Details

Time bar (total: 4.1s)

analyze292.0ms (7.2%)

Algorithm
search
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%50%0%3
62.5%37.5%0%4
68.7%31.2%0%5
71.8%28.1%0%6
73.4%26.5%0%7
74.2%25.8%0%8
74.6%25.4%0%9
74.8%25.2%0%10
74.9%25.1%0%11
74.9%25%0%12
74.9%25%0%13
75%25%0%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample64.0ms (1.6%)

Algorithm
intervals
Results
29.0ms78×body1024valid
10.0ms50×body512valid
10.0ms33×body2048valid
3.0ms73×body128valid
2.0ms22×body256valid
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
53.1b
Counts
1 → 1
Compiler

Compiled 9 to 7 computations (22.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.5b
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.3b
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.1b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite78.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
52.9b
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 log-prod_binary64
add-cbrt-cube_binary64 flip3-+_binary64 flip-+_binary64 sqrt-prod_binary64
sqrt-div_binary64 log-div_binary64 distribute-lft-out_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 log-pow_binary64 rem-log-exp_binary64 sum-log_binary64 +-commutative_binary64
Counts
3 → 42
Calls

3 calls:

6.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 703 to 424 computations (39.7% saved)

series57.0ms (1.4%)

Error
0.0b
Counts
3 → 19
Calls

3 calls:

14.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
12.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
12.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Compiler

Compiled 513 to 442 computations (13.8% saved)

simplify126.0ms (3.1%)

Algorithm
egg-herbie
Rules
436×times-frac_binary64
389×unswap-sqr_binary64
368×sub-neg_binary64
236×distribute-rgt-in_binary64
225×unsub-neg_binary64 associate-+l+_binary64
206×associate-+r+_binary64
187×distribute-lft-in_binary64
147×*-commutative_binary64
145×associate-/r*_binary64
135×neg-mul-1_binary64
131×div-sub_binary64
129×cancel-sign-sub-inv_binary64
125×associate--r+_binary64
106×+-commutative_binary64
103×neg-sub0_binary64 associate-*l*_binary64
99×associate-+l-_binary64
86×associate--l+_binary64
80×associate-*r*_binary64
76×associate-+r-_binary64
67×difference-of-squares_binary64 distribute-rgt-out_binary64
60×distribute-rgt-neg-in_binary64
58×associate-*r/_binary64
57×associate-*l/_binary64
55×associate--r-_binary64
48×log-prod_binary64 sqr-pow_binary64
47×distribute-neg-frac_binary64 associate-/l*_binary64
46×distribute-lft-neg-in_binary64
41×sub0-neg_binary64
36×cube-prod_binary64
35×unpow3_binary64
32×distribute-rgt-out--_binary64
30×*-rgt-identity_binary64
28×distribute-neg-in_binary64 associate-/l/_binary64
27×+-rgt-identity_binary64
26×pow-plus_binary64 *-lft-identity_binary64
24×associate--l-_binary64
22×log-div_binary64
21×distribute-lft-out_binary64
19×exp-prod_binary64 cube-unmult_binary64
15×--rgt-identity_binary64
12×remove-double-neg_binary64 distribute-rgt1-in_binary64
10×distribute-lft-neg-out_binary64
cube-div_binary64 difference-of-sqr--1_binary64
pow-sqr_binary64
rem-sqrt-square_binary64 distribute-lft-out--_binary64
exp-sum_binary64
log-pow_binary64 mul-1-neg_binary64 remove-double-div_binary64
prod-exp_binary64 exp-diff_binary64 cube-mult_binary64 cube-neg_binary64 +-lft-identity_binary64 mul0-lft_binary64 +-inverses_binary64 difference-of-sqr-1_binary64 count-2_binary64
log-rec_binary64 unpow1/2_binary64 sqr-neg_binary64 mul0-rgt_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64
unpow2_binary64 div0_binary64 swap-sqr_binary64 associate-/r/_binary64
exp-to-pow_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 rem-square-sqrt_binary64 distribute-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 pow-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 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64
Counts
61 → 45
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0101964
1232882
2475852
31249846
43278846
54553846
64970846
74844846

prune44.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New40545
Fresh000
Picked101
Done000
Total41546
Error
30.3b
Counts
46 → 5
Compiler

Compiled 672 to 442 computations (34.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 x (+.f64 x (/.f64 1/2 x)))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
30.3b
Rules
add-log-exp_binary64 *-un-lft-identity_binary64
sum-log_binary64 distribute-lft-out_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
1 → 15
Calls

1 calls:

8.0ms
(+.f64 x (+.f64 x (/.f64 1/2 x)))
Compiler

Compiled 209 to 138 computations (34% saved)

series16.0ms (0.4%)

Error
30.3b
Counts
1 → 6
Calls

1 calls:

14.0ms
(+.f64 x (+.f64 x (/.f64 1/2 x)))
Compiler

Compiled 90 to 81 computations (10% saved)

simplify74.0ms (1.8%)

Algorithm
egg-herbie
Rules
555×sub-neg_binary64
325×times-frac_binary64
298×unsub-neg_binary64
257×associate-*l*_binary64
234×distribute-neg-in_binary64
225×associate-/l*_binary64
192×distribute-rgt-out_binary64
191×distribute-rgt-in_binary64
179×associate-*r*_binary64
167×distribute-lft-out_binary64 distribute-lft-in_binary64
156×associate--l+_binary64
153×associate--r+_binary64
145×+-commutative_binary64
142×div-sub_binary64
139×neg-mul-1_binary64
133×neg-sub0_binary64
128×associate-+l-_binary64
96×distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 associate-+r-_binary64
77×exp-prod_binary64 associate-+l+_binary64
76×cancel-sign-sub-inv_binary64
70×associate-*l/_binary64
65×associate-*r/_binary64
64×exp-sum_binary64
60×associate-+r+_binary64
49×*-commutative_binary64
48×exp-diff_binary64
46×cube-prod_binary64
43×distribute-rgt-out--_binary64
40×unswap-sqr_binary64 cancel-sign-sub_binary64
38×log-prod_binary64
37×associate-/l/_binary64
36×distribute-neg-frac_binary64 distribute-lft-neg-out_binary64
31×distribute-rgt-neg-out_binary64
26×sqr-pow_binary64
25×sub0-neg_binary64
23×associate--r-_binary64 associate--l-_binary64
19×+-rgt-identity_binary64
15×*-rgt-identity_binary64
14×*-lft-identity_binary64
10×cube-div_binary64
distribute-rgt1-in_binary64 distribute-lft-out--_binary64
log-div_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 associate-/r/_binary64
cube-unmult_binary64
remove-double-neg_binary64 +-inverses_binary64 swap-sqr_binary64
unpow3_binary64 pow-plus_binary64 +-lft-identity_binary64 difference-of-squares_binary64
prod-exp_binary64 sqr-neg_binary64 pow-sqr_binary64 count-2_binary64
unpow1/2_binary64 div-exp_binary64 cube-mult_binary64 cube-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64
unpow1_binary64 exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 --rgt-identity_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 distribute-frac-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 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 exp-neg_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-sqrt-square_binary64 rem-square-sqrt_binary64 div0_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 associate-/r*_binary64
Counts
21 → 16
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037283
1100253
2284241
3967235
42257235
54243235
64969235

prune10.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New16016
Fresh044
Picked011
Done000
Total16521
Error
30.3b
Counts
21 → 5
Compiler

Compiled 200 to 133 computations (33.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
0.2b
(/.f64 1/8 (pow.f64 x 3))
10.9b
(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

rewrite145.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
30.3b
Rules
41×*-un-lft-identity_binary64
40×times-frac_binary64
29×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
12×unpow-prod-down_binary64 cube-prod_binary64 associate-/r*_binary64
add-exp-log_binary64
log-prod_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
pow1_binary64 distribute-lft-out_binary64 unpow3_binary64 cube-mult_binary64 sqr-pow_binary64
log-div_binary64 div-exp_binary64 associate-/l*_binary64
frac-add_binary64 flip3-+_binary64 flip-+_binary64
log-pow_binary64 rem-log-exp_binary64 pow-to-exp_binary64 pow-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 sum-log_binary64 +-commutative_binary64
Counts
3 → 96
Calls

3 calls:

33.0ms
(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
29.0ms
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
5.0ms
(/.f64 1/8 (pow.f64 x 3))
Compiler

Compiled 1483 to 1199 computations (19.2% saved)

series37.0ms (0.9%)

Error
30.3b
Counts
3 → 13
Calls

3 calls:

15.0ms
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
9.0ms
(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
8.0ms
(/.f64 1/8 (pow.f64 x 3))
Compiler

Compiled 315 to 288 computations (8.6% saved)

simplify103.0ms (2.5%)

Algorithm
egg-herbie
Rules
685×associate-*l*_binary64
387×associate-/l*_binary64
330×log-prod_binary64 associate-*l/_binary64
298×associate-*r/_binary64
284×associate-/l/_binary64
139×unswap-sqr_binary64
128×associate-/r*_binary64
124×cancel-sign-sub-inv_binary64
78×associate-/r/_binary64
75×distribute-rgt-neg-in_binary64
73×log-div_binary64
72×distribute-lft-neg-in_binary64
67×distribute-rgt-in_binary64
54×distribute-neg-frac_binary64
53×distribute-lft-in_binary64
44×associate-*r*_binary64
41×cube-prod_binary64
33×times-frac_binary64 sqr-pow_binary64
30×sub-neg_binary64
27×swap-sqr_binary64
22×log-pow_binary64
21×distribute-rgt-out_binary64
20×*-commutative_binary64
18×neg-mul-1_binary64 neg-sub0_binary64
17×distribute-lft-neg-out_binary64
15×distribute-lft-out_binary64
14×+-commutative_binary64
13×cube-div_binary64 distribute-rgt-neg-out_binary64
11×unpow3_binary64
log-rec_binary64 pow-plus_binary64 exp-prod_binary64 cube-mult_binary64 div-sub_binary64 distribute-frac-neg_binary64 distribute-rgt-out--_binary64
rem-sqrt-square_binary64 *-rgt-identity_binary64 pow-sqr_binary64 distribute-neg-in_binary64
cube-unmult_binary64
prod-exp_binary64 distribute-lft-out--_binary64 count-2_binary64
unsub-neg_binary64 /-rgt-identity_binary64 associate-+l-_binary64 associate-+r-_binary64
exp-diff_binary64 associate--l+_binary64 associate-+l+_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 *-lft-identity_binary64 difference-of-squares_binary64 distribute-neg-out_binary64 distribute-rgt1-in_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 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--r+_binary64 associate-+r+_binary64
Counts
109 → 74
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01581700
12971608
29941578
347671577
451911577

prune39.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh033
Picked011
Done011
Total74579
Error
30.3b
Counts
79 → 5
Compiler

Compiled 837 to 649 computations (22.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(log.f64 (/.f64 -1 x))
0.1b
(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
0.1b
(/.f64 1/4 (*.f64 x x))

rewrite82.0ms (2%)

Algorithm
rewrite-expression-head
Error
30.3b
Rules
29×log-prod_binary64
24×*-un-lft-identity_binary64
21×times-frac_binary64
20×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
13×associate-+r+_binary64
11×add-exp-log_binary64
pow1_binary64 add-cbrt-cube_binary64
log-pow_binary64
distribute-lft-out_binary64
div-exp_binary64 add-log-exp_binary64 div-inv_binary64 associate-/l*_binary64 associate-+l+_binary64
cbrt-undiv_binary64 log-div_binary64 rem-log-exp_binary64
prod-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r*_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
3 → 77
Calls

3 calls:

6.0ms
(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
4.0ms
(/.f64 1/4 (*.f64 x x))
2.0ms
(log.f64 (/.f64 -1 x))
Compiler

Compiled 1395 to 1020 computations (26.9% saved)

series41.0ms (1%)

Error
30.3b
Counts
3 → 9
Calls

3 calls:

16.0ms
(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
11.0ms
(log.f64 (/.f64 -1 x))
10.0ms
(/.f64 1/4 (*.f64 x x))
Compiler

Compiled 320 to 273 computations (14.7% saved)

simplify159.0ms (3.9%)

Algorithm
egg-herbie
Rules
502×times-frac_binary64
360×unsub-neg_binary64
350×sub-neg_binary64
317×cancel-sign-sub-inv_binary64
289×associate-/r*_binary64
274×associate-/l/_binary64
255×distribute-rgt-in_binary64
244×distribute-lft-in_binary64
213×associate-/l*_binary64
208×neg-sub0_binary64
201×neg-mul-1_binary64
139×log-div_binary64
127×associate-*l/_binary64
122×log-prod_binary64
98×associate-+l+_binary64
92×unswap-sqr_binary64
81×associate-+l-_binary64
79×associate-+r+_binary64
78×distribute-rgt-neg-out_binary64
76×associate-+r-_binary64
72×+-commutative_binary64
71×associate-/r/_binary64 associate--l-_binary64
70×associate-*r/_binary64
67×distribute-lft-neg-out_binary64
65×exp-sum_binary64
64×*-commutative_binary64
62×distribute-neg-in_binary64
61×associate-*l*_binary64
59×associate--l+_binary64
49×associate-*r*_binary64
47×sqr-pow_binary64
46×log-pow_binary64
42×exp-diff_binary64
37×exp-prod_binary64
36×prod-exp_binary64
32×remove-double-neg_binary64
31×distribute-rgt-out_binary64
29×associate--r+_binary64
23×unpow3_binary64 distribute-rgt-neg-in_binary64
22×swap-sqr_binary64
20×cube-prod_binary64
19×distribute-lft-neg-in_binary64
18×distribute-neg-out_binary64
17×+-rgt-identity_binary64
16×pow-plus_binary64
15×cube-div_binary64
14×exp-to-pow_binary64
12×log-rec_binary64
10×*-lft-identity_binary64 distribute-rgt-out--_binary64 distribute-lft-out_binary64
div-exp_binary64 cube-unmult_binary64 sub0-neg_binary64 associate--r-_binary64
count-2_binary64
rem-exp-log_binary64
pow-sqr_binary64
cube-mult_binary64 mul-1-neg_binary64 /-rgt-identity_binary64
sqr-neg_binary64 *-rgt-identity_binary64
rec-exp_binary64 div-sub_binary64
exp-neg_binary64 cube-neg_binary64 --rgt-identity_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
log-E_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-log-exp_binary64 rem-sqrt-square_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 pow-base-0_binary64 unpow1/3_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 e-exp-1_binary64 exp-0_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_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
Counts
86 → 52
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01461105
12851023
2677992
32248990
43913966
54794966
64956966
74999966
84871966

prune35.0ms (0.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New51152
Fresh022
Picked011
Done022
Total51657
Error
30.3b
Counts
57 → 6
Compiler

Compiled 671 to 475 computations (29.2% saved)

regimes352.0ms (8.7%)

Accuracy

Total -28.7b remaining (-6702.6%)

Threshold costs -28.7b (-6702.6%)

Compiler

Compiled 3024 to 2377 computations (21.4% saved)

bsearch34.0ms (0.8%)

Steps
ItersRangePoint
10
3.7588415531104074e-13
256833.9911487608
0.7855249968658321
10
-4045.0833086761595
-9.624771969692172e-15
-0.9051123451222073
Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 distribute-neg-frac_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 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-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
02140
12540
23340
33540
43640
53540

end1.0ms (0%)

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample2.2s (54.2%)

Algorithm
intervals
Results
904.0ms2480×body1024valid
385.0ms1188×body2048valid
272.0ms1288×body512valid
109.0ms2329×body128valid
81.0ms672×body256valid
19.0ms43×body4096valid
Compiler

Compiled 151 to 120 computations (20.5% saved)

Profiling

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