Details

Time bar (total: 8.3s)

sample30.0ms

Algorithm
intervals
Results
10.0ms276×body80valid
3.0ms101×body80nan

simplify53.0ms

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: 26.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
7.3b
(* (* x y) z)
9.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0b
(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)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
95.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify686.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (189.0ms)

IterNodesCost
01461331
13631220
216431062
done50011062

prune312.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
3.6b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
25.0b
(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))
23.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
40.0ms
(- (* z z) (* t a))
92.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
70.0ms
(sqrt (- (* z z) (* t a)))

simplify898.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (287.0ms)

IterNodesCost
01792135
14491941
217041740
done50001740

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.5b
(* x (/ z (sqrt (- (* z z) (* t a)))))
2.4b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
25.0b
(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:
3.0ms
(- (* z z) (* t a))
19.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
19.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* z z) (* t a))
61.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
94.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
114 → 114
Iterations

Useful iterations: 3 (943.0ms)

IterNodesCost
01741680
14201552
212381342
345611340
done50001340

prune321.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.1b
(* x (* z y))
9.9b
(/ (pow (* x (* z y)) 1) (sqrt (- (* z z) (* t a))))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
21×add-exp-log sqrt-prod
11×add-cbrt-cube
10×pow1
7×unpow-prod-down sqr-pow
6×prod-exp associate-/r* add-log-exp
5×div-exp associate-/l*
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down pow-exp flip-- cbrt-unprod
2×associate-/r/
1×cbrt-undiv pow-to-exp sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r* prod-diff clear-num *-commutative div-inv
Counts
4 → 114
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
6.0ms
(* x (* z y))
8.0ms
(/ (pow (* x (* z y)) 1) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
30.0ms
(* x (* z y))
97.0ms
(/ (pow (* x (* z y)) 1) (sqrt (- (* z z) (* t a))))
70.0ms
(sqrt (- (* z z) (* t a)))

simplify665.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
01902318
13861973
213321846
done50001846

prune333.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes347.0ms

Accuracy

86.7% (2.5b remaining)

Error of 5.9b against oracle of 3.3b and baseline of 22.5b

bsearch108.0ms

Steps
ItersRangePoint
9
1.5599000651954472e+122
3.251841885581708e+128
2.2349389384476415e+125
9
-8.382253253648058e+154
-1.005629218284056e+149
-9.341949798077739e+151

simplify5.0ms

Iterations

Useful iterations: 2 (2.0ms)

IterNodesCost
02230
12630
22729
33329
done3329

end0.0ms

sample805.0ms

Algorithm
intervals
Results
341.0ms8886×body80valid
104.0ms2944×body80nan