Details

Time bar (total: 17.0s)

sample54.0ms

Algorithm
intervals
Results
20.0ms279×body80valid
5.0ms90×body80nan

simplify147.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize25.0ms

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)))

rewrite114.0ms

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:
12.0ms
(- (* z z) (* t a))
36.0ms
(* (* x y) z)
40.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.0ms
(sqrt (- (* z z) (* t a)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
51.0ms
(* (* x y) z)
143.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

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)))

rewrite112.0ms

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:
45.0ms
(/ (sqrt (- (* z z) (* t a))) z)
18.0ms
(- (* z z) (* t a))
27.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (sqrt (- (* z z) (* t a))) z)
45.0ms
(- (* z z) (* t a))
126.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
95.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
154 → 154
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune691.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize35.0ms

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)))

rewrite216.0ms

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:
28.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
35.0ms
(- (pow z 2) (* a t))
100.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
37.0ms
(sqrt (- (pow z 2) (* a t)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
59.0ms
(- (pow z 2) (* a t))
153.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
86.0ms
(sqrt (- (pow z 2) (* a t)))

simplify1.9s

Counts
148 → 148
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01942307
14712076
216211872
done50011859

prune666.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize19.0ms

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)))

rewrite174.0ms

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:
31.0ms
(- (pow z 2) (* a t))
65.0ms
(* x (* y (/ z (sqrt (- (pow z 2) (* a t))))))
55.0ms
(* y (/ z (sqrt (- (pow z 2) (* a t)))))
18.0ms
(sqrt (- (pow z 2) (* a t)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (pow z 2) (* a t))
148.0ms
(* x (* y (/ z (sqrt (- (pow z 2) (* a t))))))
100.0ms
(* y (/ z (sqrt (- (pow z 2) (* a t)))))
106.0ms
(sqrt (- (pow z 2) (* a t)))

simplify3.8s

Counts
128 → 128
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01891852
14481696
212581490
347501459
done50001459

prune543.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes578.0ms

Accuracy

85.5% (2.8b remaining)

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

bsearch131.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
12829
23129
done3129

end0.0ms

sample2.3s

Algorithm
intervals
Results
764.0ms8818×body80valid
221.0ms3008×body80nan