Details

Time bar (total: 26.2s)

sample99.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
5.0ms256×pre80true

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* prod-exp add-cbrt-cube
12×pow1
11×times-frac
8×associate-*r*
6×pow-exp
5×cbrt-unprod
4×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv associate-*l/ fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
1.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
10.0ms
(pow (* -2.0 (log u1)) 0.5)
28.0ms
(* (* 2.0 PI) u2)
27.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
659.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
358.0ms
(pow (* -2.0 (log u1)) 0.5)
46.0ms
(* (* 2.0 PI) u2)
1.2s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01971340
14471286
214391166
done50001147

prune572.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×div-exp
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×unpow-prod-down frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv associate-/l* sqr-pow
Counts
4 → 75
Calls
4 calls:
0.0ms
(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
11.0ms
(pow (* -2.0 (log u1)) 0.5)
24.0ms
(* (* 2.0 PI) u2)
20.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.1s

Counts
4 → 12
Calls
4 calls:
621.0ms
(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
434.0ms
(pow (* -2.0 (log u1)) 0.5)
61.0ms
(* (* 2.0 PI) u2)
1.0s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.7s

Counts
87 → 87
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01781100
13971053
21324930
done5001911

prune445.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.3b
(* (* 2.0 PI) (sqrt u2))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
23×add-cbrt-cube
21×pow1
15×prod-exp
12×associate-*r*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×pow-prod-down cbrt-unprod
6×sqrt-prod
5×div-exp
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-/r*
2×cbrt-undiv pow-to-exp pow-pow associate-*l* *-commutative
1×unpow-prod-down frac-2neg clear-num div-inv associate-/l* sqr-pow
Counts
4 → 94
Calls
4 calls:
11.0ms
(pow (* -2.0 (log u1)) 0.5)
100.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
20.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
36.0ms
(* (* 2.0 PI) (sqrt u2))

series1.8s

Counts
4 → 12
Calls
4 calls:
410.0ms
(pow (* -2.0 (log u1)) 0.5)
59.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
1.2s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
123.0ms
(* (* 2.0 PI) (sqrt u2))

simplify1.4s

Counts
106 → 106
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02031234
14981051
21661910
done5000894

prune538.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-sqr-sqrt
33×associate-*l*
30×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
20×times-frac
19×prod-exp
16×add-cbrt-cube
14×pow1
9×associate-*r*
7×cbrt-unprod
6×pow-exp unswap-sqr
5×sqrt-div pow-prod-down sqr-pow
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow div-inv
1×frac-times associate-*r/
Counts
4 → 120
Calls
4 calls:
7.0ms
(pow (* -2.0 (log u1)) 0.5)
101.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
39.0ms
(* (* 2.0 PI) u2)
31.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.8s

Counts
4 → 12
Calls
4 calls:
408.0ms
(pow (* -2.0 (log u1)) 0.5)
1.3s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
75.0ms
(* (* 2.0 PI) u2)
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify2.0s

Counts
132 → 132
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02081857
14501623
214281494
done50011485

prune759.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes770.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01922
12322
done2322

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s8000×body80valid
323.0ms8000×pre80true