Details

Time bar (total: 11.1s)

sample30.0ms

Algorithm
intervals
Results
11.0ms276×body80valid
3.0ms101×body80nan

simplify56.0ms

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

localize12.0ms

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)))

rewrite31.0ms

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))
7.0ms
(* (* x y) z)
14.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
35.0ms
(* (* x y) z)
115.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
98 → 98
Iterations

Useful iterations: 2 (220.0ms)

IterNodesCost
01461331
13651224
216741062
done50001062

prune357.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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))
21.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ z (sqrt (- (* z z) (* t a))))
42.0ms
(- (* z z) (* t a))
114.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
134 → 134
Iterations

Useful iterations: 2 (328.0ms)

IterNodesCost
01782135
14491955
217341744
done50001744

prune442.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.0b
(- (* z z) (* t a))
1.5b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite56.0ms

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:
24.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
21.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
42.0ms
(- (* z z) (* t a))
100.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
70.0ms
(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts
114 → 114
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01731680
14211558
212511342
345281340
done50001340

prune356.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize17.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
25.0b
(sqrt (- (* z z) (* t a)))
25.0b
(sqrt (- (* z z) (* t a)))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
5.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
81.0ms
(sqrt (- (* z z) (* t a)))
82.0ms
(sqrt (- (* z z) (* t a)))
81.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: 3 (418.0ms)

IterNodesCost
01531602
12861458
27181360
320491350
done50001350

prune466.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes378.0ms

Accuracy

85.8% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 22.8b

bsearch119.0ms

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12829
23029
done3029

end0.0ms

sample816.0ms

Algorithm
intervals
Results
355.0ms8886×body80valid
97.0ms2944×body80nan