Details

Time bar (total: 3.1s)

analyze324.0ms (10.4%)

Algorithm
1×search
2×egg-herbie
Rules
1×1-exp_binary64 sub-neg_binary64 +-commutative_binary64
0×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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 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
0611
11111
21211
31011
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.4%24.3%11
31.4%44.3%24.3%12
31.4%44.2%24.3%13
31.5%44.2%24.3%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample26.0ms (0.8%)

Algorithm
1×intervals
Results
10.0ms76×body1024valid
3.0ms46×body512valid
2.0ms105×body128valid
1.0ms9×body2048valid
1.0ms20×body256valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify9.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64 sub-neg_binary64 +-commutative_binary64
0×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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 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
0611
11111
21211
31011

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
40.4b
Counts
1 → 1
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.9b
(-.f64 (exp.f64 x) 1)

rewrite107.0ms (3.4%)

Algorithm
1×rewrite-expression-head
Error
40.3b
Rules
35×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
21×times-frac_binary64
15×add-cube-cbrt_binary64
10×difference-of-squares_binary64
7×associate-/r*_binary64
5×difference-of-sqr-1_binary64 distribute-lft-out--_binary64
4×add-log-exp_binary64 add-cbrt-cube_binary64
3×add-exp-log_binary64 cancel-sign-sub-inv_binary64 associate-/l*_binary64
2×pow1_binary64 flip3--_binary64 flip--_binary64 associate-/r/_binary64
1×diff-log_binary64 sub-neg_binary64 div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
2 → 63
Calls

2 calls:

7.0ms
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 821 to 421 computations (48.7% saved)

series31.0ms (1%)

Error
0.4b
Counts
2 → 12
Calls

2 calls:

10.0ms
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
7.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 231 to 175 computations (24.2% saved)

simplify94.0ms (3%)

Algorithm
1×egg-herbie
Rules
380×distribute-rgt-in_binary64
364×distribute-lft-in_binary64
349×associate-/l*_binary64
332×associate-*r*_binary64
330×div-sub_binary64
262×associate-/l/_binary64
182×associate-/r/_binary64
178×associate-/r*_binary64
127×times-frac_binary64
121×cancel-sign-sub-inv_binary64 associate-*l/_binary64
96×associate--l+_binary64
83×associate--r+_binary64
71×*-commutative_binary64
69×sub-neg_binary64 associate-*l*_binary64
65×exp-sum_binary64
57×associate--l-_binary64
56×associate-*r/_binary64
55×associate-+l+_binary64
54×distribute-rgt-out_binary64
50×distribute-rgt-neg-in_binary64
48×exp-prod_binary64 distribute-lft-out_binary64
45×associate-+r+_binary64
43×+-commutative_binary64
40×distribute-lft-neg-in_binary64
34×prod-exp_binary64
32×div-exp_binary64 distribute-rgt-neg-out_binary64
31×cube-prod_binary64 unsub-neg_binary64
30×distribute-lft-neg-out_binary64
27×exp-diff_binary64
26×log-div_binary64 sqr-pow_binary64 distribute-neg-in_binary64
22×log-prod_binary64 neg-sub0_binary64
21×cube-div_binary64 neg-mul-1_binary64
20×*-rgt-identity_binary64 unswap-sqr_binary64
15×associate-+r-_binary64
13×/-rgt-identity_binary64
12×associate-+l-_binary64
11×*-lft-identity_binary64
10×log-rec_binary64 distribute-rgt-out--_binary64
9×rec-exp_binary64 distribute-neg-frac_binary64 distribute-rgt1-in_binary64
8×unpow3_binary64 pow-plus_binary64 cube-unmult_binary64
7×associate--r-_binary64
6×swap-sqr_binary64
5×log-pow_binary64 cube-mult_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 remove-double-div_binary64 distribute-lft-out--_binary64
4×exp-neg_binary64 rem-log-exp_binary64 mul-1-neg_binary64 +-rgt-identity_binary64 distribute-lft1-in_binary64
3×pow-sqr_binary64 difference-of-sqr-1_binary64 count-2_binary64
2×unpow1/2_binary64 exp-to-pow_binary64 cube-neg_binary64 +-inverses_binary64 difference-of-squares_binary64 distribute-neg-out_binary64
1×unpow2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 rem-3cbrt-lft_binary64 fabs-mul_binary64 sub0-neg_binary64 *-inverses_binary64 difference-of-sqr--1_binary64
0×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 e-exp-1_binary64 exp-0_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64
Counts
75 → 45
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01081272
12181207
25691199
314471195
444231195
551071195

prune30.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New42345
Fresh000
Picked101
Done000
Total43346
Error
0.0b
Counts
46 → 3
Compiler

Compiled 381 to 212 computations (44.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.0b
(/.f64 (exp.f64 x) (+.f64 x (*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.1b
(*.f64 x (+.f64 1/2 (*.f64 x 1/6)))
0.3b
(*.f64 x 1/6)

rewrite111.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
21×add-sqr-sqrt_binary64
17×add-cube-cbrt_binary64 *-un-lft-identity_binary64
15×add-cbrt-cube_binary64
14×add-exp-log_binary64
13×pow1_binary64
9×associate-*l*_binary64 times-frac_binary64
7×associate-*r*_binary64
6×associate-*r/_binary64
5×pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
4×add-log-exp_binary64
3×*-commutative_binary64 flip3-+_binary64 flip-+_binary64 associate-/l*_binary64 associate-/r*_binary64
2×unswap-sqr_binary64 associate-/r/_binary64
1×div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
4 → 93
Calls

4 calls:

6.0ms
(*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))
5.0ms
(*.f64 x (+.f64 1/2 (*.f64 x 1/6)))
5.0ms
(/.f64 (exp.f64 x) (+.f64 x (*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
4.0ms
(*.f64 x 1/6)
Compiler

Compiled 2027 to 1248 computations (38.4% saved)

series53.0ms (1.7%)

Error
0.0b
Counts
4 → 20
Calls

4 calls:

14.0ms
(*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))
12.0ms
(*.f64 x (+.f64 1/2 (*.f64 x 1/6)))
9.0ms
(/.f64 (exp.f64 x) (+.f64 x (*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
6.0ms
(*.f64 x 1/6)
Compiler

Compiled 535 to 401 computations (25% saved)

simplify120.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
610×distribute-rgt-in_binary64
599×distribute-lft-in_binary64
308×*-commutative_binary64
242×cancel-sign-sub-inv_binary64
224×neg-mul-1_binary64
188×unswap-sqr_binary64
185×distribute-neg-in_binary64
176×distribute-rgt-neg-in_binary64
169×associate-*l*_binary64
151×distribute-lft-neg-in_binary64
147×associate-*r*_binary64
99×div-sub_binary64
91×associate-/r*_binary64
80×sub-neg_binary64
79×sqr-pow_binary64
78×exp-prod_binary64
75×times-frac_binary64
69×associate-/l*_binary64
54×*-rgt-identity_binary64
51×*-lft-identity_binary64
45×neg-sub0_binary64
42×associate-/l/_binary64
41×cube-prod_binary64 associate-+l+_binary64 associate-+r+_binary64
40×log-prod_binary64
37×swap-sqr_binary64
32×distribute-rgt1-in_binary64 distribute-rgt-out_binary64
31×distribute-lft-neg-out_binary64
27×exp-sum_binary64
24×distribute-rgt-neg-out_binary64 associate-*l/_binary64
22×distribute-lft-out_binary64
21×associate-/r/_binary64 +-commutative_binary64
20×unsub-neg_binary64
19×associate--r+_binary64
18×associate-*r/_binary64
15×log-pow_binary64 pow-sqr_binary64
13×unpow3_binary64
12×log-div_binary64
10×pow-plus_binary64 exp-to-pow_binary64 cube-unmult_binary64 associate-+l-_binary64
9×exp-diff_binary64 associate-+r-_binary64
8×unpow1/2_binary64 cube-div_binary64 fabs-mul_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64
7×prod-exp_binary64
6×cube-mult_binary64
5×sub0-neg_binary64
4×rem-sqrt-square_binary64 /-rgt-identity_binary64 +-rgt-identity_binary64 associate--l-_binary64
3×div-exp_binary64
2×rec-exp_binary64 fabs-sqr_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate--r-_binary64
1×log-E_binary64 unpow2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 rem-log-exp_binary64 rem-exp-log_binary64 sqr-neg_binary64 distribute-neg-frac_binary64 count-2_binary64
0×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-rec_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 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_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-frac-neg_binary64 distribute-neg-out_binary64 associate--l+_binary64
Counts
113 → 90
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01632000
13681848
211831846
335041844
446571844
549681844

prune65.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New90090
Fresh022
Picked011
Done000
Total90393
Error
0.0b
Counts
93 → 3
Compiler

Compiled 1500 to 935 computations (37.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12)) (*.f64 (pow.f64 x 3) 1/720))
0.0b
(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.1b
(*.f64 (pow.f64 x 3) 1/720)
0.3b
(*.f64 x 1/12)

rewrite109.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
19×add-sqr-sqrt_binary64
18×add-log-exp_binary64
15×associate-*l*_binary64
11×add-exp-log_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
8×add-cbrt-cube_binary64
6×pow1_binary64 associate-*r*_binary64 sum-log_binary64
5×unswap-sqr_binary64
4×prod-exp_binary64 unpow-prod-down_binary64 cube-prod_binary64
3×diff-log_binary64
2×cbrt-unprod_binary64 *-commutative_binary64 sqr-pow_binary64
1×pow-prod-down_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64 flip3-+_binary64 flip-+_binary64 associate-+l+_binary64 +-commutative_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64 associate--l+_binary64
Counts
4 → 77
Calls

4 calls:

13.0ms
(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12)) (*.f64 (pow.f64 x 3) 1/720))
8.0ms
(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
5.0ms
(*.f64 (pow.f64 x 3) 1/720)
3.0ms
(*.f64 x 1/12)
Compiler

Compiled 1586 to 1282 computations (19.2% saved)

series54.0ms (1.7%)

Error
0.0b
Counts
4 → 27
Calls

4 calls:

14.0ms
(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
12.0ms
(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12)) (*.f64 (pow.f64 x 3) 1/720))
9.0ms
(*.f64 (pow.f64 x 3) 1/720)
9.0ms
(*.f64 x 1/12)
Compiler

Compiled 584 to 503 computations (13.9% saved)

simplify111.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
571×distribute-rgt-in_binary64
559×distribute-lft-in_binary64
250×associate-+l+_binary64
221×cancel-sign-sub-inv_binary64
188×exp-prod_binary64
173×log-prod_binary64
158×distribute-rgt-neg-in_binary64
154×associate-*l*_binary64
137×distribute-lft-neg-in_binary64
133×associate-*r*_binary64
110×cube-prod_binary64
73×unswap-sqr_binary64
66×*-commutative_binary64
48×exp-sum_binary64
46×sqr-pow_binary64 associate--l+_binary64
42×swap-sqr_binary64
37×sub-neg_binary64 associate-*l/_binary64
35×unpow3_binary64 times-frac_binary64
32×associate-*r/_binary64
30×distribute-rgt-out_binary64 +-commutative_binary64
25×cube-mult_binary64
24×neg-mul-1_binary64 neg-sub0_binary64
22×log-pow_binary64
20×associate-/r*_binary64
17×div-exp_binary64 associate--r+_binary64 associate-+r-_binary64
16×distribute-lft-neg-out_binary64 associate-/l*_binary64
15×associate-+l-_binary64
14×exp-diff_binary64 *-rgt-identity_binary64
13×*-lft-identity_binary64 distribute-rgt-out--_binary64
12×pow-plus_binary64 associate-+r+_binary64
11×distribute-lft-out_binary64
10×fabs-mul_binary64
7×cube-unmult_binary64
6×unsub-neg_binary64 distribute-neg-in_binary64
5×prod-exp_binary64 rem-sqrt-square_binary64 pow-sqr_binary64 distribute-neg-frac_binary64
4×difference-of-squares_binary64 distribute-rgt-neg-out_binary64 associate-/r/_binary64
3×+-rgt-identity_binary64 distribute-lft-out--_binary64 associate-/l/_binary64
2×unpow1/2_binary64 fabs-sqr_binary64 count-2_binary64
1×1-exp_binary64 exp-1-e_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64
0×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 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 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 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
104 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01401436
13101391
213061358
345831358
449391358
549301358

prune48.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New65166
Fresh011
Picked101
Done011
Total66369
Error
0b
Counts
69 → 3
Compiler

Compiled 1011 to 809 computations (20% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720))
0.0b
(+.f64 (+.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720)))
0.1b
(*.f64 (pow.f64 x 3) -1/720)
0.3b
(*.f64 1/12 x)

rewrite313.0ms (10%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
19×add-sqr-sqrt_binary64
18×add-log-exp_binary64
17×*-un-lft-identity_binary64
15×associate-*l*_binary64
11×add-exp-log_binary64
10×add-cube-cbrt_binary64
9×sum-log_binary64
8×add-cbrt-cube_binary64
6×pow1_binary64 associate-*r*_binary64 flip3-+_binary64 flip-+_binary64
5×unswap-sqr_binary64 distribute-lft-out_binary64
4×prod-exp_binary64 unpow-prod-down_binary64 cube-prod_binary64 frac-add_binary64
2×cbrt-unprod_binary64 *-commutative_binary64 sqr-pow_binary64 +-commutative_binary64
1×pow-prod-down_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64 div-inv_binary64 associate-+l+_binary64 associate-+r+_binary64
Counts
4 → 83
Calls

4 calls:

12.0ms
(+.f64 (+.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720)))
6.0ms
(+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720))
6.0ms
(*.f64 (pow.f64 x 3) -1/720)
4.0ms
(*.f64 1/12 x)
Compiler

Compiled 1933 to 1566 computations (19% saved)

series57.0ms (1.8%)

Error
0b
Counts
4 → 24
Calls

4 calls:

16.0ms
(+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720))
13.0ms
(+.f64 (+.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/12 x) (*.f64 (pow.f64 x 3) -1/720)))
9.0ms
(*.f64 (pow.f64 x 3) -1/720)
7.0ms
(*.f64 1/12 x)
Compiler

Compiled 535 to 461 computations (13.8% saved)

simplify106.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
942×distribute-rgt-in_binary64
290×cancel-sign-sub-inv_binary64
200×log-prod_binary64
198×exp-prod_binary64
194×associate-*l*_binary64
182×associate-*r*_binary64
145×distribute-rgt-neg-in_binary64
127×distribute-lft-neg-in_binary64
119×distribute-lft-in_binary64
97×*-commutative_binary64
72×times-frac_binary64
70×unswap-sqr_binary64
68×distribute-lft-neg-out_binary64
66×sub-neg_binary64
60×distribute-rgt-neg-out_binary64
56×cube-prod_binary64
44×sqr-pow_binary64
40×unpow3_binary64 swap-sqr_binary64
39×+-commutative_binary64
34×distribute-rgt-out_binary64
30×associate-+l+_binary64
27×distribute-neg-in_binary64
26×distribute-lft-out_binary64
25×neg-mul-1_binary64 neg-sub0_binary64
23×associate-+r+_binary64
22×distribute-rgt-out--_binary64
17×associate--l+_binary64
13×log-pow_binary64 exp-sum_binary64 distribute-neg-frac_binary64 associate-/r*_binary64
12×pow-plus_binary64 prod-exp_binary64 *-rgt-identity_binary64 associate--r+_binary64
11×*-lft-identity_binary64
9×unsub-neg_binary64
8×exp-diff_binary64 cube-mult_binary64
7×distribute-lft-out--_binary64
6×pow-sqr_binary64 associate-*l/_binary64
5×rem-sqrt-square_binary64 associate-*r/_binary64 associate-+l-_binary64
4×cube-unmult_binary64 cube-div_binary64 associate-+r-_binary64
2×fabs-mul_binary64 fabs-sqr_binary64 difference-of-squares_binary64 associate-/l*_binary64
1×log-div_binary64 unpow1/2_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 /-rgt-identity_binary64 distribute-neg-out_binary64 associate--r-_binary64 associate--l-_binary64
0×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 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 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 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64
Counts
107 → 69
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01641895
14431844
218431790
346441790
449601790

prune50.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh011
Picked011
Done011
Total69372
Error
0b
Counts
72 → 3
Compiler

Compiled 1176 to 948 computations (19.4% saved)

regimes296.0ms (9.5%)

Accuracy

Total 0.9b remaining (98.3%)

Threshold costs 0.9b (98.3%)

Compiler

Compiled 3414 to 2521 computations (26.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64 +-commutative_binary64
0×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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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
01427
12027
22027

end1.0ms (0%)

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample973.0ms (31.1%)

Algorithm
1×intervals
Results
364.0ms2614×body1024valid
109.0ms1345×body512valid
73.0ms3087×body128valid
49.0ms302×body2048valid
38.0ms652×body256valid
0.0ms1×body2048invalid
0.0ms1×body128overflowed
Compiler

Compiled 72 to 63 computations (12.5% saved)

Profiling

Loading profile data...