Details

Time bar (total: 1.1m)

sample166.0ms

Algorithm
intervals
Results
40.0ms256×body80valid
10.0ms256×pre80true

simplify579.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
578.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)
0.1b
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
12×pow1
11×add-cbrt-cube
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* associate-*l* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
25.0ms
(* u2 (* 2 PI))
25.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
10.0ms
(pow (* -2 (log u1)) 0.5)
1.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
923.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
486.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
324.0ms
(pow (* -2 (log u1)) 0.5)
39.0ms
(* u2 (* 2 PI))

simplify12.0s

Counts
68 → 105
Calls
68 calls:
Slowest
815.0ms
(+ (* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 0.5)
638.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
618.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
440.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) 1)
424.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (sqrt 6))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
0.3b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
12×pow1
11×add-cbrt-cube
5×unpow-prod-down prod-exp log1p-expm1-u associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp insert-posit16 add-log-exp
3×pow-unpow associate-/r* associate-*l* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv expm1-log1p clear-num frac-2neg associate-*r* *-commutative div-inv expm1-udef
Counts
4 → 94
Calls
4 calls:
Slowest
21.0ms
(* u2 (* 2 PI))
13.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
5.0ms
(pow (* -2 (log u1)) 0.5)
0.0ms
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))

series3.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(/ (pow (* -2 (log u1)) 0.5) 6)
1.1s
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
397.0ms
(pow (* -2 (log u1)) 0.5)
59.0ms
(* u2 (* 2 PI))

simplify12.5s

Counts
69 → 106
Calls
69 calls:
Slowest
779.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
773.0ms
(- (exp (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 1)
525.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
445.0ms
(* (* (* u2 u2) u2) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
436.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (sqrt 6))

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
1.0b
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
1.0b
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
0.5b
(cbrt (expm1 (/ (pow (* -2 (log u1)) 0.5) 6)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
7×log1p-expm1-u
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod expm1-log1p expm1-udef
1×pow1/3
Counts
4 → 50
Calls
4 calls:
Slowest
1.0ms
(cbrt (expm1 (/ (pow (* -2 (log u1)) 0.5) 6)))
0.0ms
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
0.0ms
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
0.0ms
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))

series4.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(cbrt (expm1 (/ (pow (* -2 (log u1)) 0.5) 6)))
1.2s
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
1.2s
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))
1.1s
(expm1 (/ (pow (* -2 (log u1)) 0.5) 6))

simplify7.7s

Counts
18 → 62
Calls
18 calls:
Slowest
854.0ms
(pow (- (exp (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 1) 1/3)
822.0ms
(- (exp (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 1)
822.0ms
(- (exp (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 1)
803.0ms
(- (exp (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 1)
712.0ms
(- (exp (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) 1)

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6))))
0.4b
(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))
0.3b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b
(* u2 (* 2 PI))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
15×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
11×add-cbrt-cube
9×pow1
5×log1p-expm1-u associate-/l*
4×expm1-log1p-u unpow-prod-down div-exp prod-exp insert-posit16 add-log-exp sqr-pow
3×associate-/r* associate-*l* pow-prod-down cbrt-unprod
2×expm1-log1p pow-exp expm1-udef
1×pow-to-exp cbrt-undiv clear-num frac-2neg associate-*r* *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
Slowest
12.0ms
(* u2 (* 2 PI))
7.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
0.0ms
(expm1 (expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6))))
0.0ms
(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

series3.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(expm1 (expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6))))
1.2s
(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))
1.1s
(/ (pow (* -2 (log u1)) 0.5) 6)
48.0ms
(* u2 (* 2 PI))

simplify13.1s

Counts
63 → 98
Calls
63 calls:
Slowest
871.0ms
(- (exp (* 1/6 (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5))) 1)
715.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
714.0ms
(* 1/6 (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5))
578.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
513.0ms
(* (* (* u2 u2) u2) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes329.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s8000×body80valid
391.0ms8000×pre80true