Details

Time bar (total: 22.5s)

sample68.0ms

Algorithm
intervals
Results
26.0ms294×body80valid
7.0ms91×body80nan

simplify140.0ms

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: 21.5b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
6.7b
(* (* x y) z)
7.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b
(sqrt (- (* z z) (* t a)))

rewrite70.0ms

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))
17.0ms
(* (* x y) z)
23.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms
(sqrt (- (* z z) (* t a)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* z z) (* t a))
44.0ms
(* (* x y) z)
117.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
74.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations
IterNodes
done5001
21480
1376
0146

prune747.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.9b
(sqrt (- (* z z) (* t a)))

rewrite68.0ms

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))
20.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.0ms
(sqrt (- (* z z) (* t a)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (sqrt (- (* z z) (* t a))) z)
61.0ms
(- (* z z) (* t a))
119.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
81.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
154 → 154
Iterations
IterNodes
done5000
21984
1574
0222

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.5b
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.0b
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
22.9b
(sqrt (- (* z z) (* t a)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
828×times-frac
400×add-sqr-sqrt
399×*-un-lft-identity add-cube-cbrt
147×sqrt-prod
73×associate-/r*
25×associate-/l*
22×div-inv
18×add-cbrt-cube add-exp-log
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×clear-num frac-2neg flip3-- sqrt-div flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/ associate-/l/
Counts
4 → 443
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
19.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
53.0ms
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
17.0ms
(sqrt (- (* z z) (* t a)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* z z) (* t a))
116.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
116.0ms
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
455 → 455
Iterations
IterNodes
done5000
11861
0667

prune3.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

localize75.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ x (* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y))))
3.8b
(* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y)))
23.6b
(cbrt (- (* z z) (* t a)))
23.6b
(cbrt (- (* z z) (* t a)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
391×times-frac
251×add-sqr-sqrt
190×associate-*r*
187×*-un-lft-identity add-cube-cbrt
165×cbrt-prod
116×sqrt-prod
87×add-exp-log
63×add-cbrt-cube
40×cbrt-undiv div-exp
24×prod-exp cbrt-unprod
18×unswap-sqr
9×div-inv
7×associate-*l*
6×pow1
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×associate-/r/ associate-/l*
2×frac-times flip3-- pow1/3 associate-*l/ associate-*r/ flip--
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative
Counts
4 → 319
Calls
4 calls:
49.0ms
(/ x (* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y))))
147.0ms
(* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y)))
5.0ms
(cbrt (- (* z z) (* t a)))
5.0ms
(cbrt (- (* z z) (* t a)))

series1.5s

Counts
4 → 12
Calls
4 calls:
536.0ms
(/ x (* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y))))
343.0ms
(* (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt y) (cbrt y))) (/ (/ (sqrt (cbrt (- (* z z) (* t a)))) z) (cbrt y)))
526.0ms
(cbrt (- (* z z) (* t a)))
121.0ms
(cbrt (- (* z z) (* t a)))

simplify3.2s

Counts
331 → 331
Iterations
IterNodes
done5001
12180
0642

prune2.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.5b

regimes1.2s

Accuracy

83.2% (3.3b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 22.5b

bsearch151.0ms

Steps
ItersRangePoint
9
1.0657461423981877e+72
1.4544772538077902e+79
1.8248255120520226e+78
10
-5.3775242541643475e+135
-9.966822043512241e+120
-1.4304090206238952e+130

simplify9.0ms

Iterations
IterNodes
done38
238
136
027

end0.0ms

sample1.4s

Algorithm
intervals
Results
712.0ms8830×body80valid
224.0ms3000×body80nan