Details

Time bar (total: 9.9s)

sample30.0ms

Algorithm
intervals
Results
10.0ms279×body80valid
3.0ms99×body80nan

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36814
49214
510514
done10514

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
4.7b
(* (* x y) z)
8.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
106.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify995.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
01461331
13651224
216741062
done50001062

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
2.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite40.0ms

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))))
3.0ms
(- (* z z) (* t a))
22.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
98.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
74.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
134 → 134
Iterations

Useful iterations: 2 (305.0ms)

IterNodesCost
01782135
14491955
217341744
done50001744

prune390.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

1.1b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.2b
(- (* z z) (* t a))
1.9b
(* y (/ z (sqrt (- (* z z) (* t a)))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite53.0ms

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:
23.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
37.0ms
(- (* z z) (* t a))
68.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
114 → 114
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01731680
14211558
212561342
345551340
done50001340

prune322.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
7.2b
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
28.3b
(cbrt (- (* z z) (* t a)))
28.3b
(cbrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×times-frac
33×associate-*r*
32×add-cube-cbrt *-un-lft-identity
22×sqrt-prod
17×cbrt-prod
16×add-exp-log add-cbrt-cube
13×associate-*l*
8×unswap-sqr
6×pow1 cbrt-div add-log-exp
4×cbrt-undiv expm1-log1p-u flip3-- div-exp prod-exp flip-- cbrt-unprod log1p-expm1-u
2×pow1/3 sqrt-div associate-/r/ div-inv
1×frac-times sub-neg fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative
Counts
4 → 122
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
35.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* t a))
164.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
99.0ms
(cbrt (- (* z z) (* t a)))
100.0ms
(cbrt (- (* z z) (* t a)))

simplify1.3s

Counts
134 → 134
Iterations

Useful iterations: 2 (439.0ms)

IterNodesCost
02443140
16663010
222852667
done50012667

prune526.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

regimes319.0ms

Accuracy

83.4% (3.1b remaining)

Error of 7.3b against oracle of 4.2b and baseline of 22.8b

bsearch93.0ms

Steps
ItersRangePoint
5
2.630451539791177e+79
8.765004478552205e+79
2.9066318437014138e+79
9
-5.265129340759454e+73
-8.378710405837631e+67
-2.973010024434297e+73

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02743
13443
23643
done3643

end0.0ms

sample772.0ms

Algorithm
intervals
Results
330.0ms8834×body80valid
98.0ms2913×body80nan