Details

Time bar (total: 5.0s)

analyze1.3s (25.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.4%0.2%12
12.2%87.6%0.2%13
21.8%77.8%0.4%14

sample36.0ms (0.7%)

Algorithm
intervals
Results
8.0ms214×body80valid
2.0ms59×body80invalid
2.0ms13×body640valid
1.0msbody1280valid
1.0ms10×body320valid
1.0ms11×body160valid

simplify63.0ms (1.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
0489213
1489213

prune8.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.9b

Counts
2 → 1

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (-.f64 y z) (-.f64 t x))
3.5b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.6b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite33.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
13×flip3--_binary64 flip--_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l/_binary64 frac-times_binary64
add-cube-cbrt_binary64
associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 associate-*r*_binary64 associate-*l*_binary64 times-frac_binary64
associate-*r/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate-*l/_binary64
sub-neg_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 prod-exp_binary64 div-exp_binary64
pow-prod-down_binary64 flip3-+_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
3 → 79
Calls

3 calls:

13.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
10.0ms
(*.f64 (-.f64 y z) (-.f64 t x))
8.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series119.0ms (2.4%)

Counts
3 → 9
Calls

3 calls:

62.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
45.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
11.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify44.0ms (0.9%)

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
060371081

prune137.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80888
Fresh000
Picked101
Done000
Total81889

Merged error: 2.9b

Counts
89 → 8

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (-.f64 a z))
1.5b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
7.4b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite56.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
52×times-frac_binary64
46×associate-*r*_binary64
37×cbrt-prod_binary64
27×add-cube-cbrt_binary64
25×add-exp-log_binary64
18×cbrt-div_binary64 add-cbrt-cube_binary64
17×associate-*l*_binary64
16×difference-of-squares_binary64 distribute-lft-out--_binary64
10×associate-/r/_binary64
flip3--_binary64 flip--_binary64
cbrt-unprod_binary64 prod-exp_binary64
cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 pow1_binary64 unswap-sqr_binary64
frac-times_binary64
associate-*r/_binary64 associate-*l/_binary64
pow1/3_binary64 div-inv_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 134
Calls

4 calls:

36.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
6.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
3.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series196.0ms (3.9%)

Counts
4 → 12
Calls

4 calls:

75.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
64.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
29.0ms
(cbrt.f64 (-.f64 a z))
28.0ms
(cbrt.f64 (-.f64 a z))

simplify40.0ms (0.8%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
052922530

prune179.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1424146
Fresh257
Picked101
Done000
Total1459154

Merged error: 2.5b

Counts
154 → 9

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 a z))
0.6b
(cbrt.f64 (-.f64 a z))
2.0b
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
6.9b
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite89.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt_binary64
98×times-frac_binary64
84×cbrt-prod_binary64
74×*-un-lft-identity_binary64
69×add-exp-log_binary64
61×associate-*r*_binary64
44×cbrt-div_binary64
42×add-cbrt-cube_binary64
36×add-cube-cbrt_binary64
29×associate-*l*_binary64
27×cbrt-undiv_binary64 div-exp_binary64
24×cbrt-unprod_binary64 prod-exp_binary64
19×difference-of-squares_binary64 distribute-lft-out--_binary64
18×associate-/r/_binary64
15×flip3--_binary64 flip--_binary64
12×unswap-sqr_binary64
frac-times_binary64
add-log-exp_binary64 pow1_binary64
associate-*r/_binary64 associate-*l/_binary64
div-inv_binary64
pow1/3_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 183
Calls

4 calls:

66.0ms
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
5.0ms
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
3.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series200.0ms (4%)

Counts
4 → 12
Calls

4 calls:

75.0ms
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
67.0ms
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
30.0ms
(cbrt.f64 (-.f64 a z))
28.0ms
(cbrt.f64 (-.f64 a z))

simplify76.0ms (1.5%)

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049844919
149844919

prune250.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1950195
Fresh088
Picked011
Done000
Total1959204

Merged error: 2.5b

Counts
204 → 9

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
0.6b
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
1.2b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
7.9b
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

rewrite73.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
142×cbrt-prod_binary64
100×add-sqr-sqrt_binary64
98×*-un-lft-identity_binary64
86×times-frac_binary64
44×add-cube-cbrt_binary64
27×difference-of-squares_binary64 distribute-lft-out--_binary64
26×cbrt-div_binary64
25×add-exp-log_binary64
17×associate-*l*_binary64
15×add-cbrt-cube_binary64
12×associate-/r/_binary64
11×cbrt-unprod_binary64 prod-exp_binary64
pow1_binary64 frac-times_binary64
flip3--_binary64 flip--_binary64
associate-*r/_binary64
add-log-exp_binary64
associate-*l/_binary64
cbrt-undiv_binary64 div-exp_binary64
pow-prod-down_binary64 div-inv_binary64
pow1/3_binary64 unswap-sqr_binary64
flip3-+_binary64 associate-*r*_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 170
Calls

4 calls:

40.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
11.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
9.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
5.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

series373.0ms (7.5%)

Counts
4 → 12
Calls

4 calls:

159.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
73.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
73.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
67.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

simplify49.0ms (1%)

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
055134166

prune194.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1811182
Fresh077
Picked011
Done011
Total18110191

Merged error: 2.5b

Counts
191 → 10

regimes475.0ms (9.5%)

Accuracy

Total 7.9b remaining (70.9%)

Threshold costs 0b (0%)

bsearch41.0ms (0.8%)

Steps
ItersRangePoint
9
4.62183871278111e-173
3.648303785268756e-167
1.5504634327615182e-167
4
-7.998888117147235e-69
-5.137629488081729e-69
-5.227043820240027e-69

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07169
17169

end0.0ms (0%)

sample910.0ms (18.3%)

Algorithm
intervals
Results
311.0ms6566×body80valid
87.0ms492×body640valid
56.0ms269×body1280valid
51.0ms1167×body80invalid
50.0ms403×body320valid
21.0ms255×body160valid
4.0ms15×body2560valid

Profiling

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