Details

Time bar (total: 4.0s)

sample36.0ms

Algorithm
intervals
Results
16.0ms287×body80valid
5.0ms95×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune2.0ms

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: 23.4b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.9b
(* (* x y) z)
9.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.7b
(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)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0368630
11941560
25001551

prune245.0ms

Filtered
98 candidates to 71 candidates (72.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New871198
Fresh000
Picked101
Done000
Total881199

Merged error: 2.0b

Counts
99 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
1.7b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.7b
(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))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04531067
12239963
25001942

prune289.0ms

Filtered
134 candidates to 93 candidates (69.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1313134
Fresh1910
Picked101
Done000
Total13312145

Merged error: 2.0b

Counts
145 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.6b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.7b
(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×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))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
54.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
84.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0425829
11848729
25001717

prune244.0ms

Filtered
114 candidates to 78 candidates (68.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1131114
Fresh11011
Picked101
Done000
Total11511126

Merged error: 2.0b

Counts
126 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.9b
(* (* x y) z)
9.4b
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
24.7b
(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 cbrt-unprod associate-/l* 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-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff clear-num associate-/r* *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
9.0ms
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
28.0ms
(* (* x y) z)
112.0ms
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0407644
12109575
25001568

prune217.0ms

Filtered
98 candidates to 73 candidates (74.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New97198
Fresh1910
Picked011
Done000
Total9811109

Merged error: 2.0b

Counts
109 → 11

regimes578.0ms

Accuracy

79.5% (4.4b remaining)

Error of 7.7b against oracle of 3.3b and baseline of 24.8b

bsearch96.0ms

Steps
ItersRangePoint
5
9.825461176600007e+97
3.541309604326139e+98
1.1611135688740357e+98
11
-1199119032805.3176
-6.671394545181793e-10
-1063963419286.4185

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02911
13511
23511

end0.0ms

sample996.0ms

Algorithm
intervals
Results
469.0ms8847×body80valid
153.0ms3072×body80nan