Details

Time bar (total: 19.4s)

sample58.0ms

Algorithm
intervals
Results
22.0ms280×body80valid
7.0ms106×body80nan

simplify116.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
5.6b
(* (* x y) z)
6.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.5b
(sqrt (- (* z z) (* t a)))

rewrite82.0ms

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:
7.0ms
(- (* z z) (* t a))
14.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0ms
(sqrt (- (* z z) (* t a)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
110.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
99.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations
IterNodes
done5001
21480
1376
0146

prune700.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
2.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.5b
(sqrt (- (* z z) (* t a)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
25×associate-/r*
18×add-cbrt-cube add-exp-log
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×clear-num frac-2neg prod-exp cbrt-unprod associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
13.0ms
(/ (sqrt (- (* z z) (* t a))) z)
7.0ms
(- (* z z) (* t a))
28.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
17.0ms
(sqrt (- (* z z) (* t a)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (sqrt (- (* z z) (* t a))) z)
47.0ms
(- (* z z) (* t a))
158.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
112.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
154 → 154
Iterations
IterNodes
done5000
21984
1574
0222

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

localize54.0ms

Local error

Found 4 expressions with local error:

3.1b
(cbrt (/ (sqrt (- (* z z) (* t a))) z))
22.5b
(sqrt (- (* z z) (* t a)))
22.5b
(sqrt (- (* z z) (* t a)))
22.5b
(sqrt (- (* z z) (* t a)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×cbrt-prod
20×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
1×cbrt-div pow1/3 div-inv
Counts
4 → 84
Calls
4 calls:
5.0ms
(cbrt (/ (sqrt (- (* z z) (* t a))) z))
8.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))
25.0ms
(sqrt (- (* z z) (* t a)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(cbrt (/ (sqrt (- (* z z) (* t a))) z))
102.0ms
(sqrt (- (* z z) (* t a)))
84.0ms
(sqrt (- (* z z) (* t a)))
107.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
96 → 96
Iterations
IterNodes
done5007
32318
2738
1287
0147

prune880.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
1.6b
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
23.3b
(cbrt (- (* z z) (* t a)))
23.3b
(cbrt (- (* z z) (* t a)))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
462×times-frac
309×add-sqr-sqrt
206×*-un-lft-identity add-cube-cbrt
179×associate-*r*
156×cbrt-prod
120×sqrt-prod
67×add-exp-log
55×add-cbrt-cube
32×cbrt-undiv div-exp
26×associate-*l*
24×unswap-sqr
16×prod-exp cbrt-unprod
13×div-inv
7×associate-/r*
6×pow1
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×associate-/r/ associate-/l*
2×flip3-- pow1/3 flip--
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 347
Calls
4 calls:
12.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
266.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
17.0ms
(cbrt (- (* z z) (* t a)))
9.0ms
(cbrt (- (* z z) (* t a)))

series1.0s

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
550.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (cbrt (- (* z z) (* t a)))) (cbrt z))))
118.0ms
(cbrt (- (* z z) (* t a)))
132.0ms
(cbrt (- (* z z) (* t a)))

simplify2.6s

Counts
359 → 359
Iterations
IterNodes
done5000
12496
0679

prune2.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.3b

regimes1.1s

Accuracy

86.3% (2.7b remaining)

Error of 5.7b against oracle of 3.1b and baseline of 22.5b

bsearch119.0ms

Steps
ItersRangePoint
7
4.621680354172573e+105
4.8838286355542577e+107
3.280936158314262e+107
9
-1.0872942423520943e+158
-2.0715321217766484e+152
-5.979373433067622e+153

simplify8.0ms

Iterations
IterNodes
done42
242
139
031

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s8871×body80valid
243.0ms2937×body80nan