Details

Time bar (total: 16.1s)

sample57.0ms

Algorithm
intervals
Results
24.0ms279×body80valid
7.0ms90×body80nan

simplify160.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.8b
(* (* x y) z)
10.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite146.0ms

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:
18.0ms
(- (* z z) (* t a))
46.0ms
(* (* x y) z)
59.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms
(sqrt (- (* z z) (* t a)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
36.0ms
(* (* x y) z)
177.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
115.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune422.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
2.5b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
13.0ms
(- (* z z) (* t a))
35.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
20.0ms
(sqrt (- (* z z) (* t a)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (sqrt (- (* z z) (* t a))) z)
41.0ms
(- (* z z) (* t a))
166.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
154 → 154
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune606.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (pow z 2) (* a t))))
0.6b
(- (pow z 2) (* a t))
2.5b
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
28.2b
(sqrt (- (pow z 2) (* a t)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×add-cube-cbrt *-un-lft-identity
36×times-frac
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
8×fma-neg prod-diff
6×unpow-prod-down 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 unpow2 sqr-pow
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 136
Calls
4 calls:
20.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
24.0ms
(- (pow z 2) (* a t))
74.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
21.0ms
(sqrt (- (pow z 2) (* a t)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
67.0ms
(- (pow z 2) (* a t))
131.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
94.0ms
(sqrt (- (pow z 2) (* a t)))

simplify1.8s

Counts
148 → 148
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01942307
14712076
216211872
done50011859

prune685.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow z 2) (* a t))
1.1b
(* x (* y (/ z (sqrt (- (pow z 2) (* a t))))))
2.1b
(* y (/ z (sqrt (- (pow z 2) (* a t)))))
28.2b
(sqrt (- (pow z 2) (* a t)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×associate-*r*
24×add-cube-cbrt *-un-lft-identity
20×times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
8×fma-neg prod-diff
7×prod-exp cbrt-unprod
6×unpow-prod-down 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 unpow2 sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 116
Calls
4 calls:
33.0ms
(- (pow z 2) (* a t))
70.0ms
(* x (* y (/ z (sqrt (- (pow z 2) (* a t))))))
71.0ms
(* y (/ z (sqrt (- (pow z 2) (* a t)))))
33.0ms
(sqrt (- (pow z 2) (* a t)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (pow z 2) (* a t))
132.0ms
(* x (* y (/ z (sqrt (- (pow z 2) (* a t))))))
87.0ms
(* y (/ z (sqrt (- (pow z 2) (* a t)))))
116.0ms
(sqrt (- (pow z 2) (* a t)))

simplify3.6s

Counts
128 → 128
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
01891852
14481696
212581490
347501459
done50001459

prune414.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes549.0ms

Accuracy

85.5% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 22.5b

bsearch137.0ms

Steps
ItersRangePoint
10
4.3064310246787576e+110
1.1096282980114098e+126
2.811098440010323e+123
9
-5.269798588618117e+155
-1.769171722317776e+149
-1.3870375139541522e+152

simplify19.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
12829
23129
done3129

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8818×body80valid
299.0ms3008×body80nan