Details

Time bar (total: 13.3s)

analyze1.2s (9.3%)

Algorithm
search
egg-herbie
Rules
520×sub-neg_binary64
373×div-sub_binary64
267×log-prod_binary64
240×associate-/r*_binary64
225×sqr-pow_binary64
204×difference-of-squares_binary64
202×distribute-rgt-in_binary64
195×associate-/l*_binary64
192×cancel-sign-sub-inv_binary64
173×distribute-lft-in_binary64
168×*-commutative_binary64
155×associate-/l/_binary64
145×neg-mul-1_binary64
135×neg-sub0_binary64 pow-sqr_binary64
126×unsub-neg_binary64
116×times-frac_binary64
112×distribute-rgt-neg-in_binary64 associate-*l*_binary64
105×distribute-lft-neg-in_binary64
104×associate-*r/_binary64
103×exp-prod_binary64
101×associate-*r*_binary64
99×associate-*l/_binary64
80×unswap-sqr_binary64
75×associate-/r/_binary64
69×log-div_binary64
62×*-lft-identity_binary64
53×+-commutative_binary64
46×div0_binary64 distribute-neg-in_binary64
44×*-rgt-identity_binary64 distribute-neg-frac_binary64 distribute-rgt-neg-out_binary64
43×exp-diff_binary64
40×sub0-neg_binary64
38×associate--r+_binary64
35×distribute-lft-neg-out_binary64
29×prod-exp_binary64 exp-sum_binary64
23×exp-sqrt_binary64 associate-+l-_binary64
21×remove-double-neg_binary64
20×rem-sqrt-square_binary64 associate-+r+_binary64
19×associate-+l+_binary64
18×cube-prod_binary64
16×cube-unmult_binary64 associate-+r-_binary64
15×unpow3_binary64 /-rgt-identity_binary64 +-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64
14×pow-plus_binary64
13×exp-lft-sqr_binary64
12×associate--r-_binary64
11×+-lft-identity_binary64 distribute-frac-neg_binary64
10×--rgt-identity_binary64
associate--l+_binary64
div-exp_binary64 rec-exp_binary64
cube-mult_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64
sqr-neg_binary64 distribute-lft-out--_binary64
unpow2_binary64 unpow-1_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 cube-div_binary64 cube-neg_binary64 rem-square-sqrt_binary64 distribute-lft-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 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 exp-lft-cube_binary64 exp-cbrt_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 mul-1-neg_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 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01764
14961
211759
329255
468955
5139255
6338155
7457855
8421255
9479555
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14
Compiler

Compiled 38 to 31 computations (18.4% saved)

sample229.0ms (1.7%)

Algorithm
intervals
Results
77.0ms135×body1024valid
54.0ms109×body1024nan
22.0ms58×body512valid
20.0ms18×body2048valid
18.0ms52×body512nan
9.0ms35×body256nan
6.0ms25×body256valid
3.0ms20×body128valid
0.0msbody128overflowed
Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify85.0ms (0.6%)

Algorithm
egg-herbie
Rules
520×sub-neg_binary64
373×div-sub_binary64
267×log-prod_binary64
240×associate-/r*_binary64
225×sqr-pow_binary64
204×difference-of-squares_binary64
202×distribute-rgt-in_binary64
195×associate-/l*_binary64
192×cancel-sign-sub-inv_binary64
173×distribute-lft-in_binary64
168×*-commutative_binary64
155×associate-/l/_binary64
145×neg-mul-1_binary64
135×neg-sub0_binary64 pow-sqr_binary64
126×unsub-neg_binary64
116×times-frac_binary64
112×distribute-rgt-neg-in_binary64 associate-*l*_binary64
105×distribute-lft-neg-in_binary64
104×associate-*r/_binary64
103×exp-prod_binary64
101×associate-*r*_binary64
99×associate-*l/_binary64
80×unswap-sqr_binary64
75×associate-/r/_binary64
69×log-div_binary64
62×*-lft-identity_binary64
53×+-commutative_binary64
46×div0_binary64 distribute-neg-in_binary64
44×*-rgt-identity_binary64 distribute-neg-frac_binary64 distribute-rgt-neg-out_binary64
43×exp-diff_binary64
40×sub0-neg_binary64
38×associate--r+_binary64
35×distribute-lft-neg-out_binary64
29×prod-exp_binary64 exp-sum_binary64
23×exp-sqrt_binary64 associate-+l-_binary64
21×remove-double-neg_binary64
20×rem-sqrt-square_binary64 associate-+r+_binary64
19×associate-+l+_binary64
18×cube-prod_binary64
16×cube-unmult_binary64 associate-+r-_binary64
15×unpow3_binary64 /-rgt-identity_binary64 +-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64
14×pow-plus_binary64
13×exp-lft-sqr_binary64
12×associate--r-_binary64
11×+-lft-identity_binary64 distribute-frac-neg_binary64
10×--rgt-identity_binary64
associate--l+_binary64
div-exp_binary64 rec-exp_binary64
cube-mult_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64
sqr-neg_binary64 distribute-lft-out--_binary64
unpow2_binary64 unpow-1_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 cube-div_binary64 cube-neg_binary64 rem-square-sqrt_binary64 distribute-lft-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 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 exp-lft-cube_binary64 exp-cbrt_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 mul-1-neg_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 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01764
14961
211759
329255
468955
5139255
6338155
7457855
8421255
9479555

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
61.1b
Counts
2 → 1
Compiler

Compiled 64 to 48 computations (25% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
1.2b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
4.3b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

rewrite513.0ms (3.9%)

Algorithm
rewrite-expression-head
Error
61.1b
Rules
75×add-sqr-sqrt_binary64
63×*-un-lft-identity_binary64
48×times-frac_binary64
35×add-cube-cbrt_binary64
26×associate-*l*_binary64
18×difference-of-squares_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
unpow-prod-down_binary64
pow1_binary64 distribute-lft-out_binary64
sqr-pow_binary64 cancel-sign-sub-inv_binary64 associate-/r*_binary64
add-log-exp_binary64 distribute-lft-out--_binary64 associate-*r*_binary64
associate-/l*_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
div-exp_binary64 cbrt-undiv_binary64 div-inv_binary64
flip3--_binary64 flip--_binary64 associate-/l/_binary64 associate-/r/_binary64 pow-prod-down_binary64 associate-*l/_binary64 *-commutative_binary64
diff-log_binary64 sub-neg_binary64 frac-2neg_binary64 clear-num_binary64 flip3-+_binary64 flip-+_binary64
Counts
4 → 141
Calls

4 calls:

13.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
8.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 5775 to 3852 computations (33.3% saved)

series84.0ms (0.6%)

Error
1.9b
Counts
4 → 12
Calls

4 calls:

30.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
22.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
11.0ms
(*.f64 (/.f64 PI.f64 4) f)
10.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 1112 to 841 computations (24.4% saved)

simplify192.0ms (1.4%)

Algorithm
egg-herbie
Rules
609×associate-*l*_binary64
558×times-frac_binary64
545×associate-*r*_binary64
231×associate-*l/_binary64
214×exp-prod_binary64
188×*-commutative_binary64
187×associate-/l*_binary64
178×associate-*r/_binary64
143×distribute-rgt-in_binary64
132×distribute-lft-in_binary64
88×cube-prod_binary64
86×associate-/l/_binary64
81×cancel-sign-sub-inv_binary64
71×associate-/r*_binary64
57×sqr-pow_binary64
56×distribute-rgt-neg-in_binary64
53×unswap-sqr_binary64
50×sub-neg_binary64
49×associate-/r/_binary64 +-commutative_binary64
43×distribute-lft-neg-in_binary64
37×distribute-rgt-out_binary64
36×neg-mul-1_binary64
34×associate-+l+_binary64
32×log-div_binary64 neg-sub0_binary64
30×log-prod_binary64
29×cube-div_binary64
25×exp-sum_binary64
23×pow-sqr_binary64 distribute-lft-neg-out_binary64
22×cube-unmult_binary64 associate-+r+_binary64
21×associate-+l-_binary64
20×associate-+r-_binary64
18×*-rgt-identity_binary64
17×div-sub_binary64
16×swap-sqr_binary64 distribute-rgt-neg-out_binary64
14×unpow3_binary64
12×cube-mult_binary64 difference-of-squares_binary64
11×exp-diff_binary64
10×rem-sqrt-square_binary64
*-lft-identity_binary64
prod-exp_binary64 distribute-rgt-out--_binary64
unsub-neg_binary64 distribute-neg-frac_binary64 distribute-lft-out_binary64
pow-plus_binary64 distribute-neg-in_binary64
exp-sqrt_binary64 associate--l-_binary64
log-rec_binary64 pow-base-1_binary64 /-rgt-identity_binary64 count-2_binary64 associate--r+_binary64
+-rgt-identity_binary64 distribute-neg-out_binary64
div-exp_binary64 rec-exp_binary64 rem-square-sqrt_binary64 distribute-rgt1-in_binary64 associate--r-_binary64
unpow1/2_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-log-exp_binary64 cube-neg_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 remove-double-neg_binary64 *-inverses_binary64 distribute-lft1-in_binary64 distribute-lft-out--_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 log-pow_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 exp-to-pow_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 e-exp-1_binary64 exp-0_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 mul-1-neg_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64
Counts
153 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02195780
14675401
211535399
339155387
451725387

prune152.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1316137
Fresh000
Picked101
Done000
Total1326138
Error
1.9b
Counts
138 → 6
Compiler

Compiled 4868 to 3280 computations (32.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2))))
0.3b
(*.f64 f (*.f64 PI.f64 1/2))
0.3b
(/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))
0.4b
(*.f64 (log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

rewrite155.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
1.5b
Rules
33×add-exp-log_binary64
23×add-cbrt-cube_binary64
22×add-sqr-sqrt_binary64
17×add-cube-cbrt_binary64 *-un-lft-identity_binary64
16×times-frac_binary64
14×associate-*r*_binary64
13×pow1_binary64
11×prod-exp_binary64
cbrt-unprod_binary64
div-exp_binary64 associate-*l*_binary64 log-prod_binary64
pow-prod-down_binary64 add-log-exp_binary64 cbrt-undiv_binary64 rem-log-exp_binary64
div-inv_binary64 associate-/l*_binary64
unswap-sqr_binary64 log-pow_binary64 *-commutative_binary64
associate-*r/_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r*_binary64 log-div_binary64
Counts
4 → 94
Calls

4 calls:

10.0ms
(*.f64 (log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
6.0ms
(/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))
5.0ms
(log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2))))
5.0ms
(*.f64 f (*.f64 PI.f64 1/2))
Compiler

Compiled 1666 to 1268 computations (23.9% saved)

series61.0ms (0.5%)

Error
1.7b
Counts
4 → 12
Calls

4 calls:

20.0ms
(*.f64 (log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
14.0ms
(log.f64 (/.f64 2 (*.f64 f (*.f64 PI.f64 1/2))))
8.0ms
(/.f64 2 (*.f64 f (*.f64 PI.f64 1/2)))
7.0ms
(*.f64 f (*.f64 PI.f64 1/2))
Compiler

Compiled 376 to 328 computations (12.8% saved)

simplify92.0ms (0.7%)

Algorithm
egg-herbie
Rules
373×associate-/r*_binary64
355×distribute-rgt-in_binary64
341×distribute-lft-in_binary64
290×associate-/l*_binary64
266×associate-/l/_binary64
256×times-frac_binary64
166×div-sub_binary64
136×associate-*l*_binary64
116×associate-*r*_binary64
108×exp-sum_binary64
84×log-div_binary64
82×*-commutative_binary64
71×associate-/r/_binary64
67×sub-neg_binary64
59×exp-diff_binary64
52×associate-*r/_binary64
46×exp-prod_binary64
45×log-prod_binary64
37×associate-*l/_binary64
20×distribute-lft-neg-out_binary64
19×sqr-pow_binary64
18×*-rgt-identity_binary64 *-lft-identity_binary64 swap-sqr_binary64 distribute-rgt-neg-out_binary64
14×div-exp_binary64 cube-div_binary64 associate--r+_binary64
13×neg-mul-1_binary64 neg-sub0_binary64
12×cube-prod_binary64 distribute-rgt-neg-in_binary64 +-commutative_binary64
11×unpow3_binary64 prod-exp_binary64
10×distribute-neg-in_binary64 distribute-lft-neg-in_binary64
log-rec_binary64
cube-unmult_binary64
exp-to-pow_binary64 cancel-sign-sub-inv_binary64 associate-+r-_binary64
rem-exp-log_binary64 /-rgt-identity_binary64 associate-+l-_binary64
unpow1/2_binary64 exp-neg_binary64 associate-+l+_binary64
pow-sqr_binary64 associate-+r+_binary64
log-pow_binary64 unsub-neg_binary64 distribute-rgt-out_binary64 count-2_binary64
log-E_binary64 pow-plus_binary64 exp-lft-sqr_binary64 rec-exp_binary64 1-exp_binary64 exp-1-e_binary64 unswap-sqr_binary64 distribute-neg-frac_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 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-mult_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 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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 associate--r-_binary64 associate--l+_binary64
Counts
106 → 85
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01681996
13591498
213321497
346991497
450451497

prune93.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New731285
Fresh055
Picked101
Done000
Total741791
Error
1.5b
Counts
91 → 17
Compiler

Compiled 1376 to 979 computations (28.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b
(*.f64 PI.f64 f)
0.3b
(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
0.3b
(/.f64 4 (*.f64 PI.f64 f))

rewrite136.0ms (1%)

Algorithm
rewrite-expression-head
Error
1.5b
Rules
21×add-sqr-sqrt_binary64
19×add-exp-log_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
18×times-frac_binary64
13×add-cbrt-cube_binary64
11×pow1_binary64
associate-/l*_binary64 log-prod_binary64
div-exp_binary64 log-pow_binary64
add-log-exp_binary64 associate-/r*_binary64
prod-exp_binary64 cbrt-undiv_binary64 div-inv_binary64 associate-*l*_binary64 associate-*r*_binary64 rem-log-exp_binary64
cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 log-div_binary64
div-sub_binary64 pow-prod-down_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
4 → 90
Calls

4 calls:

6.0ms
(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
4.0ms
(/.f64 4 (*.f64 PI.f64 f))
4.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
4.0ms
(*.f64 PI.f64 f)
Compiler

Compiled 1324 to 820 computations (38.1% saved)

series52.0ms (0.4%)

Error
1.5b
Counts
4 → 12
Calls

4 calls:

18.0ms
(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
15.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
8.0ms
(/.f64 4 (*.f64 PI.f64 f))
6.0ms
(*.f64 PI.f64 f)
Compiler

Compiled 325 to 288 computations (11.4% saved)

simplify102.0ms (0.8%)

Algorithm
egg-herbie
Rules
869×div-sub_binary64
450×associate-/r/_binary64
231×prod-exp_binary64
194×sub-neg_binary64
184×associate-/r*_binary64
163×associate-*l*_binary64
153×times-frac_binary64
152×div-exp_binary64
133×distribute-rgt-in_binary64
132×associate-/l*_binary64
130×distribute-lft-in_binary64
116×associate-/l/_binary64
112×associate-*r*_binary64
108×associate-*l/_binary64
97×distribute-rgt-neg-out_binary64
89×unsub-neg_binary64
84×exp-sum_binary64 associate-*r/_binary64
80×exp-diff_binary64 distribute-lft-neg-out_binary64
74×log-div_binary64
72×*-commutative_binary64
66×exp-prod_binary64
65×distribute-neg-in_binary64
64×log-prod_binary64
56×distribute-frac-neg_binary64
46×cancel-sign-sub-inv_binary64
45×neg-sub0_binary64
43×associate-+r-_binary64
37×neg-mul-1_binary64
33×sqr-pow_binary64
31×associate--r+_binary64
30×associate-+l-_binary64
27×/-rgt-identity_binary64
25×+-commutative_binary64
24×swap-sqr_binary64
23×associate-+r+_binary64
22×associate--r-_binary64
20×distribute-rgt-neg-in_binary64
18×exp-to-pow_binary64
17×cube-div_binary64 distribute-neg-frac_binary64 associate-+l+_binary64
15×cube-prod_binary64 distribute-lft-neg-in_binary64
13×*-lft-identity_binary64
11×+-rgt-identity_binary64
10×rem-exp-log_binary64
log-pow_binary64 rec-exp_binary64 *-rgt-identity_binary64
log-rec_binary64
unpow3_binary64
cube-unmult_binary64 pow-sqr_binary64 unswap-sqr_binary64
associate--l+_binary64
cube-mult_binary64 remove-double-neg_binary64 sub0-neg_binary64 count-2_binary64
--rgt-identity_binary64
unpow1/2_binary64 sqr-neg_binary64 distribute-neg-out_binary64 associate--l-_binary64
1-exp_binary64 exp-1-e_binary64 mul0-rgt_binary64 mul0-lft_binary64 +-inverses_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-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 unpow2_binary64 pow-plus_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-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-neg_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 mul-1-neg_binary64 +-lft-identity_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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64
Counts
102 → 77
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01371586
12461425
27451425
322121425
443601423
550681423

prune88.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh61016
Picked101
Done000
Total801494
Error
1.5b
Counts
94 → 14
Compiler

Compiled 1266 to 851 computations (32.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
0.4b
(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
2.0b
(log.f64 (/.f64 4 PI.f64))

rewrite143.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
1.5b
Rules
40×*-un-lft-identity_binary64
31×add-sqr-sqrt_binary64
29×log-prod_binary64
28×times-frac_binary64
26×add-cube-cbrt_binary64
16×pow1_binary64
13×associate-*r*_binary64 associate-+r+_binary64
12×distribute-lft-out_binary64
11×log-pow_binary64 add-exp-log_binary64
associate-*l*_binary64
add-cbrt-cube_binary64 distribute-rgt-neg-in_binary64
add-log-exp_binary64
div-inv_binary64 flip3-+_binary64 flip-+_binary64 distribute-neg-in_binary64 associate-+l+_binary64
log-div_binary64 div-exp_binary64 rem-log-exp_binary64 prod-exp_binary64 cbrt-unprod_binary64 frac-times_binary64 unswap-sqr_binary64 associate-*l/_binary64 sum-log_binary64
pow-prod-down_binary64 cbrt-undiv_binary64 associate-*r/_binary64 *-commutative_binary64 neg-log_binary64 neg-sub0_binary64 associate-+l-_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
3 → 102
Calls

3 calls:

14.0ms
(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
9.0ms
(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
3.0ms
(log.f64 (/.f64 4 PI.f64))
Compiler

Compiled 1831 to 1156 computations (36.9% saved)

series51.0ms (0.4%)

Error
1.5b
Counts
3 → 6
Calls

3 calls:

24.0ms
(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
19.0ms
(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
0.0ms
(log.f64 (/.f64 4 PI.f64))
Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify106.0ms (0.8%)

Algorithm
egg-herbie
Rules
693×times-frac_binary64
496×associate-*l*_binary64
424×distribute-rgt-in_binary64
403×distribute-lft-in_binary64
261×associate-*r/_binary64
257×associate-*l/_binary64
171×sub-neg_binary64
169×associate-/l*_binary64
112×div-sub_binary64
74×log-div_binary64
68×associate-*r*_binary64
66×associate-/l/_binary64
64×distribute-rgt-neg-out_binary64
61×*-commutative_binary64
57×distribute-lft-neg-out_binary64
55×exp-sum_binary64
53×associate-/r*_binary64
45×associate-+l-_binary64
42×log-prod_binary64 associate-/r/_binary64
41×unsub-neg_binary64 associate-+r-_binary64
32×exp-diff_binary64 cancel-sign-sub-inv_binary64
31×neg-sub0_binary64
30×+-commutative_binary64
28×neg-mul-1_binary64
26×exp-prod_binary64
21×*-lft-identity_binary64
20×cube-prod_binary64 sqr-pow_binary64
18×*-rgt-identity_binary64
16×sub0-neg_binary64
13×cube-div_binary64 distribute-neg-out_binary64 distribute-rgt-neg-in_binary64
12×+-rgt-identity_binary64
log-rec_binary64 exp-to-pow_binary64 distribute-lft-neg-in_binary64
/-rgt-identity_binary64 swap-sqr_binary64 associate--l-_binary64
unpow3_binary64 cube-mult_binary64 distribute-rgt-out_binary64
rem-exp-log_binary64 cube-unmult_binary64 distribute-lft-out_binary64
exp-neg_binary64 distribute-lft-out--_binary64 count-2_binary64
distribute-frac-neg_binary64 associate--r-_binary64 associate-+l+_binary64
log-pow_binary64 div-exp_binary64 prod-exp_binary64 cube-neg_binary64 difference-of-squares_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64
sqr-neg_binary64 remove-double-neg_binary64 distribute-neg-frac_binary64 associate--l+_binary64
unpow1/2_binary64 rec-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-log-exp_binary64 --rgt-identity_binary64 pow-sqr_binary64 cancel-sign-sub_binary64 associate-+r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 pow-plus_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 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-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_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 unswap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--r+_binary64
Counts
108 → 87
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01832184
14061967
213761939
343651939
452371939

prune80.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New87087
Fresh01313
Picked011
Done000
Total8714101
Error
1.5b
Counts
101 → 14
Compiler

Compiled 1286 to 847 computations (34.1% saved)

regimes2.1s (15.5%)

Accuracy

Total 1.0b remaining (69.9%)

Threshold costs 1.0b (69.9%)

Compiler

Compiled 30006 to 24152 computations (19.5% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 5 to 5 computations (0% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_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-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
01833
12233
22633
32833
42933
52933

end1.0ms (0%)

Compiler

Compiled 20 to 17 computations (15% saved)

sample7.5s (56.5%)

Algorithm
intervals
Results
2.1s3920×body1024valid
1.9s3812×body1024nan
745.0ms1935×body512valid
700.0ms1936×body512nan
551.0ms504×body2048valid
266.0ms985×body256valid
242.0ms1002×body256nan
93.0ms656×body128valid
0.0msbody128overflowed
0.0msbody128nan
Compiler

Compiled 428 to 344 computations (19.6% saved)

Profiling

Loading profile data...