Details

Time bar (total: 20.8s)

analyze2.0s (9.6%)

Algorithm
1×search
2×egg-herbie
Rules
506×times-frac_binary64
396×cancel-sign-sub-inv_binary64
336×associate-/r*_binary64
265×swap-sqr_binary64
250×associate-*l/_binary64 associate-*r/_binary64
203×associate-/l*_binary64
167×*-commutative_binary64
160×associate-*l*_binary64
149×associate-*r*_binary64
137×distribute-rgt-in_binary64 distribute-lft-in_binary64
103×sub-neg_binary64
61×+-commutative_binary64
31×difference-of-squares_binary64
30×+-rgt-identity_binary64 associate-+r-_binary64
15×sub0-neg_binary64 associate-/r/_binary64 associate-+l-_binary64
12×neg-mul-1_binary64 neg-sub0_binary64
6×distribute-lft-neg-out_binary64 distribute-rgt-neg-in_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 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 div-sub_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-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 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 unswap-sqr_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-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01591248
16761248
236441248
344671248
456241248
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
0%98.1%1.9%13
0%98.1%1.9%14
Compiler

Compiled 53 to 22 computations (58.5% saved)

sample173.0ms (0.8%)

Algorithm
1×intervals
Results
31.0ms57×body4096valid
30.0ms47×body8192valid
28.0ms366×body128nan
19.0ms49×body2048valid
10.0ms133×body128invalid
5.0ms71×body128valid
5.0ms17×body1024valid
2.0ms9×body512valid
1.0ms6×body256valid
1.0ms1×body8192exit
0.0ms1×body512invalid
Compiler

Compiled 105 to 49 computations (53.3% saved)

simplify45.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
599×times-frac_binary64
518×distribute-neg-frac_binary64
304×associate-/l*_binary64
217×cancel-sign-sub-inv_binary64
190×associate-/r*_binary64
188×associate-*r*_binary64
187×associate-*l/_binary64
186×associate-*l*_binary64
162×associate-*r/_binary64
144×distribute-neg-in_binary64
123×neg-mul-1_binary64
122×neg-sub0_binary64
115×swap-sqr_binary64
112×associate-/l/_binary64
55×associate-/r/_binary64
44×*-commutative_binary64
22×distribute-rgt-in_binary64 distribute-lft-in_binary64
10×unsub-neg_binary64 sub-neg_binary64
8×+-commutative_binary64
4×unswap-sqr_binary64 distribute-rgt-out_binary64
3×unpow3_binary64 cube-unmult_binary64 sqr-pow_binary64
2×sub0-neg_binary64 +-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 difference-of-squares_binary64 distribute-lft-neg-out_binary64 distribute-lft-out_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
1×cube-div_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-neg-in_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 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-mult_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 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02278
16378
229078
3303969
4361969
5501969

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
59.2b
Counts
2 → 2
Compiler

Compiled 144 to 75 computations (47.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.4b
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
16.4b
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
16.4b
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
29.9b
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))

rewrite676.0ms (3.3%)

Algorithm
1×rewrite-expression-head
Error
59.2b
Rules
211×add-exp-log_binary64 add-cbrt-cube_binary64
117×prod-exp_binary64 cbrt-unprod_binary64
45×div-exp_binary64 cbrt-undiv_binary64
6×add-log-exp_binary64 *-un-lft-identity_binary64
4×pow1_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
3×frac-2neg_binary64 times-frac_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64
2×sqrt-div_binary64 frac-add_binary64
1×sum-log_binary64 flip3--_binary64 flip--_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
4 → 143
Calls

4 calls:

45.0ms
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))
16.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
13.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
12.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
Compiler

Compiled 10014 to 1186 computations (88.2% saved)

series913.0ms (4.4%)

Error
33.2b
Counts
4 → 71
Calls

4 calls:

228.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
226.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
225.0ms
(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))
200.0ms
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))
Compiler

Compiled 6232 to 3915 computations (37.2% saved)

simplify336.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
553×times-frac_binary64
265×associate-*l*_binary64
225×associate-*r*_binary64
214×cancel-sign-sub-inv_binary64
202×associate-/r*_binary64
198×associate-/l*_binary64
181×unpow3_binary64
148×swap-sqr_binary64
146×log-div_binary64
139×distribute-rgt-neg-in_binary64
133×distribute-lft-neg-in_binary64
111×cube-prod_binary64 *-commutative_binary64
101×cube-div_binary64
98×log-prod_binary64
88×distribute-neg-frac_binary64 associate-*l/_binary64
78×sub-neg_binary64
68×unswap-sqr_binary64 associate-*r/_binary64
57×distribute-rgt-out_binary64
52×sqr-pow_binary64
44×neg-sub0_binary64 distribute-rgt-out--_binary64
42×neg-mul-1_binary64
39×distribute-lft-out--_binary64
32×+-commutative_binary64
26×distribute-neg-in_binary64
23×exp-prod_binary64
17×cube-mult_binary64 distribute-rgt-in_binary64
16×associate--r+_binary64
15×associate--l+_binary64
13×distribute-lft-in_binary64 associate-/r/_binary64 associate-+l+_binary64
12×difference-of-squares_binary64
10×distribute-lft-neg-out_binary64
9×cube-unmult_binary64 associate-+r+_binary64
8×pow-plus_binary64 unsub-neg_binary64
7×pow-sqr_binary64
5×distribute-rgt-neg-out_binary64 associate-/l/_binary64
4×log-pow_binary64
3×unpow2_binary64 unpow1/2_binary64 unpow1_binary64 div-sub_binary64 associate-+r-_binary64
2×mul-1-neg_binary64 cancel-sign-sub_binary64 count-2_binary64 associate-+l-_binary64
1×prod-exp_binary64 1-exp_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 +-inverses_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 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-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-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64
Counts
214 → 202
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01725808
14785324
228925243
348205195
450465195

prune105.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1957202
Fresh101
Picked101
Done000
Total1977204
Error
33.4b
Counts
204 → 7
Compiler

Compiled 3087 to 805 computations (73.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.0b
(*.f64 (*.f64 D D) h)
10.5b
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 1/2 (/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))))
12.7b
(/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))
13.5b
(*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h)))

rewrite1.0s (4.8%)

Algorithm
1×rewrite-expression-head
Error
23.3b
Rules
917×add-exp-log_binary64 add-cbrt-cube_binary64
623×prod-exp_binary64 cbrt-unprod_binary64
166×div-exp_binary64 cbrt-undiv_binary64
46×pow1_binary64
30×pow-prod-down_binary64
9×associate-*l*_binary64
8×add-sqr-sqrt_binary64
7×add-cube-cbrt_binary64 *-un-lft-identity_binary64
5×associate-*r*_binary64
4×add-log-exp_binary64 times-frac_binary64
3×*-commutative_binary64 associate-*r/_binary64
2×div-inv_binary64
1×frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 associate-/r*_binary64 frac-times_binary64 associate-*l/_binary64 unswap-sqr_binary64
Counts
4 → 315
Calls

4 calls:

31.0ms
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 1/2 (/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))))
18.0ms
(/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))
12.0ms
(*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h)))
6.0ms
(*.f64 (*.f64 D D) h)
Compiler

Compiled 14850 to 3482 computations (76.6% saved)

series722.0ms (3.5%)

Error
25.7b
Counts
4 → 54
Calls

4 calls:

300.0ms
(/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))
249.0ms
(*.f64 (/.f64 c0 (*.f64 2 w)) (*.f64 1/2 (/.f64 (*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h))) (*.f64 (*.f64 d d) c0))))
119.0ms
(*.f64 (*.f64 M M) (*.f64 w (*.f64 (*.f64 D D) h)))
38.0ms
(*.f64 (*.f64 D D) h)
Compiler

Compiled 2430 to 2283 computations (6% saved)

simplify598.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
841×times-frac_binary64
533×associate-*l*_binary64
365×associate-*r/_binary64
363×associate-/r*_binary64
337×associate-/l*_binary64
305×associate-*l/_binary64
166×*-commutative_binary64
145×associate-*r*_binary64
121×log-div_binary64
64×associate-+r+_binary64
58×associate-+l-_binary64
39×sub-neg_binary64
31×+-commutative_binary64
29×swap-sqr_binary64
27×associate-+r-_binary64
26×log-prod_binary64
19×exp-prod_binary64 associate-/r/_binary64
16×associate--l+_binary64
15×cube-unmult_binary64 unswap-sqr_binary64
14×distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
12×associate--r+_binary64
9×sqr-pow_binary64
8×neg-mul-1_binary64 neg-sub0_binary64 cancel-sign-sub-inv_binary64
6×associate-+l+_binary64
5×distribute-neg-in_binary64
3×log-pow_binary64 unpow2_binary64 pow-plus_binary64 unpow1_binary64 pow-sqr_binary64 count-2_binary64
2×*-rgt-identity_binary64 associate-/l/_binary64
1×1-exp_binary64 *-lft-identity_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 unpow3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-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 div-sub_binary64 unsub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_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 associate--r-_binary64 associate--l-_binary64
Counts
369 → 347
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047318972
176212573
2483112573
3501612573

prune246.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3434347
Fresh156
Picked101
Done000
Total3459354
Error
23.0b
Counts
354 → 9
Compiler

Compiled 2584 to 1108 computations (57.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 1/4 (/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d)))
9.0b
(*.f64 (*.f64 D D) h)
9.8b
(/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d))
15.5b
(*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h))

rewrite886.0ms (4.3%)

Algorithm
1×rewrite-expression-head
Error
18.6b
Rules
176×add-exp-log_binary64 add-cbrt-cube_binary64
107×prod-exp_binary64 cbrt-unprod_binary64
32×pow1_binary64
28×div-exp_binary64 cbrt-undiv_binary64
19×pow-prod-down_binary64
10×add-sqr-sqrt_binary64
9×associate-*r*_binary64
7×add-cube-cbrt_binary64 *-un-lft-identity_binary64
5×associate-*l*_binary64
4×add-log-exp_binary64
3×*-commutative_binary64
2×times-frac_binary64 div-inv_binary64 unswap-sqr_binary64
1×frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*r/_binary64
Counts
4 → 137
Calls

4 calls:

30.0ms
(*.f64 1/4 (/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d)))
26.0ms
(/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d))
19.0ms
(*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h))
11.0ms
(*.f64 (*.f64 D D) h)
Compiler

Compiled 3558 to 677 computations (81% saved)

series385.0ms (1.9%)

Error
23.0b
Counts
4 → 39
Calls

4 calls:

144.0ms
(*.f64 1/4 (/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d)))
132.0ms
(/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) (*.f64 d d))
75.0ms
(*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h))
29.0ms
(*.f64 (*.f64 D D) h)
Compiler

Compiled 1215 to 1319 computations (-8.6% saved)

simplify164.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
345×associate-/r/_binary64
315×times-frac_binary64
252×unswap-sqr_binary64
250×associate-/l/_binary64
240×log-prod_binary64
221×associate-*l*_binary64
209×associate-*r*_binary64
167×log-div_binary64
161×cube-prod_binary64
151×associate-/l*_binary64
150×sqr-pow_binary64
144×exp-prod_binary64
122×associate-/r*_binary64
108×*-commutative_binary64
104×sub-neg_binary64
102×associate-+l+_binary64
85×associate-+r+_binary64
84×cube-div_binary64
83×associate--l+_binary64
69×associate-*r/_binary64
65×+-commutative_binary64
51×associate-*l/_binary64
50×distribute-rgt-neg-in_binary64
48×swap-sqr_binary64
44×distribute-lft-neg-in_binary64
42×unpow3_binary64
39×cube-mult_binary64
34×neg-mul-1_binary64 neg-sub0_binary64
26×cancel-sign-sub-inv_binary64
24×pow-sqr_binary64
22×associate-+r-_binary64
20×unsub-neg_binary64
14×associate--r+_binary64
11×cube-unmult_binary64
10×associate-+l-_binary64
9×log-pow_binary64 pow-plus_binary64
8×*-rgt-identity_binary64 *-lft-identity_binary64
6×+-rgt-identity_binary64
5×log-rec_binary64
4×unpow1/2_binary64
3×unpow2_binary64 unpow1_binary64 rem-sqrt-square_binary64 /-rgt-identity_binary64 distribute-lft-neg-out_binary64 count-2_binary64
2×distribute-rgt-out--_binary64 distribute-lft-out_binary64
1×1-exp_binary64 exp-1-e_binary64 sub0-neg_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64 distribute-rgt-in_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 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 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_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 div-sub_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 difference-of-squares_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 distribute-lft-out--_binary64 distribute-lft-in_binary64 associate--r-_binary64
Counts
176 → 135
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01824767
13563276
217503276
336373238
449213238
549913238

prune48.0ms (0.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1287135
Fresh088
Picked011
Done000
Total12816144
Error
19.4b
Counts
144 → 16
Compiler

Compiled 873 to 459 computations (47.4% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

2.8b
(/.f64 (*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h)) d)
6.3b
(/.f64 (*.f64 M M) d)
9.0b
(*.f64 (*.f64 D D) h)
13.8b
(*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h))

rewrite243.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
17.5b
Rules
97×add-exp-log_binary64 add-cbrt-cube_binary64
46×prod-exp_binary64 cbrt-unprod_binary64
24×div-exp_binary64 cbrt-undiv_binary64
18×pow1_binary64
12×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64 *-un-lft-identity_binary64
9×pow-prod-down_binary64 times-frac_binary64
8×associate-*l*_binary64
6×associate-/r*_binary64
4×add-log-exp_binary64 associate-*r*_binary64
3×div-inv_binary64
2×associate-*l/_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64 associate-/l*_binary64
1×unswap-sqr_binary64 associate-/l/_binary64
Counts
4 → 116
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h)) d)
10.0ms
(*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h))
7.0ms
(/.f64 (*.f64 M M) d)
5.0ms
(*.f64 (*.f64 D D) h)
Compiler

Compiled 2698 to 612 computations (77.3% saved)

series174.0ms (0.8%)

Error
19.4b
Counts
4 → 36
Calls

4 calls:

68.0ms
(/.f64 (*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h)) d)
62.0ms
(*.f64 (/.f64 (*.f64 M M) d) (*.f64 (*.f64 D D) h))
18.0ms
(*.f64 (*.f64 D D) h)
17.0ms
(/.f64 (*.f64 M M) d)
Compiler

Compiled 1140 to 1197 computations (-5% saved)

simplify165.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
593×associate-/r/_binary64
539×*-commutative_binary64
266×log-prod_binary64
232×unswap-sqr_binary64
206×sub-neg_binary64
187×associate-*r*_binary64
182×cube-prod_binary64 associate-*l*_binary64
164×associate-/l*_binary64
141×log-div_binary64
133×times-frac_binary64
123×sqr-pow_binary64
119×associate-*l/_binary64
107×exp-prod_binary64
94×unpow3_binary64
93×cube-div_binary64
85×associate-/l/_binary64
78×associate-/r*_binary64
75×associate-+l+_binary64
74×associate-+r+_binary64
73×associate-*r/_binary64
60×associate--l+_binary64
49×associate-+l-_binary64
44×distribute-rgt-neg-in_binary64
43×+-commutative_binary64
41×neg-mul-1_binary64 neg-sub0_binary64
40×div-sub_binary64
38×distribute-lft-neg-in_binary64
36×cube-mult_binary64
33×swap-sqr_binary64
31×associate-+r-_binary64
29×associate--l-_binary64
28×distribute-neg-frac_binary64
24×*-rgt-identity_binary64
20×cancel-sign-sub-inv_binary64
19×pow-sqr_binary64
15×unsub-neg_binary64 /-rgt-identity_binary64
13×log-pow_binary64 *-lft-identity_binary64 associate--r+_binary64
12×log-rec_binary64
9×cube-unmult_binary64
8×pow-plus_binary64 associate--r-_binary64
7×+-rgt-identity_binary64
5×div0_binary64 distribute-neg-in_binary64
4×unpow1/2_binary64 remove-double-neg_binary64
3×unpow2_binary64 unpow1_binary64 rem-sqrt-square_binary64 distribute-lft-neg-out_binary64
2×sub0-neg_binary64 distribute-rgt-neg-out_binary64 count-2_binary64
1×1-exp_binary64 exp-1-e_binary64 --rgt-identity_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-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 mul-1-neg_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_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
Counts
152 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01593178
13782323
216482323
336542319
449322319
549602319
650382319

prune71.0ms (0.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New10811119
Fresh8614
Picked011
Done101
Total11718135
Error
17.1b
Counts
135 → 18
Compiler

Compiled 748 to 226 computations (69.8% saved)

regimes4.6s (22.2%)

Accuracy

Total 6.8b remaining (26.4%)

Threshold costs 0b (0%)

Compiler

Compiled 78416 to 49099 computations (37.4% saved)

bsearch10.0ms (0%)

Compiler

Compiled 3 to 7 computations (-133.3% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
1×1-exp_binary64 /-rgt-identity_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 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 *-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 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12532
22432

end1.0ms (0%)

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample7.1s (34.3%)

Algorithm
1×intervals
Results
1.3s2134×body4096valid
1.1s11803×body128nan
904.0ms1164×body8192valid
598.0ms1282×body2048valid
387.0ms4000×body128invalid
232.0ms2363×body128valid
232.0ms614×body1024valid
82.0ms292×body512valid
27.0ms151×body256valid
25.0ms48×body2048invalid
20.0ms54×body1024invalid
12.0ms42×body512invalid
10.0ms16×body4096invalid
5.0ms28×body256invalid
2.0ms3×body8192exit
Compiler

Compiled 547 to 405 computations (26% saved)

Profiling

Loading profile data...