Details

Time bar (total: 1.8m)

sample140.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
10.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Calls
1 calls:
Slowest
1.0s
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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
29.0ms
(* u2 (* 2 PI))
13.0ms
(pow (* -2 (log u1)) 0.5)
10.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
0.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
998.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
530.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
381.0ms
(pow (* -2 (log u1)) 0.5)
47.0ms
(* u2 (* 2 PI))

simplify12.0s

Counts
68 → 105
Calls
68 calls:
Slowest
855.0ms
(+ (* 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)
607.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
533.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
487.0ms
(* (* (* u2 u2) u2) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
428.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) 1)

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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
14.0ms
(* u2 (* 2 PI))
12.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
5.0ms
(pow (* -2 (log u1)) 0.5)
0.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
980.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
435.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
425.0ms
(pow (* -2 (log u1)) 0.5)
35.0ms
(* u2 (* 2 PI))

simplify12.8s

Counts
68 → 105
Calls
68 calls:
Slowest
886.0ms
(+ (* 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)
759.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (sqrt 6))
615.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
576.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
423.0ms
(* (* (* u2 u2) u2) (* (* (* 2 2) 2) (* (* PI PI) PI)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5) 0.5)
0.3b
(* u2 PI)
0.1b
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
0.0b
(* 1/6 (cos (* 2 (* u2 PI))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
59×pow-exp prod-exp
29×pow-to-exp
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-pow *-commutative cbrt-unprod unswap-sqr
1×unpow-prod-down fma-udef sqr-pow
Counts
4 → 102
Calls
4 calls:
Slowest
55.0ms
(* 1/6 (cos (* 2 (* u2 PI))))
49.0ms
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
21.0ms
(* u2 PI)
1.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5) 0.5)

series2.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
841.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5) 0.5)
78.0ms
(* 1/6 (cos (* 2 (* u2 PI))))
37.0ms
(* u2 PI)

simplify13.5s

Counts
67 → 114
Calls
67 calls:
Slowest
734.0ms
(* (log (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0))) 0.5)
665.0ms
(* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0))
476.0ms
(* (+ (+ (* (log -2) 1.0) (* (log (- (log u1))) 1.0)) (* (log -1) 1.0)) 0.5)
465.0ms
(* (+ (+ (* (log -2) 1.0) (* (log (- (log u1))) 1.0)) (* (log -1) 1.0)) 0.5)
457.0ms
(* (+ (+ (* (log -2) 1.0) (* (log (- (log u1))) 1.0)) (* (log -1) 1.0)) 0.5)

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 6 (pow (* -2 (log u1)) 0.5))
0.3b
(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))
0.3b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
72×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
52×add-exp-log
26×div-exp
24×associate-/r*
17×unpow-prod-down sqr-pow
16×add-cbrt-cube
13×pow1
10×pow-exp
8×prod-exp
6×div-inv associate-/l*
5×pow-to-exp rec-exp 1-exp
4×expm1-log1p-u cbrt-undiv pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-*l* cbrt-unprod
2×clear-num pow-pow frac-2neg
1×associate-*r* associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 194
Calls
4 calls:
Slowest
14.0ms
(* u2 (* 2 PI))
11.0ms
(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))
7.0ms
(pow (* -2 (log u1)) 0.5)
6.0ms
(/ 6 (pow (* -2 (log u1)) 0.5))

series3.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(/ 6 (pow (* -2 (log u1)) 0.5))
1.0s
(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))
414.0ms
(pow (* -2 (log u1)) 0.5)
47.0ms
(* u2 (* 2 PI))

simplify48.7s

Counts
218 → 206
Calls
218 calls:
Slowest
1.0s
(/ (sqrt 1) (/ (* (cbrt 6) (cbrt 6)) (pow (* -2 (log u1)) (/ 0.5 2))))
793.0ms
(* 6 (pow (/ 1 (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5))
782.0ms
(/ 1 (/ 1 (pow (* -2 (log u1)) 0.5)))
774.0ms
(/ 1 (/ 1 (pow (* -2 (log u1)) (/ 0.5 2))))
624.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))

prune2.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes359.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.1s8000×body80valid
694.0ms8000×pre80true