Details

Time bar (total: 4.1s)

sample31.0ms

Algorithm
intervals
Results
10.0ms276×body80valid
4.0ms100×body80nan

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

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: 23.9b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
9.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
14.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
101.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0346584
11863515
25002510

prune243.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New79988
Fresh000
Picked011
Done000
Total791089

Merged error: 4.1b

Counts
89 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
2.7b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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))))
4.0ms
(- (* z z) (* t a))
13.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
99.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
69.0ms
(sqrt (- (* z z) (* t a)))

simplify70.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
04311015
12166912
25002893

prune291.0ms

Filtered
124 candidates to 81 candidates (65.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1222124
Fresh268
Picked101
Done011
Total1259134

Merged error: 3.8b

Counts
134 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
2.7b
(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
24.1b
(cbrt (- (* z z) (* t a)))
24.1b
(cbrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
11×prod-exp cbrt-unprod
9×pow1 associate-*r*
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod cbrt-div add-log-exp
4×cbrt-undiv flip3-- div-exp flip--
3×times-frac associate-*r/ pow-prod-down
2×pow1/3 sqrt-div associate-/r/
1×sub-neg diff-log associate-*l* *-commutative div-inv
Counts
4 → 71
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
13.0ms
(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
4.0ms
(cbrt (- (* z z) (* t a)))
4.0ms
(cbrt (- (* z z) (* t a)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
231.0ms
(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
97.0ms
(cbrt (- (* z z) (* t a)))
97.0ms
(cbrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04651013
12253807
25001803

prune291.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New83083
Fresh077
Picked011
Done011
Total83992

Merged error: 3.8b

Counts
92 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.5b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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:
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))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
67.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
99.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
70.0ms
(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0403775
11781676
25001667

prune219.0ms

Filtered
104 candidates to 67 candidates (64.4%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1031104
Fresh066
Picked011
Done022
Total10310113

Merged error: 3.8b

Counts
113 → 10

regimes452.0ms

Accuracy

85.1% (2.9b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 22.7b

bsearch104.0ms

Steps
ItersRangePoint
6
2.0423552891968378e+141
1.1834367794354304e+142
2.383081941608218e+141
11
-5.551295714995566e+178
-7.74568282368766e+152
-1.2908464800405662e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02917
13517
23517

end0.0ms

sample833.0ms

Algorithm
intervals
Results
348.0ms8903×body80valid
111.0ms3061×body80nan