Details

Time bar (total: 36.2s)

sample172.0ms

Algorithm
intervals
Results
59.0ms256×body80valid
13.0ms256×pre80true

simplify772.0ms

Calls
1 calls:
Slowest
772.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))
0.3b
(* u2 (* 2 PI))
0.2b
(pow (* -2 (log u1)) 0.5)
0.1b
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity associate-*r* add-exp-log add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×unpow-prod-down *-commutative
1×pow-to-exp pow-pow pow-exp fma-udef
Calls
4 calls:
Slowest
9.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
3.0ms
(pow (* -2 (log u1)) 0.5)
2.0ms
(* u2 (* 2 PI))
0.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)

series1.6s

Calls
4 calls:
Slowest
931.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
329.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
285.0ms
(pow (* -2 (log u1)) 0.5)
64.0ms
(* u2 (* 2 PI))

simplify1.2s

Calls
19 calls:
Slowest
290.0ms
(- (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
206.0ms
(pow (* -2 (- (log -1) (log (/ -1 u1)))) 0.5)
202.0ms
(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
125.0ms
(+ (* 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)
108.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))

prune930.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))
0.3b
(* u2 (* 2 PI))
0.2b
(exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.2b
(log (* 1/6 (pow (* -2 (log u1)) 0.5)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
5×associate-*r* add-exp-log
4×expm1-log1p-u exp-prod add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×log-prod log-pow *-commutative
1×unpow-prod-down rem-log-exp exp-sum rem-exp-log
Calls
4 calls:
Slowest
11.0ms
(exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))
10.0ms
(log (* 1/6 (pow (* -2 (log u1)) 0.5)))
6.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
2.0ms
(* u2 (* 2 PI))

series2.9s

Calls
4 calls:
Slowest
983.0ms
(log (* 1/6 (pow (* -2 (log u1)) 0.5)))
941.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
909.0ms
(exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))
73.0ms
(* u2 (* 2 PI))

simplify1.3s

Calls
23 calls:
Slowest
281.0ms
(log (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
164.0ms
(log (* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5)))
138.0ms
(log (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))
133.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
131.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))

prune986.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.5b
(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
0.4b
(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
0.3b
(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
66×prod-exp
34×pow-to-exp pow-exp
12×associate-*r*
11×add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×associate-*l*
4×expm1-log1p-u pow1 cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-down pow-prod-down *-commutative pow-prod-up
2×cbrt-prod pow2 pow3
1×pow-plus pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
29.0ms
(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
28.0ms
(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
19.0ms
(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
11.0ms
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series3.6s

Calls
4 calls:
Slowest
946.0ms
(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
896.0ms
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
883.0ms
(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
826.0ms
(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

simplify12.5s

Calls
80 calls:
Slowest
464.0ms
(+ (+ (log (pow (* -2 (log u1)) 0.5)) (log (pow (* -2 (log u1)) 0.5))) (* (log (* -2 (log u1))) 0.5))
441.0ms
(+ (+ (* (log (* -2 (log u1))) 0.5) (log (pow (* -2 (log u1)) 0.5))) (* (log (* -2 (log u1))) 0.5))
437.0ms
(+ (+ (log (pow (* -2 (log u1)) 0.5)) (* (log (* -2 (log u1))) 0.5)) (* (log (* -2 (log u1))) 0.5))
427.0ms
(+ (+ (* (log (* -2 (log u1))) 0.5) (log (pow (* -2 (log u1)) 0.5))) (log (pow (* -2 (log u1)) 0.5)))
424.0ms
(+ (+ (log (pow (* -2 (log u1)) 0.5)) (log (pow (* -2 (log u1)) 0.5))) (* (log (* -2 (log u1))) 0.5))

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))
0.3b
(* u2 (* 2 PI))
0.2b
(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity associate-*r* add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×log1p-udef expm1-log1p unpow-prod-down log1p-expm1 expm1-udef
Calls
4 calls:
Slowest
3.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
1.0ms
(* u2 (* 2 PI))
0.0ms
(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))
0.0ms
(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))

series2.8s

Calls
4 calls:
Slowest
1.0s
(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))
1.0s
(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))
773.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
53.0ms
(* u2 (* 2 PI))

simplify722.0ms

Calls
17 calls:
Slowest
142.0ms
(log (+ (* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5)) 1))
140.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
103.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
84.0ms
(log (+ (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)) 1))
64.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))

prune931.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes407.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.2s8000×body80valid
823.0ms8000×pre80true