Details

Time bar (total: 24.0s)

sample125.0ms

Algorithm
intervals
Results
44.0ms256×body80valid
39.0ms256×pre80true

simplify199.0ms

Calls
1 calls:
Slowest
199.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

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
4.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
1.0ms
(pow (* -2 (log u1)) 0.5)
1.0ms
(* u2 (* 2 PI))
0.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)

series2.3s

Calls
4 calls:
Slowest
1.3s
(* 1/6 (pow (* -2 (log u1)) 0.5))
530.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
356.0ms
(pow (* -2 (log u1)) 0.5)
40.0ms
(* u2 (* 2 PI))

simplify1.1s

Calls
19 calls:
Slowest
298.0ms
(- (+ 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
(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
181.0ms
(pow (* -2 (- (log -1) (log (/ -1 u1)))) 0.5)
115.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
82.0ms
(+ (* 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)

prune903.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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
8.0ms
(exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))
7.0ms
(log (* 1/6 (pow (* -2 (log u1)) 0.5)))
6.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
1.0ms
(* u2 (* 2 PI))

series3.1s

Calls
4 calls:
Slowest
1.1s
(log (* 1/6 (pow (* -2 (log u1)) 0.5)))
1.0s
(* 1/6 (pow (* -2 (log u1)) 0.5))
919.0ms
(exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))
46.0ms
(* u2 (* 2 PI))

simplify1.2s

Calls
23 calls:
Slowest
200.0ms
(log (* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
168.0ms
(log (* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5)))
138.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
106.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
104.0ms
(exp (* (cbrt (log (* 1/6 (pow (* -2 (log u1)) 0.5)))) (cbrt (log (* 1/6 (pow (* -2 (log u1)) 0.5))))))

prune932.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 log-prod
5×associate-*r* add-exp-log
4×expm1-log1p-u exp-prod add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum
2×log-pow *-commutative
1×unpow-prod-down rem-log-exp rem-exp-log
Calls
4 calls:
Slowest
3.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
2.0ms
(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
1.0ms
(* u2 (* 2 PI))
1.0ms
(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))

series2.2s

Calls
4 calls:
Slowest
1.0s
(* 1/6 (pow (* -2 (log u1)) 0.5))
588.0ms
(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
536.0ms
(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
41.0ms
(* u2 (* 2 PI))

simplify2.1s

Calls
28 calls:
Slowest
376.0ms
(- (log (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))) (* 1/3 (* (/ (* (pow u2 2) (pow PI 2)) (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
351.0ms
(- (+ 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))))
209.0ms
(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
198.0ms
(log (+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5))
112.0ms
(+ (* 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)

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×associate-*r* log1p-expm1-u add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16
3×exp-prod
2×*-commutative rem-exp-log
1×log1p-udef expm1-log1p unpow-prod-down expm1-udef
Calls
4 calls:
Slowest
6.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
2.0ms
(exp (log1p (expm1 (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))))
1.0ms
(expm1 (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
1.0ms
(* u2 (* 2 PI))

series2.4s

Calls
4 calls:
Slowest
1.0s
(* 1/6 (pow (* -2 (log u1)) 0.5))
663.0ms
(exp (log1p (expm1 (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))))
658.0ms
(expm1 (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
53.0ms
(* u2 (* 2 PI))

simplify1.8s

Calls
21 calls:
Slowest
344.0ms
(- (+ 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))))
331.0ms
(- (* 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))) 0.5))
174.0ms
(- (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
165.0ms
(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
119.0ms
(- (* 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)

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes597.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.9s8000×body80valid
837.0ms8000×pre80true