.0ms580×body128invalid
Compiler

Compiled 64 to 64 computations (0% saved)

Profiling

Loading profile data...