Details

Time bar (total: 35.6s)

sample202.0ms

Algorithm
intervals
Results
63.0ms256×body80valid
19.0ms256×pre80true

simplify209.0ms

Calls
1 calls:
Slowest
208.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))
0.2b
(* 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)

rewrite12.0ms

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
7.0ms
(* 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)

series1.7s

Calls
4 calls:
Slowest
926.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
436.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
307.0ms
(pow (* -2 (log u1)) 0.5)
60.0ms
(* u2 (* 2 PI))

simplify1.2s

Calls
19 calls:
Slowest
287.0ms
(- (+ 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))))
192.0ms
(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
176.0ms
(pow (* -2 (- (log -1) (log (/ -1 u1)))) 0.5)
139.0ms
(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
99.0ms
(+ (* 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)

prune762.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.2b
(* u2 PI)
0.1b
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
0.0b
(* 1/6 (cos (* 2 (* u2 PI))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
27×prod-exp
21×pow-exp
18×pow-to-exp
5×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×pow-pow pow-prod-down *-commutative
1×unpow-prod-down fma-udef
Calls
4 calls:
Slowest
12.0ms
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
5.0ms
(* 1/6 (cos (* 2 (* u2 PI))))
0.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.0ms
(* u2 PI)

series2.1s

Calls
4 calls:
Slowest
1.5s
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
586.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
33.0ms
(* u2 PI)
29.0ms
(* 1/6 (cos (* 2 (* u2 PI))))

simplify7.6s

Calls
34 calls:
Slowest
459.0ms
(* (+ (log (pow (- (log u1)) 1.0)) (+ (* (log -2) 1.0) (* (log -1) 1.0))) 0.5)
448.0ms
(* (+ (log (pow (- (log u1)) 1.0)) (+ (log (pow -2 1.0)) (* (log -1) 1.0))) 0.5)
440.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (* (log -2) 1.0) (log (pow -1 1.0)))) 0.5)
439.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (log (pow -2 1.0)) (* (log -1) 1.0))) 0.5)
435.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (* (log -2) 1.0) (* (log -1) 1.0))) 0.5)

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize2.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.2b
(* u2 PI)
0.1b
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
0.0b
(* 1/6 (cos (* 2 (* u2 PI))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
27×prod-exp
21×pow-exp
18×pow-to-exp
5×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×pow-pow pow-prod-down *-commutative
1×unpow-prod-down fma-udef
Calls
4 calls:
Slowest
17.0ms
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
11.0ms
(* 1/6 (cos (* 2 (* u2 PI))))
0.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.0ms
(* u2 PI)

series2.3s

Calls
4 calls:
Slowest
1.5s
(pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5)
660.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
50.0ms
(* u2 PI)
30.0ms
(* 1/6 (cos (* 2 (* u2 PI))))

simplify8.1s

Calls
34 calls:
Slowest
765.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (* (log -2) 1.0) (* (log -1) 1.0))) 0.5)
506.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (log (pow -2 1.0)) (* (log -1) 1.0))) 0.5)
492.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (* (log -2) 1.0) (log (pow -1 1.0)))) 0.5)
427.0ms
(* (+ (* (log (- (log u1))) 1.0) (+ (log (pow -2 1.0)) (log (pow -1 1.0)))) 0.5)
409.0ms
(* (+ (log (pow (- (log u1)) 1.0)) (+ (* (log -2) 1.0) (log (pow -1 1.0)))) 0.5)

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.3b
(exp (log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)))
0.3b
(log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5))
0.2b
(* u2 PI)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 log-prod
5×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
1×rem-log-exp *-commutative fma-udef rem-exp-log
Calls
4 calls:
Slowest
3.0ms
(exp (log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)))
1.0ms
(log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5))
0.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
0.0ms
(* u2 PI)

series1.9s

Calls
4 calls:
Slowest
675.0ms
(log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5))
613.0ms
(fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)
556.0ms
(exp (log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)))
44.0ms
(* u2 PI)

simplify2.8s

Calls
24 calls:
Slowest
343.0ms
(+ (* 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))) (log (- 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))))
210.0ms
(- 0.5 (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))))
199.0ms
(- (+ (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) 0.5) (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))
186.0ms
(- (+ (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) 0.5) (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))
186.0ms
(exp (* (cbrt (log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5))) (cbrt (log (fma (* 1/6 (cos (* 2 (* u2 PI)))) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) 0.5)))))

prune975.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes390.0ms

Accuracy

0% (0.4b remaining)

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

bsearch9.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.3s8000×body80valid
389.0ms8000×pre80true