Details

Time bar (total: 3.0s)

sample64.0ms

Algorithm
intervals
Results
19.0ms289×body80valid
4.0ms81×body80nan

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.6b
(* (* x y) z)
8.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
21.7b
(sqrt (- (* z z) (* t a)))

rewrite21.0ms

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)
8.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
32.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0343583
11850515
25003510

prune133.0ms

Filtered
60 candidates to 88 candidates (-46.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New781088
Fresh000
Picked101
Done000
Total791089

Merged error: 4.0b

Counts
89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.7b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
21.7b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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))))
5.0ms
(- (* 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))
30.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04281014
12153912
25002894

prune119.0ms

Filtered
80 candidates to 124 candidates (-55.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1231124
Fresh279
Picked011
Done000
Total1259134

Merged error: 3.9b

Counts
134 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
0.6b
(- (* z z) (* t a))
1.6b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
21.7b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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:
10.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
9.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
3.0ms
(sqrt (- (* z z) (* t a)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(- (* z z) (* t a))
30.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0400774
11768676
25001668

prune102.0ms

Filtered
66 candidates to 104 candidates (-57.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh167
Picked011
Done011
Total1049113

Merged error: 3.9b

Counts
113 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.6b
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
6.0b
(/ (* y z) (sqrt (- (* z z) (* t a))))
21.7b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac associate-*r* sqrt-prod
7×pow1
6×sqrt-div associate-/r* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv flip3-- div-exp associate-/r/ flip--
3×associate-*l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
9.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
7.0ms
(/ (* y z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
32.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
18.0ms
(/ (* y z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify43.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0357755
11654664
25001656

prune76.0ms

Filtered
67 candidates to 100 candidates (-49.3%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1000100
Fresh066
Picked011
Done022
Total1009109

Merged error: 3.9b

Counts
109 → 9

regimes714.0ms

Accuracy

83.5% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 22.8b

bsearch44.0ms

Steps
ItersRangePoint
8
4.991403399298958e+32
7.959643890777834e+35
7.821275161291146e+35
5
-2.911238148907189e+111
-1.1988401156082606e+111
-1.2637973560862005e+111

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample1.1s

Algorithm
intervals
Results
460.0ms8885×body80valid
140.0ms2921×body80nan

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