Details

Time bar (total: 15.3s)

sample69.0ms

Algorithm
intervals
Results
25.0ms281×body80valid
6.0ms79×body80nan

simplify149.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37314
49814
511914
done11914

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z z) (* t a))
3.2b
(* (* x y) z)
7.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite145.0ms

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:
17.0ms
(- (* z z) (* t a))
42.0ms
(* (* x y) z)
58.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.0ms
(sqrt (- (* z z) (* t a)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* z z) (* t a))
52.0ms
(* (* x y) z)
124.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
94.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461331
13861225
222651080
done50001077

prune474.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z z) (* t a))
0.1b
(/ z (sqrt (- (* z z) (* t a))))
2.1b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite136.0ms

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:
18.0ms
(- (* z z) (* t a))
29.0ms
(/ z (sqrt (- (* z z) (* t a))))
59.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.0ms
(sqrt (- (* z z) (* t a)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* z z) (* t a))
72.0ms
(/ z (sqrt (- (* z z) (* t a))))
164.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
103.0ms
(sqrt (- (* z z) (* t a)))

simplify2.9s

Counts
134 → 134
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01792135
14941953
230671754
done50011749

prune638.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(* x (/ z (sqrt (- (* z z) (* t a)))))
1.4b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×times-frac
35×add-cube-cbrt *-un-lft-identity
25×associate-*r* sqrt-prod
20×add-exp-log add-cbrt-cube
12×pow1
7×prod-exp cbrt-unprod
6×sqrt-div associate-*l* associate-/r*
4×expm1-log1p-u pow-prod-down associate-/r/ log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-- associate-*r/ div-exp flip-- associate-/l* unswap-sqr
2×*-commutative div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 129
Calls
4 calls:
27.0ms
(/ z (sqrt (- (* z z) (* t a))))
59.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
90.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
33.0ms
(sqrt (- (* z z) (* t a)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ z (sqrt (- (* z z) (* t a))))
71.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
135.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
81.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
141 → 141
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01822260
14622085
221391870
done50001869

prune546.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ z (sqrt (fma z z (- (* a t)))))
2.1b
(* (* y x) (/ z (sqrt (fma z z (- (* a t))))))
23.4b
(sqrt (fma z z (- (* a t))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
24×sqrt-prod
22×associate-*r*
17×add-exp-log add-cbrt-cube
9×pow1
6×prod-exp associate-/r* cbrt-unprod
3×cbrt-undiv expm1-log1p-u div-exp pow-prod-down log1p-expm1-u associate-/l* add-log-exp
2×div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l* clear-num *-commutative
Counts
3 → 100
Calls
3 calls:
12.0ms
(/ z (sqrt (fma z z (- (* a t)))))
48.0ms
(* (* y x) (/ z (sqrt (fma z z (- (* a t))))))
3.0ms
(sqrt (fma z z (- (* a t))))

series284.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ z (sqrt (fma z z (- (* a t)))))
116.0ms
(* (* y x) (/ z (sqrt (fma z z (- (* a t))))))
94.0ms
(sqrt (fma z z (- (* a t))))

simplify1.6s

Counts
109 → 109
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461795
13801626
222311472
done50001471

prune499.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.9b

regimes766.0ms

Accuracy

84.9% (3.0b remaining)

Error of 6.6b against oracle of 3.6b and baseline of 23.2b

bsearch148.0ms

Steps
ItersRangePoint
8
8.123581701571455e+93
3.7790309889164093e+96
3.742227003601956e+96
10
-5.351987414543535e+167
-3.329626013588087e+149
-1.3146714561089265e+154

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12729
23029
done3029

end0.0ms

sample2.3s

Algorithm
intervals
Results
673.0ms8824×body80valid
306.0ms2892×body80nan