Details

Time bar (total: 3.8s)

sample30.0ms

Algorithm
intervals
Results
10.0ms277×body80valid
4.0ms116×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 23.6b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
10.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms
(sqrt (- (* z z) (* t a)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
55.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0368630
11941560
25001551

prune258.0ms

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: 3.9b

Counts
99 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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:
10.0ms
(/ 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)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
85.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04531067
12239963
25001942

prune315.0ms

Filtered
134 candidates to 92 candidates (68.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1295134
Fresh549
Picked101
Done000
Total1359144

Merged error: 3.9b

Counts
144 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
24.1b
(sqrt (- (* z z) (* t a)))
24.1b
(sqrt (- (* z z) (* t a)))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
6.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))
54.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0286857
1859832
23232817
35001814

prune411.0ms

Filtered
98 candidates to 80 candidates (81.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh088
Picked011
Done000
Total989107

Merged error: 3.9b

Counts
107 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
1.6b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite40.0ms

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))
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
55.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
55.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0425829
11848729
25001717

prune260.0ms

Filtered
114 candidates to 81 candidates (71.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1122114
Fresh257
Picked011
Done011
Total1149123

Merged error: 3.9b

Counts
123 → 9

regimes323.0ms

Accuracy

81.2% (3.7b remaining)

Error of 6.7b against oracle of 3.0b and baseline of 22.6b

bsearch92.0ms

Steps
ItersRangePoint
8
6.3736077767258876e+97
2.771218538638004e+101
1.1534159093312974e+100
9
-2.0153199407633189e+124
-1.9189580122017433e+117
-2.4660126757819895e+117

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03418
13718
24518
34518

end0.0ms

sample768.0ms

Algorithm
intervals
Results
334.0ms8834×body80valid
93.0ms2807×body80nan