Details

Time bar (total: 10.2s)

analyze523.0ms (5.1%)

Algorithm
search
egg-herbie
Rules
756×neg-mul-1_binary64
741×neg-sub0_binary64
638×associate-/l*_binary64
470×distribute-frac-neg_binary64
468×div-sub_binary64
448×unsub-neg_binary64
352×sub-neg_binary64
260×distribute-rgt-in_binary64
256×times-frac_binary64
236×distribute-lft-neg-out_binary64
234×distribute-rgt-neg-out_binary64
198×distribute-lft-in_binary64 associate-*l/_binary64
187×associate-*l*_binary64
177×cancel-sign-sub-inv_binary64
173×associate-*r/_binary64
172×distribute-neg-frac_binary64
170×associate-*r*_binary64
155×associate-/r/_binary64
149×associate-/r*_binary64
122×*-lft-identity_binary64
117×associate-/l/_binary64
103×*-rgt-identity_binary64
97×*-commutative_binary64
90×remove-double-neg_binary64
82×distribute-rgt-neg-in_binary64
78×cancel-sign-sub_binary64
77×/-rgt-identity_binary64
53×div0_binary64
44×distribute-rgt-out_binary64 associate--r+_binary64 +-commutative_binary64
42×distribute-lft-neg-in_binary64
40×distribute-rgt-out--_binary64
34×+-lft-identity_binary64
32×associate-+l-_binary64 associate-+r+_binary64
29×distribute-neg-in_binary64
28×sub0-neg_binary64 distribute-neg-out_binary64
24×associate-+r-_binary64
22×associate-+l+_binary64
19×+-rgt-identity_binary64
17×remove-double-div_binary64
16×difference-of-squares_binary64
15×mul0-rgt_binary64 mul0-lft_binary64
12×distribute-lft-out_binary64
10×associate--r-_binary64
associate--l+_binary64
swap-sqr_binary64
associate--l-_binary64
sqr-neg_binary64 --rgt-identity_binary64
mul-1-neg_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054208
1161200
2483200
31371192
42735192
53995192
64316192
74707192
85013192
033
133
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
0%99.9%0.1%5
12.5%68.6%18.9%6
18.7%62.4%18.9%7
18.7%59.3%22%8
28.1%39%32.9%9
32.8%34.3%32.9%10
32.8%32%35.3%11
38.2%20.7%41.1%12
41%17.9%41.1%13
41%16.6%42.5%14
Compiler

Compiled 38 to 24 computations (36.8% saved)

sample56.0ms (0.5%)

Algorithm
intervals
Results
39.0ms238×body256valid
3.0ms39×body128nan
1.0ms18×body128valid
Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify230.0ms (2.2%)

Algorithm
egg-herbie
Rules
637×associate-/l*_binary64
634×div-sub_binary64
582×unsub-neg_binary64
519×sub-neg_binary64
502×times-frac_binary64
356×distribute-rgt-out--_binary64
307×neg-mul-1_binary64
295×distribute-rgt-neg-in_binary64
286×associate-/l/_binary64
280×neg-sub0_binary64
252×associate-/r/_binary64
250×distribute-lft-neg-out_binary64
246×distribute-neg-out_binary64
212×associate-/r*_binary64 *-commutative_binary64
210×+-commutative_binary64
208×distribute-rgt-out_binary64
203×distribute-rgt-in_binary64
199×distribute-rgt-neg-out_binary64
186×distribute-neg-frac_binary64
160×associate-*r/_binary64
145×cancel-sign-sub-inv_binary64
137×associate-*l/_binary64
133×distribute-neg-in_binary64
123×distribute-lft-in_binary64
113×associate-+l+_binary64
106×distribute-lft-out--_binary64
100×distribute-frac-neg_binary64
98×associate-+l-_binary64
90×associate-*l*_binary64
81×associate-+r+_binary64
78×associate-*r*_binary64 associate--r-_binary64
63×associate--r+_binary64
59×distribute-lft-neg-in_binary64
46×*-lft-identity_binary64
44×associate-+r-_binary64
43×*-rgt-identity_binary64 distribute-lft-out_binary64
35×remove-double-neg_binary64 sub0-neg_binary64
34×associate--l+_binary64
27×mul0-rgt_binary64 swap-sqr_binary64
25×mul0-lft_binary64
24×distribute-rgt1-in_binary64
23×associate--l-_binary64
20×mul-1-neg_binary64
18×div0_binary64
14×cancel-sign-sub_binary64
+-lft-identity_binary64
+-rgt-identity_binary64
sqr-neg_binary64
/-rgt-identity_binary64 --rgt-identity_binary64 +-inverses_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 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_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 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02052
15350
213950
338148
473548
5118948
6140948
7189348
8185348
9223548
10288948
11345748
12363948
13374948
14379748
15382148
16387148
17485848
18479948
19498048
20483448

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
38.1b
Counts
2 → 2
Compiler

Compiled 99 to 59 computations (40.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.4b
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
9.8b
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite196.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
33.9b
Rules
10×cbrt-div_binary64
add-sqr-sqrt_binary64 sqrt-prod_binary64
pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 frac-times_binary64 associate-*r/_binary64
pow1/2_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 rem-sqrt-square_binary64 pow1/3_binary64 associate-*l/_binary64 cbrt-prod_binary64 flip3-+_binary64 flip-+_binary64
Counts
4 → 60
Calls

4 calls:

15.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
14.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2902 to 1013 computations (65.1% saved)

series312.0ms (3%)

Error
33.3b
Counts
4 → 37
Calls

4 calls:

97.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
90.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
31.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
25.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 4142 to 3077 computations (25.7% saved)

simplify106.0ms (1%)

Algorithm
egg-herbie
Rules
799×times-frac_binary64
272×distribute-rgt-in_binary64
269×distribute-lft-in_binary64
124×distribute-rgt-neg-out_binary64
120×cancel-sign-sub-inv_binary64
117×distribute-lft-neg-out_binary64
115×sub-neg_binary64
102×*-commutative_binary64
100×associate-*r*_binary64
90×exp-prod_binary64 div-sub_binary64
88×associate-*l*_binary64
79×distribute-rgt-neg-in_binary64
77×exp-diff_binary64
73×unsub-neg_binary64
71×distribute-lft-neg-in_binary64
66×log-prod_binary64 sqr-pow_binary64
63×exp-sum_binary64
61×neg-sub0_binary64
54×neg-mul-1_binary64
44×unswap-sqr_binary64
40×distribute-neg-out_binary64
39×distribute-rgt-out_binary64 +-commutative_binary64
33×distribute-frac-neg_binary64
32×unpow1/3_binary64
28×associate-/l*_binary64
27×log-div_binary64
26×associate-/r*_binary64
24×difference-of-squares_binary64 associate-*l/_binary64
22×exp-to-pow_binary64 associate-*r/_binary64
19×cube-prod_binary64
18×distribute-neg-in_binary64
17×*-lft-identity_binary64
16×distribute-neg-frac_binary64 distribute-lft-out_binary64 associate-+l-_binary64
14×pow-sqr_binary64
13×*-rgt-identity_binary64 associate-+r-_binary64
12×distribute-rgt-out--_binary64
10×unpow3_binary64 associate-+l+_binary64
pow-plus_binary64
associate-+r+_binary64
remove-double-neg_binary64 swap-sqr_binary64 associate--r-_binary64 associate--l-_binary64
log-pow_binary64 cube-unmult_binary64 cube-mult_binary64
log-rec_binary64 exp-neg_binary64 cube-neg_binary64 mul-1-neg_binary64
sqr-neg_binary64 +-rgt-identity_binary64 associate--l+_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-lft-sqr_binary64 rem-3cbrt-lft_binary64 rem-sqrt-square_binary64 sub0-neg_binary64 cancel-sign-sub_binary64 associate-/r/_binary64
rec-exp_binary64 prod-exp_binary64 1-exp_binary64 rem-square-sqrt_binary64 /-rgt-identity_binary64 --rgt-identity_binary64 +-inverses_binary64 distribute-rgt1-in_binary64 distribute-lft-out--_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 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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-lft1-in_binary64 count-2_binary64 associate-/l/_binary64
Counts
97 → 69
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02332192
15662152
216342064
348122032
449382032

prune174.0ms (1.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New501969
Fresh011
Picked101
Done000
Total512071
Error
33.3b
Counts
71 → 20
Compiler

Compiled 3494 to 1640 computations (53.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
9.8b
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite304.0ms (3%)

Algorithm
rewrite-expression-head
Error
33.3b
Rules
13×add-sqr-sqrt_binary64
sqrt-prod_binary64 *-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64 add-log-exp_binary64
flip3--_binary64 flip--_binary64 cbrt-div_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64 difference-of-squares_binary64
cancel-sign-sub-inv_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 frac-times_binary64 associate-*r/_binary64
pow1/3_binary64 associate-*l/_binary64 cbrt-prod_binary64 diff-log_binary64 sub-neg_binary64 distribute-lft-out--_binary64
Counts
4 → 63
Calls

4 calls:

14.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2740 to 917 computations (66.5% saved)

series306.0ms (3%)

Error
32.3b
Counts
4 → 36
Calls

4 calls:

92.0ms
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))
31.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
29.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
25.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3482 to 2549 computations (26.8% saved)

simplify101.0ms (1%)

Algorithm
egg-herbie
Rules
532×div-sub_binary64
408×times-frac_binary64
216×*-commutative_binary64
212×distribute-rgt-in_binary64
210×distribute-lft-in_binary64
182×exp-sum_binary64
168×associate-/l*_binary64
147×associate-/r*_binary64
106×exp-diff_binary64
103×sub-neg_binary64
101×cancel-sign-sub-inv_binary64
97×exp-prod_binary64
88×associate-+r-_binary64
82×distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
78×associate-+r+_binary64
75×associate-*l/_binary64
74×cube-prod_binary64
72×associate-+l+_binary64
70×associate-+l-_binary64
67×distribute-rgt-neg-in_binary64
64×associate-*r*_binary64
62×log-prod_binary64
57×unsub-neg_binary64
56×distribute-lft-neg-in_binary64 associate-*l*_binary64
52×neg-sub0_binary64 associate-*r/_binary64
51×log-div_binary64 sqr-pow_binary64
50×neg-mul-1_binary64
42×+-commutative_binary64
41×unswap-sqr_binary64
39×distribute-rgt-out_binary64
31×distribute-neg-out_binary64
30×associate--r-_binary64
29×difference-of-squares_binary64
28×associate--l+_binary64
23×associate--l-_binary64
21×distribute-neg-in_binary64
19×exp-to-pow_binary64 rem-exp-log_binary64 associate--r+_binary64
18×unpow1/3_binary64
17×distribute-frac-neg_binary64
16×swap-sqr_binary64
13×unpow3_binary64 associate-/r/_binary64
10×pow-plus_binary64 cube-unmult_binary64 *-lft-identity_binary64
sqr-neg_binary64 pow-sqr_binary64
exp-neg_binary64 cube-mult_binary64 cube-neg_binary64
*-rgt-identity_binary64 remove-double-neg_binary64 distribute-lft-out_binary64
log-pow_binary64 +-rgt-identity_binary64 distribute-rgt-out--_binary64
log-rec_binary64 rem-sqrt-square_binary64
mul-1-neg_binary64 distribute-neg-frac_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 sub0-neg_binary64 cancel-sign-sub_binary64
div-exp_binary64 1-exp_binary64 /-rgt-identity_binary64 +-inverses_binary64 distribute-rgt1-in_binary64 associate-/l/_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64
Counts
99 → 64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02001902
14541837
212571782
342731738
457401738

prune261.0ms (2.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New531164
Fresh91019
Picked101
Done000
Total632184
Error
32.2b
Counts
84 → 21
Compiler

Compiled 3003 to 1409 computations (53.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b
(-.f64 (*.f64 g g) (*.f64 h h))
2.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite310.0ms (3%)

Algorithm
rewrite-expression-head
Error
32.2b
Rules
13×add-sqr-sqrt_binary64
sqrt-prod_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
pow1_binary64
difference-of-squares_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 cancel-sign-sub-inv_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 diff-log_binary64 sub-neg_binary64
distribute-lft-out--_binary64
Counts
4 → 62
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
6.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
Compiler

Compiled 2506 to 798 computations (68.2% saved)

series232.0ms (2.3%)

Error
32.2b
Counts
4 → 39
Calls

4 calls:

34.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
30.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
29.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
26.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3042 to 2186 computations (28.1% saved)

simplify103.0ms (1%)

Algorithm
egg-herbie
Rules
360×cancel-sign-sub-inv_binary64
333×neg-mul-1_binary64
284×unswap-sqr_binary64
283×associate-*l*_binary64
272×associate-*r*_binary64
190×exp-prod_binary64
138×times-frac_binary64
120×distribute-lft-neg-out_binary64 distribute-rgt-out_binary64
112×distribute-rgt-neg-out_binary64 distribute-lft-in_binary64
111×distribute-rgt-in_binary64
104×distribute-rgt-neg-in_binary64
98×sub-neg_binary64
93×distribute-lft-neg-in_binary64
84×unsub-neg_binary64 distribute-lft-out_binary64
82×associate-/l*_binary64
81×*-commutative_binary64
79×cube-prod_binary64 div-sub_binary64
70×sqr-pow_binary64
67×exp-sum_binary64
63×associate-/r*_binary64
51×+-commutative_binary64
50×swap-sqr_binary64
46×difference-of-squares_binary64
44×neg-sub0_binary64
39×associate-+l+_binary64
30×exp-diff_binary64 associate-+r+_binary64
25×unpow3_binary64 pow-plus_binary64
24×associate-*l/_binary64
23×cube-unmult_binary64
21×associate-+l-_binary64
20×associate-+r-_binary64
17×mul0-rgt_binary64 mul0-lft_binary64
16×associate-*r/_binary64
13×sub0-neg_binary64 +-rgt-identity_binary64
12×cube-mult_binary64 pow-sqr_binary64 distribute-neg-frac_binary64
11×sqr-neg_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64 associate--l+_binary64
mul-1-neg_binary64
log-prod_binary64 associate-/r/_binary64
rem-sqrt-square_binary64 distribute-lft-out--_binary64
cube-neg_binary64 distribute-neg-out_binary64
unpow2_binary64 exp-neg_binary64 distribute-frac-neg_binary64 associate--r+_binary64
unpow1/2_binary64 unpow1_binary64 div-exp_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 cancel-sign-sub_binary64 count-2_binary64 associate--l-_binary64
1-exp_binary64 rem-3cbrt-lft_binary64 *-lft-identity_binary64 --rgt-identity_binary64 +-inverses_binary64 distribute-lft1-in_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 log-pow_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-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_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 distribute-rgt1-in_binary64 associate-/l/_binary64
Counts
101 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01111472
12421384
26101381
324901381
444191381
550331381

prune225.0ms (2.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New60262
Fresh21820
Picked101
Done000
Total632083
Error
32.2b
Counts
83 → 20
Compiler

Compiled 2534 to 1212 computations (52.2% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b
(-.f64 (*.f64 g g) (*.f64 h h))
2.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.4b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite300.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
32.2b
Rules
13×add-sqr-sqrt_binary64
sqrt-prod_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
pow1_binary64
difference-of-squares_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 cancel-sign-sub-inv_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 diff-log_binary64 sub-neg_binary64
distribute-lft-out--_binary64
Counts
4 → 62
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
Compiler

Compiled 2506 to 798 computations (68.2% saved)

series223.0ms (2.2%)

Error
32.2b
Counts
4 → 39
Calls

4 calls:

33.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
32.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
29.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)
24.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3042 to 2186 computations (28.1% saved)

simplify100.0ms (1%)

Algorithm
egg-herbie
Rules
360×cancel-sign-sub-inv_binary64
333×neg-mul-1_binary64
284×unswap-sqr_binary64
283×associate-*l*_binary64
272×associate-*r*_binary64
190×exp-prod_binary64
138×times-frac_binary64
120×distribute-lft-neg-out_binary64 distribute-rgt-out_binary64
112×distribute-rgt-neg-out_binary64 distribute-lft-in_binary64
111×distribute-rgt-in_binary64
104×distribute-rgt-neg-in_binary64
98×sub-neg_binary64
93×distribute-lft-neg-in_binary64
84×unsub-neg_binary64 distribute-lft-out_binary64
82×associate-/l*_binary64
81×*-commutative_binary64
79×cube-prod_binary64 div-sub_binary64
70×sqr-pow_binary64
67×exp-sum_binary64
63×associate-/r*_binary64
51×+-commutative_binary64
50×swap-sqr_binary64
46×difference-of-squares_binary64
44×neg-sub0_binary64
39×associate-+l+_binary64
30×exp-diff_binary64 associate-+r+_binary64
25×unpow3_binary64 pow-plus_binary64
24×associate-*l/_binary64
23×cube-unmult_binary64
21×associate-+l-_binary64
20×associate-+r-_binary64
17×mul0-rgt_binary64 mul0-lft_binary64
16×associate-*r/_binary64
13×sub0-neg_binary64 +-rgt-identity_binary64
12×cube-mult_binary64 pow-sqr_binary64 distribute-neg-frac_binary64
11×sqr-neg_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64 associate--l+_binary64
mul-1-neg_binary64
log-prod_binary64 associate-/r/_binary64
rem-sqrt-square_binary64 distribute-lft-out--_binary64
cube-neg_binary64 distribute-neg-out_binary64
unpow2_binary64 exp-neg_binary64 distribute-frac-neg_binary64 associate--r+_binary64
unpow1/2_binary64 unpow1_binary64 div-exp_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 cancel-sign-sub_binary64 count-2_binary64 associate--l-_binary64
1-exp_binary64 rem-3cbrt-lft_binary64 *-lft-identity_binary64 --rgt-identity_binary64 +-inverses_binary64 distribute-lft1-in_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 log-pow_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-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_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 distribute-rgt1-in_binary64 associate-/l/_binary64
Counts
101 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01111472
12421384
26101381
324901381
444191381
550331381

prune205.0ms (2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New61162
Fresh01919
Picked101
Done000
Total622082
Error
32.2b
Counts
82 → 20
Compiler

Compiled 1725 to 709 computations (58.9% saved)

regimes3.5s (34.1%)

Accuracy

Total 1.9b remaining (6.3%)

Threshold costs 0b (0%)

Compiler

Compiled 67320 to 42957 computations (36.2% saved)

bsearch12.0ms (0.1%)

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify15.0ms (0.1%)

Algorithm
egg-herbie
Rules
15×*-commutative_binary64 +-commutative_binary64
11×sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64
unsub-neg_binary64 distribute-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64
1-exp_binary64 cancel-sign-sub-inv_binary64 distribute-neg-frac_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-in_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 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_binary64 distribute-frac-neg_binary64 distribute-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
058336
175336
286336
399336
4106328
5113328
6116328
7117328
8115328

end3.0ms (0%)

Compiler

Compiled 210 to 94 computations (55.2% saved)

sample2.4s (23.1%)

Algorithm
intervals
Results
1.3s7563×body256valid
100.0ms1209×body128nan
36.0ms437×body128valid
Compiler

Compiled 1057 to 638 computations (39.6% saved)

Profiling

Loading profile data...