Details

Time bar (total: 2.9s)

analyze311.0ms (10.9%)

Algorithm
search
egg-herbie
Rules
839×unsub-neg_binary64
739×sub-neg_binary64
608×neg-mul-1_binary64
563×+-commutative_binary64
473×distribute-neg-in_binary64
431×neg-sub0_binary64
406×distribute-lft-neg-out_binary64
402×distribute-rgt-out--_binary64
326×distribute-rgt-in_binary64
313×distribute-neg-out_binary64
297×associate--r-_binary64
292×distribute-rgt-out_binary64
284×associate--l-_binary64
260×distribute-rgt-neg-in_binary64
234×distribute-lft-in_binary64
224×cancel-sign-sub-inv_binary64
191×remove-double-neg_binary64
184×distribute-lft-neg-in_binary64
179×distribute-rgt-neg-out_binary64
165×cancel-sign-sub_binary64
150×associate--r+_binary64
126×associate-*l*_binary64
122×associate-+r+_binary64
102×distribute-lft-out_binary64
101×associate-+l+_binary64
99×associate-*r*_binary64
91×associate--l+_binary64
75×associate-+l-_binary64
72×sub0-neg_binary64
56×distribute-lft-out--_binary64
52×*-commutative_binary64
36×mul0-lft_binary64
34×mul0-rgt_binary64
24×sqr-pow_binary64
21×associate-+r-_binary64
20×+-rgt-identity_binary64 distribute-rgt1-in_binary64
18×--rgt-identity_binary64
14×cube-prod_binary64 +-lft-identity_binary64 swap-sqr_binary64
12×mul-1-neg_binary64
10×*-lft-identity_binary64 count-2_binary64
sqr-neg_binary64
cube-unmult_binary64 distribute-lft1-in_binary64
difference-of-squares_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-mult_binary64 cube-div_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 times-frac_binary64 div-sub_binary64 /-rgt-identity_binary64 *-rgt-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 unswap-sqr_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01976
14766
211166
329140
478140
5237240
6331040
7439940
8490440
9460240
10458140
11426640
12489540
13493140
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
31.2%50%18.8%7
40.6%37.5%22%8
45.3%26.5%28.2%9
46.8%19.5%33.7%10
48.8%14%37.2%11
51.7%10.1%38.1%12
52.8%7.1%40.1%13
53.3%5.1%41.6%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample22.0ms (0.8%)

Algorithm
intervals
Results
11.0ms256×body128valid
1.0ms19×body128invalid
Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify148.0ms (5.2%)

Algorithm
egg-herbie
Rules
686×unsub-neg_binary64
584×sub-neg_binary64
484×distribute-rgt-neg-in_binary64
430×distribute-neg-in_binary64
428×distribute-lft-neg-out_binary64
399×cancel-sign-sub-inv_binary64
320×neg-sub0_binary64
299×neg-mul-1_binary64
287×distribute-rgt-out_binary64
266×+-commutative_binary64
257×distribute-neg-out_binary64
255×distribute-rgt-out--_binary64
250×unswap-sqr_binary64
244×associate--l+_binary64
242×distribute-lft-out--_binary64
239×distribute-rgt-neg-out_binary64
189×associate-+l-_binary64
169×*-commutative_binary64
156×distribute-rgt-in_binary64
152×remove-double-neg_binary64
145×associate-*r*_binary64
132×associate-*l*_binary64
127×distribute-lft-neg-in_binary64
114×distribute-lft-in_binary64
74×associate-+r+_binary64
71×sub0-neg_binary64
68×associate-+r-_binary64
61×associate-+l+_binary64
60×associate--l-_binary64
59×associate--r-_binary64
58×sqr-pow_binary64
54×distribute-lft-out_binary64
51×associate--r+_binary64
24×*-lft-identity_binary64
23×mul0-rgt_binary64 mul0-lft_binary64
18×+-rgt-identity_binary64
17×pow-sqr_binary64
16×--rgt-identity_binary64
15×cube-prod_binary64
14×distribute-rgt1-in_binary64
11×cube-unmult_binary64 count-2_binary64
pow-plus_binary64
unpow3_binary64 mul-1-neg_binary64 swap-sqr_binary64 cancel-sign-sub_binary64
rem-sqrt-square_binary64
unpow2_binary64 +-lft-identity_binary64
unpow1_binary64
unpow1/2_binary64 cube-neg_binary64 sqr-neg_binary64 difference-of-squares_binary64 distribute-lft1-in_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 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 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-mult_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01438
12933
26833
317720
446820
5128820
6221720
7320120
8366720
9374220
10382820
11395920
12429020
13495620

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.1b
Counts
2 → 2
Compiler

Compiled 41 to 29 computations (29.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (pow.f64 x.re 3) (*.f64 x.re (*.f64 (*.f64 x.im x.im) -3)))
0.2b
(*.f64 (*.f64 x.im x.im) -3)
8.0b
(*.f64 x.re (*.f64 (*.f64 x.im x.im) -3))

rewrite90.0ms (3.2%)

Algorithm
rewrite-expression-head
Error
8.0b
Rules
17×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
add-sqr-sqrt_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64 associate-*r*_binary64
*-commutative_binary64
unswap-sqr_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 cube-mult_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
3 → 52
Calls

3 calls:

12.0ms
(+.f64 (pow.f64 x.re 3) (*.f64 x.re (*.f64 (*.f64 x.im x.im) -3)))
7.0ms
(*.f64 x.re (*.f64 (*.f64 x.im x.im) -3))
6.0ms
(*.f64 (*.f64 x.im x.im) -3)
Compiler

Compiled 869 to 502 computations (42.2% saved)

series66.0ms (2.3%)

Error
7.9b
Counts
3 → 21
Calls

3 calls:

33.0ms
(+.f64 (pow.f64 x.re 3) (*.f64 x.re (*.f64 (*.f64 x.im x.im) -3)))
18.0ms
(*.f64 x.re (*.f64 (*.f64 x.im x.im) -3))
9.0ms
(*.f64 (*.f64 x.im x.im) -3)
Compiler

Compiled 403 to 366 computations (9.2% saved)

simplify101.0ms (3.5%)

Algorithm
egg-herbie
Rules
416×distribute-rgt-neg-in_binary64
381×*-commutative_binary64
363×cancel-sign-sub-inv_binary64
312×distribute-lft-neg-in_binary64
294×distribute-rgt-in_binary64
232×cube-prod_binary64
227×exp-prod_binary64
218×log-prod_binary64
190×distribute-rgt-out_binary64
182×unswap-sqr_binary64
161×associate-*l*_binary64
157×associate-*r*_binary64
147×distribute-lft-neg-out_binary64
142×distribute-lft-out_binary64
134×distribute-rgt-neg-out_binary64
117×sqr-pow_binary64
94×neg-sub0_binary64
93×neg-mul-1_binary64
88×swap-sqr_binary64
81×unsub-neg_binary64
66×distribute-rgt-out--_binary64
56×distribute-lft-in_binary64
55×sub-neg_binary64
51×times-frac_binary64
34×unpow3_binary64
28×associate-+l+_binary64
26×cube-mult_binary64 distribute-neg-out_binary64 +-commutative_binary64
25×associate-+r+_binary64
22×exp-diff_binary64 distribute-lft-out--_binary64
21×exp-sum_binary64
19×cube-neg_binary64 sqr-neg_binary64 pow-sqr_binary64
16×pow-plus_binary64
12×exp-lft-cube_binary64 remove-double-neg_binary64
11×distribute-neg-in_binary64
cube-unmult_binary64 *-rgt-identity_binary64 difference-of-squares_binary64
associate-+l-_binary64 associate-+r-_binary64
unpow1/2_binary64 *-lft-identity_binary64 sub0-neg_binary64 associate-/l*_binary64
rem-sqrt-square_binary64 +-rgt-identity_binary64
log-pow_binary64 prod-exp_binary64 exp-neg_binary64
unpow2_binary64 unpow1_binary64 associate--r-_binary64
1-exp_binary64 exp-1-e_binary64 div-sub_binary64 --rgt-identity_binary64 distribute-frac-neg_binary64 count-2_binary64 associate--l-_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-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r+_binary64
Counts
73 → 48
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0911141
12281053
28631041
319991038
445641038
549511038

prune47.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New43548
Fresh011
Picked011
Done000
Total43750
Error
8.0b
Counts
50 → 7
Compiler

Compiled 587 to 453 computations (22.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re)) (pow.f64 x.re 3))
0.2b
(*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re))
8.1b
(*.f64 (pow.f64 x.im 2) x.re)

rewrite95.0ms (3.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
18×add-exp-log_binary64
13×add-sqr-sqrt_binary64
11×associate-*l*_binary64
10×prod-exp_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-log-exp_binary64
cbrt-unprod_binary64 unpow-prod-down_binary64 unswap-sqr_binary64 associate-*r*_binary64
pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64 *-commutative_binary64
pow-prod-down_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
3 → 57
Calls

3 calls:

8.0ms
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re)) (pow.f64 x.re 3))
5.0ms
(*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re))
5.0ms
(*.f64 (pow.f64 x.im 2) x.re)
Compiler

Compiled 979 to 721 computations (26.4% saved)

series71.0ms (2.5%)

Error
8.0b
Counts
3 → 24
Calls

3 calls:

32.0ms
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re)) (pow.f64 x.re 3))
20.0ms
(*.f64 -3 (*.f64 (pow.f64 x.im 2) x.re))
15.0ms
(*.f64 (pow.f64 x.im 2) x.re)
Compiler

Compiled 458 to 418 computations (8.7% saved)

simplify122.0ms (4.3%)

Algorithm
egg-herbie
Rules
318×*-commutative_binary64
286×cancel-sign-sub-inv_binary64
285×distribute-rgt-neg-in_binary64
278×log-prod_binary64
273×distribute-rgt-in_binary64
270×unswap-sqr_binary64
255×exp-prod_binary64
251×cube-prod_binary64
219×distribute-lft-neg-in_binary64
201×distribute-lft-out_binary64
200×distribute-rgt-out_binary64
129×associate-*r*_binary64
122×associate-*l*_binary64
121×distribute-lft-neg-out_binary64
112×distribute-rgt-neg-out_binary64
110×sqr-pow_binary64
99×unpow3_binary64
92×unsub-neg_binary64
74×neg-sub0_binary64
73×neg-mul-1_binary64
65×swap-sqr_binary64
63×distribute-rgt-out--_binary64
52×sub-neg_binary64 distribute-lft-in_binary64
34×distribute-lft-out--_binary64
33×distribute-neg-out_binary64
27×cube-mult_binary64
26×associate-+l+_binary64
23×associate-+r+_binary64
22×log-pow_binary64 pow-plus_binary64
21×exp-diff_binary64
19×pow-sqr_binary64 +-commutative_binary64
15×distribute-neg-in_binary64
14×exp-sum_binary64 cube-unmult_binary64
11×remove-double-neg_binary64
10×exp-lft-cube_binary64
*-rgt-identity_binary64 difference-of-squares_binary64
associate-+r-_binary64
rem-sqrt-square_binary64 *-lft-identity_binary64 associate-+l-_binary64
unpow1/2_binary64
cube-neg_binary64 +-rgt-identity_binary64 associate-/l*_binary64
unpow2_binary64 sqr-neg_binary64 sub0-neg_binary64
unpow1_binary64 prod-exp_binary64
associate--r-_binary64
exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-square-sqrt_binary64 --rgt-identity_binary64 cancel-sign-sub_binary64 associate--l-_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-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 times-frac_binary64 div-sub_binary64 mul-1-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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r+_binary64
Counts
81 → 55
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0981275
12281158
27741154
318031151
445191149
549431149
649621149

prune50.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New53255
Fresh145
Picked011
Done011
Total54862
Error
0.0b
Counts
62 → 8
Compiler

Compiled 625 to 468 computations (25.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))) (pow.f64 x.re 3))
0.2b
(*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)))
0.2b
(*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))

rewrite109.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
37×add-exp-log_binary64
25×prod-exp_binary64
17×add-cbrt-cube_binary64
10×associate-*l*_binary64
cbrt-unprod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-log-exp_binary64
pow-to-exp_binary64 pow-exp_binary64
unpow-prod-down_binary64
associate-*r*_binary64 *-commutative_binary64
sqr-pow_binary64 pow-prod-down_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
3 → 58
Calls

3 calls:

9.0ms
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))) (pow.f64 x.re 3))
8.0ms
(*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)))
6.0ms
(*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))
Compiler

Compiled 1305 to 901 computations (31% saved)

series72.0ms (2.5%)

Error
0.0b
Counts
3 → 24
Calls

3 calls:

34.0ms
(+.f64 (*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))) (pow.f64 x.re 3))
18.0ms
(*.f64 -3 (*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)))
17.0ms
(*.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re))
Compiler

Compiled 458 to 418 computations (8.7% saved)

simplify133.0ms (4.7%)

Algorithm
egg-herbie
Rules
460×*-commutative_binary64
405×exp-prod_binary64
403×distribute-rgt-neg-in_binary64
395×log-prod_binary64
378×cancel-sign-sub-inv_binary64
335×distribute-lft-neg-in_binary64
201×distribute-rgt-out_binary64
199×associate-*r*_binary64
176×cube-prod_binary64
174×associate-*l*_binary64
157×unswap-sqr_binary64
146×sqr-pow_binary64
143×distribute-lft-neg-out_binary64
132×distribute-rgt-neg-out_binary64
106×swap-sqr_binary64
93×neg-sub0_binary64
92×neg-mul-1_binary64 unsub-neg_binary64
78×unpow3_binary64
71×distribute-rgt-out--_binary64
67×distribute-rgt-in_binary64
56×sub-neg_binary64 distribute-lft-in_binary64
33×log-pow_binary64 distribute-neg-out_binary64
31×associate-+l+_binary64
28×associate-+r+_binary64
27×pow-sqr_binary64
26×pow-plus_binary64
24×+-commutative_binary64
20×cube-mult_binary64 distribute-neg-in_binary64
17×distribute-lft-out_binary64
14×remove-double-neg_binary64
13×exp-lft-cube_binary64
11×cube-unmult_binary64
10×associate-/l*_binary64
exp-diff_binary64 difference-of-squares_binary64
prod-exp_binary64 associate-+r-_binary64
distribute-lft-out--_binary64 associate-+l-_binary64
rem-sqrt-square_binary64
cube-neg_binary64 +-rgt-identity_binary64 cancel-sign-sub_binary64
exp-sum_binary64 sqr-neg_binary64 sub0-neg_binary64
unpow1/2_binary64 unpow1_binary64
unpow2_binary64 *-rgt-identity_binary64 associate--r-_binary64
1-exp_binary64 --rgt-identity_binary64 distribute-rgt1-in_binary64 associate--l-_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-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-lft-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r+_binary64
Counts
82 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01071283
12411172
29671157
323281157
444711155
549411155
649431155

prune48.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New62264
Fresh145
Picked011
Done022
Total63972
Error
0.0b
Counts
72 → 9
Compiler

Compiled 670 to 513 computations (23.4% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 (*.f64 x.im -3) (*.f64 x.im x.re)) (pow.f64 x.re 3))
0.3b
(*.f64 (*.f64 x.im -3) (*.f64 x.im x.re))

rewrite59.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
14×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
add-log-exp_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64 associate-*r*_binary64 *-commutative_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
2 → 33
Calls

2 calls:

9.0ms
(+.f64 (*.f64 (*.f64 x.im -3) (*.f64 x.im x.re)) (pow.f64 x.re 3))
8.0ms
(*.f64 (*.f64 x.im -3) (*.f64 x.im x.re))
Compiler

Compiled 598 to 346 computations (42.1% saved)

series55.0ms (1.9%)

Error
0.0b
Counts
2 → 18
Calls

2 calls:

32.0ms
(+.f64 (*.f64 (*.f64 x.im -3) (*.f64 x.im x.re)) (pow.f64 x.re 3))
18.0ms
(*.f64 (*.f64 x.im -3) (*.f64 x.im x.re))
Compiler

Compiled 326 to 298 computations (8.6% saved)

simplify113.0ms (4%)

Algorithm
egg-herbie
Rules
404×cancel-sign-sub-inv_binary64
371×*-commutative_binary64
343×distribute-rgt-neg-in_binary64
306×neg-mul-1_binary64
281×distribute-lft-out_binary64
277×distribute-lft-neg-in_binary64
218×distribute-rgt-out_binary64
217×unswap-sqr_binary64
209×exp-prod_binary64
188×cube-prod_binary64
186×log-prod_binary64
167×associate-*l*_binary64
163×distribute-lft-neg-out_binary64
151×associate-*r*_binary64
143×distribute-rgt-neg-out_binary64
95×unsub-neg_binary64
86×sqr-pow_binary64
85×neg-sub0_binary64
81×distribute-rgt-out--_binary64
78×swap-sqr_binary64
65×sub-neg_binary64 distribute-rgt-in_binary64
56×distribute-lft-in_binary64
46×unpow3_binary64
39×distribute-lft-out--_binary64
33×distribute-neg-out_binary64
27×associate-+l+_binary64
23×+-commutative_binary64
22×exp-diff_binary64 distribute-neg-in_binary64
21×cube-mult_binary64 associate-+r+_binary64
17×cube-neg_binary64
16×exp-sum_binary64 pow-sqr_binary64
15×remove-double-neg_binary64
13×sqr-neg_binary64
11×exp-lft-cube_binary64
10×pow-plus_binary64 div-sub_binary64
difference-of-squares_binary64
associate-+r-_binary64
cube-unmult_binary64 associate-+l-_binary64
log-pow_binary64 +-rgt-identity_binary64
sub0-neg_binary64
times-frac_binary64 cancel-sign-sub_binary64
unpow2_binary64 prod-exp_binary64 associate-/l*_binary64
unpow1/2_binary64 unpow1_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 rem-sqrt-square_binary64 --rgt-identity_binary64 count-2_binary64 associate--r-_binary64 associate--l-_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-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r+_binary64
Counts
51 → 32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
074920
1208850
2772836
31910829
44481827
54939827
64953827

prune20.0ms (0.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New32032
Fresh055
Picked011
Done033
Total32941
Error
0.0b
Counts
41 → 9
Compiler

Compiled 291 to 225 computations (22.7% saved)

regimes232.0ms (8.1%)

Accuracy

Total 0.1b remaining (83.8%)

Threshold costs 0.1b (83.8%)

Compiler

Compiled 2910 to 2283 computations (21.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
11620
21620

end1.0ms (0%)

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample846.0ms (29.7%)

Algorithm
intervals
Results
374.0ms8000×body128valid
18.0ms415×body128invalid
Compiler

Compiled 185 to 153 computations (17.3% saved)

Profiling

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