Details

Time bar (total: 2.8m)

sample190.0ms

Algorithm
intervals
Results
60.0ms256×body80valid
14.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Calls
1 calls:
Slowest
1.1s
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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)

rewrite44.0ms

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
19.0ms
(* u2 (* 2 PI))
11.0ms
(pow (* -2 (log u1)) 0.5)
9.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
1.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (pow (* -2 (log u1)) 0.5) 6)
544.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
311.0ms
(pow (* -2 (log u1)) 0.5)
49.0ms
(* u2 (* 2 PI))

simplify12.6s

Counts
68 → 105
Calls
68 calls:
Slowest
867.0ms
(+ (* 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)
830.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
672.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
443.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) 1)
424.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (sqrt 6))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(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
(cos (* 2 (* u2 PI)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
66×add-exp-log
59×pow-exp
58×prod-exp
29×pow-to-exp
9×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l* pow-prod-down
2×pow-pow
1×unpow-prod-down *-commutative cbrt-unprod fma-udef cos-2 unswap-sqr sqr-pow
Counts
4 → 92
Calls
4 calls:
Slowest
54.0ms
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
25.0ms
(cos (* 2 (* u2 PI)))
6.0ms
(* u2 PI)
0.0ms
(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)

series2.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.9s
(pow (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0)) 0.5)
754.0ms
(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)
25.0ms
(cos (* 2 (* u2 PI)))
21.0ms
(* u2 PI)

simplify12.9s

Counts
58 → 104
Calls
58 calls:
Slowest
708.0ms
(pow (pow (pow (pow (pow (pow (pow (pow (pow (pow (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 3.0))) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 0.5)
689.0ms
(* (log (* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0))) 0.5)
562.0ms
(* (* (pow -2 1.0) (pow (- (log u1)) 1.0)) (pow -1 1.0))
493.0ms
(* (+ (+ (* (log -2) 1.0) (* (log (- (log u1))) 1.0)) (* (log -1) 1.0)) 0.5)
432.0ms
(* (+ (+ (* (log -2) 1.0) (* (log (- (log u1))) 1.0)) (* (log -1) 1.0)) 0.5)

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (log (/ (pow (* -2 (log u1)) 0.5) 6)))
0.3b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b
(* u2 (* 2 PI))
0.2b
(log (/ (pow (* -2 (log u1)) 0.5) 6))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
38×log-prod
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×add-exp-log
19×exp-sum
11×pow1 add-cbrt-cube
10×unpow-prod-down sqr-pow
8×div-exp
5×rem-log-exp prod-exp associate-/l*
4×expm1-log1p-u exp-prod pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* pow-prod-down cbrt-unprod div-inv
2×pow-to-exp log-div log-pow
1×cbrt-undiv clear-num frac-2neg exp-diff associate-*r* *-commutative rem-exp-log
Counts
4 → 133
Calls
4 calls:
Slowest
28.0ms
(* u2 (* 2 PI))
14.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
11.0ms
(log (/ (pow (* -2 (log u1)) 0.5) 6))
7.0ms
(exp (log (/ (pow (* -2 (log u1)) 0.5) 6)))

series3.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(log (/ (pow (* -2 (log u1)) 0.5) 6))
1.1s
(/ (pow (* -2 (log u1)) 0.5) 6)
995.0ms
(exp (log (/ (pow (* -2 (log u1)) 0.5) 6)))
72.0ms
(* u2 (* 2 PI))

simplify23.3s

Counts
111 → 145
Calls
111 calls:
Slowest
844.0ms
(log (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
721.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
683.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
631.0ms
(log (/ (pow (* -2 (log u1)) (/ 0.5 2)) 1))
512.0ms
(log (/ (pow (* -2 (log u1)) (/ 0.5 2)) (* (cbrt 6) (cbrt 6))))

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b
(* u2 (* 2 PI))
0.2b
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))
0.2b
(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
0.1b
(pow (* -2 (log u1)) (/ 0.5 2))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
209×times-frac
96×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
76×add-exp-log
43×unpow-prod-down sqr-pow
40×div-exp
24×associate-/r*
22×pow-exp
16×add-cbrt-cube
14×prod-exp
13×pow-unpow
12×pow1
11×pow-to-exp
9×div-inv
8×associate-/l*
4×expm1-log1p-u cbrt-undiv pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* cbrt-unprod
2×clear-num pow-pow frac-2neg
1×associate-*r* associate-/r/ *-commutative
Counts
4 → 247
Calls
4 calls:
Slowest
22.0ms
(* u2 (* 2 PI))
13.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))
10.0ms
(pow (* -2 (log u1)) (/ 0.5 2))
6.0ms
(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))

series2.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
1.1s
(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))
393.0ms
(pow (* -2 (log u1)) (/ 0.5 2))
36.0ms
(* u2 (* 2 PI))

simplify1.6m

Counts
316 → 259
Calls
316 calls:
Slowest
1.2s
(/ (pow -2 (/ 0.5 2)) (/ (sqrt 6) (pow (* -2 (log u1)) (/ (/ 0.5 2) 2))))
999.0ms
(/ (pow (* -2 (log u1)) (/ (/ 0.5 2) 2)) (/ 1 (sqrt (pow (* -2 (log u1)) (/ 0.5 2)))))
961.0ms
(/ (pow (* -2 (log u1)) (/ (/ 0.5 2) 2)) (/ 1 (pow -2 (/ 0.5 2))))
888.0ms
(/ (pow (log u1) (/ 0.5 2)) (/ 1 (pow (* -2 (log u1)) (/ 0.5 2))))
887.0ms
(/ 1 (/ 1 (pow -2 (/ 0.5 2))))

prune3.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes505.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.5s8000×body80valid
375.0ms8000×pre80true