Details

Time bar (total: 4.0s)

sample40.0ms

Algorithm
intervals
Results
14.0ms279×body80valid
9.0ms129×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: 25.2b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
4.1b
(* (* x y) z)
8.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.5b
(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)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368630
11941560
25001551

prune249.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.5b
(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)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04531067
12239963
25001942

prune302.0ms

Filtered
134 candidates to 94 candidates (70.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1322134
Fresh1910
Picked101
Done000
Total13411145

Merged error: 2.0b

Counts
145 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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))
12.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
52.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
80.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0425829
11848729
25001717

prune230.0ms

Filtered
114 candidates to 79 candidates (69.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1140114
Fresh01010
Picked011
Done000
Total11411125

Merged error: 2.0b

Counts
125 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (sqrt (- (* z z) (* t a))) z)
31.0ms
(- (* z z) (* t a))
78.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05431379
124481281
250011260

prune299.0ms

Filtered
154 candidates to 110 candidates (71.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1513154
Fresh369
Picked011
Done011
Total15411165

Merged error: 2.0b

Counts
165 → 11

regimes463.0ms

Accuracy

87.4% (2.4b remaining)

Error of 5.6b against oracle of 3.2b and baseline of 22.5b

bsearch80.0ms

Steps
ItersRangePoint
7
1.7765630896242644e+150
3.3191566616173884e+151
2.3486344484962516e+151
8
-8.825863841160675e+156
-4.347244425542823e+153
-1.3069480601769862e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02925
13525
23525

end0.0ms

sample982.0ms

Algorithm
intervals
Results
463.0ms8854×body80valid
152.0ms2981×body80nan