Details

Time bar (total: 7.3s)

sample43.0ms

Algorithm
intervals
Results
13.0ms280×body80valid
4.0ms93×body80nan

simplify42.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36914
49314
510614
done10614

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify568.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
01461331
13721224
217851062
done50001062

prune299.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
2.4b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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

series236.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
34.0ms
(- (* z z) (* t a))
86.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify685.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
01792135
14611955
219351744
done50001744

prune372.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.9b
(* x (/ z (sqrt (- (* z z) (* t a)))))
1.0b
(- (* z z) (* t a))
1.7b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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:
19.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
20.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
33.0ms
(- (* z z) (* t a))
87.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify504.0ms

Counts
114 → 114
Iterations

Useful iterations: done (501.0ms)

IterNodesCost
01741680
14241558
214441342
done50011341

prune325.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b
(* y (* (* x (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
22.0b
(sqrt (- (* z z) (* t a)))
22.0b
(sqrt (- (* z z) (* t a)))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite412.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
46×add-cbrt-cube
43×prod-exp cbrt-unprod
16×pow1
14×cbrt-undiv div-exp
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div associate-*r/ pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* flip--
1×frac-times associate-*r* associate-*l/ *-commutative
Counts
4 → 97
Calls
4 calls:
395.0ms
(* y (* (* x (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* y (* (* x (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
59.0ms
(sqrt (- (* z z) (* t a)))
65.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
109 → 109
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01843533
16363272
228171707
done50001695

prune394.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.3b

regimes497.0ms

Accuracy

85% (2.8b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 22.2b

bsearch85.0ms

Steps
ItersRangePoint
7
4.43464859477407e+147
1.5123157394476474e+149
6.926066888201142e+147
9
-2.7283838574175814e+156
-2.1161453073457986e+149
-8.618354790122042e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12829
23029
done3029

end0.0ms

sample826.0ms

Algorithm
intervals
Results
357.0ms8864×body80valid
100.0ms2952×body80nan