Details

Time bar (total: 31.3s)

sample145.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
7.0ms256×pre80true

simplify4.2s

Counts
1 → 1
Iterations
IterNodes
done5000
51408
4387
3148
272
135
018

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* PI u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
25×add-sqr-sqrt
16×associate-*l*
15×*-un-lft-identity add-cube-cbrt
12×prod-exp
11×times-frac add-cbrt-cube
9×pow1
8×associate-*r*
6×pow-exp
5×unswap-sqr
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp pow-unpow cbrt-unprod
2×unpow-prod-down pow-pow pow-prod-down *-commutative
1×cbrt-undiv associate-*l/ fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
0.0ms
(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
5.0ms
(pow (* -2.0 (log u1)) 0.5)
5.0ms
(* PI u2)
39.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
562.0ms
(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
463.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* PI u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify3.6s

Counts
104 → 104
Iterations
IterNodes
done5000
34988
21370
1468
0194

prune868.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* PI u2)
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
11×add-sqr-sqrt add-cbrt-cube
9×pow1 *-un-lft-identity add-cube-cbrt
7×prod-exp
5×div-exp
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* times-frac associate-*r* associate-*l*
2×pow-to-exp cbrt-undiv pow-pow pow-prod-down cbrt-unprod
1×clear-num unpow-prod-down frac-2neg *-commutative fma-udef div-inv associate-/l* unswap-sqr sqr-pow
Counts
4 → 75
Calls
4 calls:
0.0ms
(fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)
5.0ms
(pow (* -2.0 (log u1)) 0.5)
5.0ms
(* PI u2)
11.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
575.0ms
(fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)
398.0ms
(pow (* -2.0 (log u1)) 0.5)
26.0ms
(* PI u2)
1.0s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.7s

Counts
87 → 87
Iterations
IterNodes
done5000
21298
1436
0175

prune766.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)))
0.2b
(* PI u2)
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
1.0b
(expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
11×add-cbrt-cube
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 prod-exp
5×div-exp log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-/r* times-frac associate-*r* associate-*l*
2×cbrt-undiv pow-exp cbrt-unprod
1×pow-to-exp log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 *-commutative div-inv associate-/l* expm1-udef unswap-sqr
Counts
4 → 68
Calls
4 calls:
0.0ms
(log1p (expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)))
6.0ms
(* PI u2)
28.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.0ms
(expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5))

series2.5s

Counts
4 → 12
Calls
4 calls:
646.0ms
(log1p (expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5)))
48.0ms
(* PI u2)
1.1s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
740.0ms
(expm1 (fma (cos (* 2.0 (* PI u2))) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 0.5))

simplify1.9s

Counts
80 → 80
Iterations
IterNodes
done5000
21218
1414
0176

prune663.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b
(cos (* (* 2.0 PI) u2))
0.1b
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
0.2b
(fma (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5) 0.5)
0.2b
(* (* 2.0 PI) u2)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
60×prod-exp
59×pow-exp
29×pow-to-exp
10×pow1
9×add-cbrt-cube
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* cbrt-unprod
2×pow-pow
1×unpow-prod-down associate-*l* *-commutative fma-udef sqr-pow
Counts
4 → 87
Calls
4 calls:
19.0ms
(cos (* (* 2.0 PI) u2))
33.0ms
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
0.0ms
(fma (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5) 0.5)
27.0ms
(* (* 2.0 PI) u2)

series2.8s

Counts
4 → 12
Calls
4 calls:
56.0ms
(cos (* (* 2.0 PI) u2))
1.9s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
830.0ms
(fma (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5) 0.5)
67.0ms
(* (* 2.0 PI) u2)

simplify4.0s

Counts
99 → 99
Iterations
IterNodes
done5000
21540
1550
0219

prune710.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes904.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done23
123
019

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s8000×body80valid
281.0ms8000×pre80true