Details

Time bar (total: 4.9s)

sample50.0ms

Algorithm
intervals
Results
14.0ms291×body80valid
4.0ms88×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.4b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
10.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
4.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
15.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0343583
11850515
25003510

prune303.0ms

Filtered
88 candidates to 60 candidates (31.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New79988
Fresh000
Picked011
Done000
Total791089

Merged error: 2.9b

Counts
89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.8b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(sqrt (- (* z z) (* t a)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ z (sqrt (- (* z z) (* t a))))
7.0ms
(- (* z z) (* t a))
31.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04281014
12153912
25002894

prune457.0ms

Filtered
124 candidates to 81 candidates (34.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1222124
Fresh358
Picked011
Done011
Total1259134

Merged error: 2.6b

Counts
134 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.8b
(- (* z z) (* t a))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
6.0ms
(sqrt (- (* z z) (* t a)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms
(- (* z z) (* t a))
28.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0400774
11768676
25001668

prune451.0ms

Filtered
104 candidates to 67 candidates (35.6%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1031104
Fresh066
Picked011
Done022
Total10310113

Merged error: 2.6b

Counts
113 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* z z) (* t a))
2.0b
(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
23.6b
(cbrt (- (* z z) (* t a)))
23.6b
(cbrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
9×pow1
8×prod-exp cbrt-unprod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
4×cbrt-div
3×flip3-- associate-*l* pow-prod-down flip--
2×cbrt-undiv pow1/3 associate-*r/ div-exp
1×sub-neg diff-log associate-*r* *-commutative
Counts
4 → 61
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
11.0ms
(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
4.0ms
(cbrt (- (* z z) (* t a)))
3.0ms
(cbrt (- (* z z) (* t a)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
82.0ms
(* x (* y (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))))
21.0ms
(cbrt (- (* z z) (* t a)))
24.0ms
(cbrt (- (* z z) (* t a)))

simplify48.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0447864
11853702
25001690

prune516.0ms

Filtered
73 candidates to 57 candidates (21.9%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New73073
Fresh066
Picked011
Done033
Total731083

Merged error: 2.6b

Counts
83 → 10

regimes1.2s

Accuracy

85.6% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 23.0b

bsearch99.0ms

Steps
ItersRangePoint
6
2.4342395188774056e+92
3.6163568079466423e+93
1.9374966239837004e+93
8
-1.9206346708680486e+155
-9.99712492405684e+151
-7.331144116356359e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample1.2s

Algorithm
intervals
Results
423.0ms8854×body80valid
128.0ms2847×body80nan

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