Details

Time bar (total: 4.8s)

sample32.0ms

Algorithm
intervals
Results
14.0ms279×body80valid
3.0ms72×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.9b
(* (* x y) z)
9.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
28.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0368630
11941560
25001551

prune248.0ms

Filtered
98 candidates to 71 candidates (72.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New881098
Fresh000
Picked101
Done000
Total891099

Merged error: 3.6b

Counts
99 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
4.0ms
(- (* z z) (* t a))
12.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
80.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
04531067
12239963
25001942

prune277.0ms

Filtered
134 candidates to 93 candidates (69.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1322134
Fresh099
Picked011
Done000
Total13212144

Merged error: 3.6b

Counts
144 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.2b
(* y (/ z (sqrt (- (* z z) (* t a)))))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite36.0ms

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×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
15.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
55.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0425829
11848729
25001717

prune240.0ms

Filtered
114 candidates to 78 candidates (68.4%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh01010
Picked011
Done011
Total11412126

Merged error: 3.6b

Counts
126 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
5.9b
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
25.1b
(cbrt (- (* z z) (* t a)))
25.1b
(cbrt (- (* z z) (* t a)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
413×times-frac
157×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
114×sqrt-prod
63×cbrt-prod
34×add-exp-log add-cbrt-cube
24×div-inv
22×associate-/r*
19×associate-/l*
17×cbrt-undiv div-exp
13×associate-/r/
6×cbrt-div
4×pow1 expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-- flip--
2×frac-2neg pow1/3 sqrt-div clear-num
1×associate-/l/
Counts
4 → 292
Calls
4 calls:
16.0ms
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
6.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
3.0ms
(cbrt (- (* z z) (* t a)))
4.0ms
(cbrt (- (* z z) (* t a)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
65.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
85.0ms
(cbrt (- (* z z) (* t a)))
91.0ms
(cbrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012736567
150016234

prune876.0ms

Filtered
304 candidates to 231 candidates (76.0%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New3013304
Fresh459
Picked011
Done022
Total30511316

Merged error: 3.6b

Counts
316 → 11

regimes472.0ms

Accuracy

76.7% (4.5b remaining)

Error of 8.0b against oracle of 3.4b and baseline of 22.8b

bsearch91.0ms

Steps
ItersRangePoint
9
4.5418805312590315e+84
1.0915535352690582e+92
6.86640182930296e+84
8
-3.435885906476597e+114
-1.333018747280528e+112
-2.939191418457513e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample995.0ms

Algorithm
intervals
Results
464.0ms8827×body80valid
147.0ms2948×body80nan

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