Details

Time bar (total: 17.6s)

sample63.0ms

Algorithm
intervals
Results
23.0ms282×body80valid
8.0ms102×body80nan

simplify103.0ms

Counts
1 → 1
Iterations
IterNodes
done106
6106
597
477
358
237
122
012

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
6.1b
(* (* x y) z)
11.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac prod-exp 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×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
13.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) z)
22.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
17.0ms
(sqrt (- (* z z) (* t a)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* z z) (* t a))
40.0ms
(* (* x y) z)
127.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
98 → 98
Iterations
IterNodes
done5001
21480
1376
0146

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
24×associate-*r* sqrt-prod
18×add-cbrt-cube add-exp-log
10×pow1
6×associate-/r* sqrt-div prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u flip3-- associate-/r/ log1p-expm1-u flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff associate-*r/ *-commutative
Counts
4 → 122
Calls
4 calls:
19.0ms
(/ z (sqrt (- (* z z) (* t a))))
6.0ms
(- (* z z) (* t a))
48.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
18.0ms
(sqrt (- (* z z) (* t a)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
137.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
107.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
134 → 134
Iterations
IterNodes
done5001
21819
1493
0178

prune964.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt z)
0.6b
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a))))) x) y)
23.8b
(cbrt (- (* z z) (* t a)))
23.8b
(cbrt (- (* z z) (* t a)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
16×add-cbrt-cube
9×cbrt-prod pow1
8×add-sqr-sqrt *-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down
2×cbrt-undiv flip3-- div-exp associate-*l/ flip--
1×associate-*l* *-commutative
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt z)
76.0ms
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a))))) x) y)
20.0ms
(cbrt (- (* z z) (* t a)))
9.0ms
(cbrt (- (* z z) (* t a)))

series1.0s

Counts
4 → 12
Calls
4 calls:
297.0ms
(cbrt z)
469.0ms
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a))))) x) y)
120.0ms
(cbrt (- (* z z) (* t a)))
159.0ms
(cbrt (- (* z z) (* t a)))

simplify1.8s

Counts
80 → 80
Iterations
IterNodes
done5003
21377
1419
0152

prune702.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize85.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) x) y)
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))
23.8b
(cbrt (- (* z z) (* t a)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
16×add-cbrt-cube
11×pow1
10×add-sqr-sqrt
8×*-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
6×sqrt-prod
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×cbrt-prod flip3-- associate-*r* pow-prod-down flip--
2×cbrt-undiv rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 div-exp associate-*l/
1×pow1/3 associate-*l* *-commutative
Counts
4 → 74
Calls
4 calls:
80.0ms
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) x) y)
9.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))
10.0ms
(cbrt (- (* z z) (* t a)))

series835.0ms

Counts
4 → 12
Calls
4 calls:
501.0ms
(* (* (/ (* (cbrt z) (cbrt z)) (fabs (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) x) y)
84.0ms
(sqrt (- (* z z) (* t a)))
116.0ms
(sqrt (- (* z z) (* t a)))
133.0ms
(cbrt (- (* z z) (* t a)))

simplify2.1s

Counts
86 → 86
Iterations
IterNodes
done5000
21448
1432
0163

prune843.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

regimes1.2s

Accuracy

87.2% (2.4b remaining)

Error of 5.8b against oracle of 3.3b and baseline of 22.2b

bsearch127.0ms

Steps
ItersRangePoint
8
4.271611683557293e+96
5.363233345281319e+99
8.80124926176556e+98
6
-8.608795433027066e+122
-1.0846037281689326e+122
-2.099203142812841e+122

simplify14.0ms

Iterations
IterNodes
done40
240
137
030

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.2s8855×body80valid
227.0ms2804×body80nan