Details

Time bar (total: 6.7s)

analyze2.2s (32.1%)

Algorithm
search
egg-herbie
Rules
45×+-commutative_binary64
24×associate-+l+_binary64
15×associate-+r+_binary64 *-commutative_binary64
swap-x-y swap-z-t swap-a-b
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 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*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
062256
1100256
2126256
3122256
4121256
066
166
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.6%98.1%0.3%13
3.1%96.6%0.3%14
Symmetry

(sort x y)

(sort z t)

(sort a b)

Compiler

Compiled 12 to 12 computations (0% saved)

sample55.0ms (0.8%)

Algorithm
intervals
Results
9.0ms256×body128valid
5.0ms128×body128invalid
Compiler

Compiled 23 to 29 computations (-26.1% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 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 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*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
01216
11916
22516
32516
42516

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Compiled 11 to 11 computations (0% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite31.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-log-exp_binary64
sum-log_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 *-un-lft-identity_binary64 flip-+_binary64 +-commutative_binary64
associate-+l+_binary64
Counts
2 → 24
Calls

2 calls:

6.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))
4.0ms
(+.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 510 to 94 computations (81.6% saved)

series129.0ms (1.9%)

Error
0.0b
Counts
2 → 60
Calls

2 calls:

74.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))
43.0ms
(+.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 874 to 920 computations (-5.3% saved)

simplify99.0ms (1.5%)

Algorithm
egg-herbie
Rules
498×unswap-sqr_binary64
371×sub-neg_binary64
326×associate-*l*_binary64
297×cancel-sign-sub-inv_binary64
278×distribute-rgt-in_binary64
254×distribute-lft-in_binary64
238×associate-*r*_binary64
205×+-commutative_binary64
175×distribute-rgt-out_binary64
173×neg-mul-1_binary64
133×distribute-neg-in_binary64
124×*-commutative_binary64
123×distribute-rgt-neg-in_binary64
103×distribute-lft-neg-in_binary64
95×associate--r+_binary64
91×neg-sub0_binary64
88×associate-+l+_binary64
84×sqr-pow_binary64
83×unsub-neg_binary64
78×distribute-lft-out_binary64
76×associate-+l-_binary64
65×associate--l+_binary64
64×associate-+r+_binary64
60×associate-+r-_binary64
44×distribute-lft-neg-out_binary64
37×exp-sum_binary64
34×exp-prod_binary64 sub0-neg_binary64
33×distribute-rgt-out--_binary64
22×+-rgt-identity_binary64
21×pow-sqr_binary64
19×distribute-rgt-neg-out_binary64
18×unpow3_binary64
14×exp-diff_binary64 cube-prod_binary64
13×cube-unmult_binary64
12×distribute-neg-out_binary64
10×cube-mult_binary64 distribute-lft-out--_binary64
remove-double-neg_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64
associate--r-_binary64
cube-neg_binary64 sqr-neg_binary64 div-sub_binary64 swap-sqr_binary64
prod-exp_binary64
pow-plus_binary64
associate-/l/_binary64 associate-*r/_binary64
*-lft-identity_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 unpow2_binary64 unpow1/2_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-1-e_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-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 mul-1-neg_binary64 /-rgt-identity_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate--l-_binary64
Counts
84 → 32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0581095
11971062
26681056
321401056
435361056
548721056
650191056

prune20.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New28432
Fresh000
Picked011
Done000
Total28533
Error
0b
Counts
33 → 5
Compiler

Compiled 459 to 128 computations (72.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))) (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))))
0.7b
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
0.7b
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
0.7b
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))

rewrite103.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
18×cbrt-div_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
pow1/3_binary64 flip3-+_binary64 flip-+_binary64
add-exp-log_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 frac-times_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64 associate-*l/_binary64 associate-*r/_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 87
Calls

4 calls:

11.0ms
(*.f64 (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))) (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))))
3.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
3.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
3.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
Compiler

Compiled 3547 to 415 computations (88.3% saved)

series501.0ms (7.4%)

Error
0b
Counts
4 → 96
Calls

4 calls:

117.0ms
(*.f64 (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))) (cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y))))
103.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
102.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
101.0ms
(cbrt.f64 (+.f64 (*.f64 t z) (*.f64 x y)))
Compiler

Compiled 10780 to 6689 computations (37.9% saved)

simplify140.0ms (2.1%)

Algorithm
egg-herbie
Rules
885×associate-/l*_binary64
320×associate-/r/_binary64
213×associate-*r*_binary64
180×times-frac_binary64
163×associate-*l*_binary64
162×*-commutative_binary64
120×unswap-sqr_binary64 distribute-rgt-in_binary64
109×distribute-lft-in_binary64
108×associate-/r*_binary64
99×sqr-pow_binary64
88×cancel-sign-sub-inv_binary64
74×associate-/l/_binary64
72×sub-neg_binary64
64×exp-sum_binary64 associate-*l/_binary64 associate-*r/_binary64
63×distribute-rgt-neg-in_binary64
60×distribute-lft-neg-in_binary64
50×exp-prod_binary64
43×+-commutative_binary64
42×neg-mul-1_binary64 neg-sub0_binary64
37×distribute-rgt-out_binary64
32×log-prod_binary64 distribute-lft-neg-out_binary64
28×unsub-neg_binary64 distribute-lft-out_binary64
25×distribute-rgt-neg-out_binary64
20×unpow1/3_binary64 distribute-neg-out_binary64
16×exp-diff_binary64 div-sub_binary64 pow-sqr_binary64 distribute-lft-out--_binary64
15×cube-prod_binary64
12×distribute-neg-in_binary64
log-pow_binary64 *-rgt-identity_binary64 distribute-rgt-out--_binary64
log-div_binary64 *-lft-identity_binary64 remove-double-neg_binary64 associate--r-_binary64
unpow3_binary64 cube-mult_binary64 swap-sqr_binary64
log-rec_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-unmult_binary64
pow-plus_binary64 rem-sqrt-square_binary64
rem-3cbrt-lft_binary64 count-2_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 difference-of-squares_binary64 associate-+l-_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 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-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_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 +-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-rgt1-in_binary64 distribute-lft1-in_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
Counts
183 → 166
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02755414
17605122
222824826
351734826

prune103.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1660166
Fresh033
Picked011
Done011
Total1665171
Error
0b
Counts
171 → 5
Compiler

Compiled 4740 to 1060 computations (77.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 x y) (*.f64 x y))
0.3b
(*.f64 (*.f64 t z) (*.f64 t z))
1.6b
(-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z)))
25.4b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z))) (-.f64 (*.f64 x y) (*.f64 t z)))

rewrite130.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
82×pow1_binary64
34×pow-prod-down_binary64
30×add-exp-log_binary64 add-cbrt-cube_binary64
16×prod-exp_binary64 cbrt-unprod_binary64
13×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
12×times-frac_binary64
pow-prod-up_binary64 pow-sqr_binary64
add-log-exp_binary64
difference-of-squares_binary64
associate-/l*_binary64 pow-plus_binary64
flip3--_binary64 flip--_binary64 associate-/r*_binary64
associate-/l/_binary64 associate-/r/_binary64 pow2_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64 *-commutative_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
4 → 117
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z))) (-.f64 (*.f64 x y) (*.f64 t z)))
8.0ms
(-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z)))
6.0ms
(*.f64 (*.f64 t z) (*.f64 t z))
6.0ms
(*.f64 (*.f64 x y) (*.f64 x y))
Compiler

Compiled 3613 to 464 computations (87.2% saved)

series242.0ms (3.6%)

Error
0b
Counts
4 → 60
Calls

4 calls:

98.0ms
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z))) (-.f64 (*.f64 x y) (*.f64 t z)))
91.0ms
(-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 t z) (*.f64 t z)))
22.0ms
(*.f64 (*.f64 t z) (*.f64 t z))
21.0ms
(*.f64 (*.f64 x y) (*.f64 x y))
Compiler

Compiled 2030 to 1657 computations (18.4% saved)

simplify128.0ms (1.9%)

Algorithm
egg-herbie
Rules
248×associate-*l*_binary64
247×distribute-rgt-in_binary64
236×times-frac_binary64
230×distribute-lft-in_binary64
227×cancel-sign-sub-inv_binary64
209×associate-/l/_binary64
192×associate-*r*_binary64
169×distribute-rgt-neg-in_binary64
167×exp-prod_binary64
162×unswap-sqr_binary64
153×distribute-lft-neg-in_binary64
135×div-sub_binary64
120×associate-/l*_binary64
94×log-prod_binary64
90×swap-sqr_binary64
88×cube-prod_binary64
65×distribute-neg-frac_binary64
62×sqr-pow_binary64
61×*-commutative_binary64
51×distribute-rgt-out_binary64
44×log-div_binary64 exp-sum_binary64
41×cube-div_binary64
40×sub-neg_binary64
35×neg-sub0_binary64
34×neg-mul-1_binary64
33×unpow3_binary64
28×distribute-lft-out_binary64
26×distribute-lft-neg-out_binary64
21×associate-/r*_binary64
20×pow-plus_binary64
19×cube-mult_binary64
18×+-commutative_binary64
16×exp-diff_binary64
15×distribute-rgt-neg-out_binary64 associate-/r/_binary64
13×associate-*l/_binary64
12×log-pow_binary64 cube-unmult_binary64 pow-sqr_binary64 difference-of-squares_binary64 distribute-neg-in_binary64 associate-+l+_binary64 associate-+r+_binary64
11×log-rec_binary64 associate-*r/_binary64
/-rgt-identity_binary64
unpow2_binary64
*-rgt-identity_binary64
unpow1/2_binary64 unpow1_binary64 *-inverses_binary64 count-2_binary64
unsub-neg_binary64
exp-neg_binary64 rem-sqrt-square_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64 associate--r-_binary64 associate--r+_binary64 associate-+r-_binary64
div-exp_binary64 1-exp_binary64 mul-1-neg_binary64 *-lft-identity_binary64 cancel-sign-sub_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 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 sub0-neg_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-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate--l-_binary64 associate--l+_binary64 associate-+l-_binary64
Counts
177 → 150
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01543365
14012840
216862834
345452402
450232402

prune71.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1500150
Fresh022
Picked011
Done022
Total1505155
Error
0b
Counts
155 → 5
Compiler

Compiled 1956 to 573 computations (70.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))
0.1b
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
0.1b
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
0.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))) (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))))

rewrite106.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
30×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
21×pow1_binary64
16×sqrt-div_binary64
14×add-cube-cbrt_binary64 *-un-lft-identity_binary64
10×pow1/2_binary64 sqrt-pow1_binary64
add-log-exp_binary64 flip3-+_binary64 flip-+_binary64
swap-sqr_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64 associate-*r*_binary64
pow-prod-up_binary64
rem-sqrt-square_binary64 frac-times_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-sqr_binary64 sum-log_binary64
associate-*l/_binary64 associate-*r/_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 sqrt-unprod_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 *-commutative_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
4 → 101
Calls

4 calls:

16.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))) (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))))
6.0ms
(+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
5.0ms
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
Compiler

Compiled 3467 to 330 computations (90.5% saved)

series330.0ms (4.9%)

Error
0b
Counts
4 → 120
Calls

4 calls:

82.0ms
(+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))
79.0ms
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
78.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))) (sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b)))))
77.0ms
(sqrt.f64 (+.f64 (*.f64 x y) (+.f64 (*.f64 t z) (*.f64 a b))))
Compiler

Compiled 5007 to 3289 computations (34.3% saved)

simplify228.0ms (3.4%)

Algorithm
egg-herbie
Rules
566×associate-*l*_binary64
456×associate-*r*_binary64
346×distribute-rgt-in_binary64
322×distribute-lft-in_binary64
250×distribute-rgt-out_binary64
204×cancel-sign-sub-inv_binary64
198×*-commutative_binary64
171×unswap-sqr_binary64
163×distribute-lft-out_binary64
138×distribute-rgt-neg-in_binary64
124×distribute-lft-neg-in_binary64
123×neg-mul-1_binary64
113×associate--l+_binary64
106×exp-prod_binary64
76×log-prod_binary64
72×sub-neg_binary64 distribute-neg-in_binary64
66×associate-+l+_binary64
62×sqr-pow_binary64 associate-+r+_binary64
51×swap-sqr_binary64
50×cube-prod_binary64
44×distribute-lft-neg-out_binary64
40×neg-sub0_binary64
35×unsub-neg_binary64
33×distribute-rgt-out--_binary64
31×distribute-rgt-neg-out_binary64
24×*-rgt-identity_binary64 *-lft-identity_binary64 +-commutative_binary64
23×unpow3_binary64 associate--r+_binary64
22×exp-sum_binary64 rem-sqrt-square_binary64
19×pow-plus_binary64 pow-sqr_binary64
14×log-pow_binary64
13×associate-/l*_binary64
12×cube-unmult_binary64
associate-/r*_binary64
rem-square-sqrt_binary64 associate-/l/_binary64 associate-*r/_binary64 associate--l-_binary64
cube-mult_binary64 associate-+l-_binary64 associate-+r-_binary64
times-frac_binary64 +-rgt-identity_binary64
prod-exp_binary64
count-2_binary64 associate-/r/_binary64
unpow2_binary64 sub0-neg_binary64 difference-of-squares_binary64 associate--r-_binary64
unpow1/2_binary64 distribute-lft-out--_binary64
exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_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 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-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_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 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-*l/_binary64
Counts
221 → 157
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01204377
12474180
27964124
329464027
447224027
549644027
649744027

prune46.0ms (0.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1570157
Fresh011
Picked011
Done033
Total1575162
Error
0b
Counts
162 → 5
Compiler

Compiled 1965 to 256 computations (87% saved)

regimes839.0ms (12.5%)

Accuracy

Total 0.0b remaining (28%)

Threshold costs 0.0b (28%)

Compiler

Compiled 11748 to 8360 computations (28.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (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
01216
11716
21716

end46.0ms (0.7%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 77 to 77 computations (0% saved)

sample1.2s (17.1%)

Algorithm
intervals
Results
299.0ms8000×body128valid
142.0ms3959×body128invalid
Compiler

Compiled 133 to 117 computations (12% saved)

Profiling

Loading profile data...