Details

Time bar (total: 30.7s)

sample370.0ms

Algorithm
intervals
Results
48.0ms256×body80valid
12.0ms256×pre80true

simplify4.1s

Counts
1 → 1

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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
27.0ms
(* u2 (* 2 PI))
17.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
11.0ms
(pow (* -2 (log u1)) 0.5)
1.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (pow (* -2 (log u1)) 0.5) 6)
567.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
342.0ms
(pow (* -2 (log u1)) 0.5)
37.0ms
(* u2 (* 2 PI))

simplify1.9s

Counts
105 → 105

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5))
0.3b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.2b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)

rewrite35.0ms

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 log1p-expm1-u associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp insert-posit16 add-log-exp
3×pow-unpow associate-/r* associate-*l* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv expm1-log1p clear-num frac-2neg associate-*r* *-commutative div-inv expm1-udef
Counts
4 → 94
Calls
4 calls:
Slowest
14.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
13.0ms
(* u2 (* 2 PI))
5.0ms
(pow (* -2 (log u1)) 0.5)
0.0ms
(expm1 (fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
959.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
620.0ms
(expm1 (fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5))
415.0ms
(pow (* -2 (log u1)) 0.5)
66.0ms
(* u2 (* 2 PI))

simplify1.7s

Counts
106 → 106

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5))
0.3b
(fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5)
0.2b
(* (* PI 2) u2)
0.1b
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
16×pow-exp
12×prod-exp
10×pow1
9×add-cbrt-cube
7×pow-to-exp
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u pow-prod-down insert-posit16 add-log-exp
3×pow-unpow associate-*r* cbrt-unprod
2×pow-pow
1×expm1-log1p unpow-prod-down associate-*l* *-commutative fma-udef expm1-udef sqr-pow
Counts
4 → 72
Calls
4 calls:
Slowest
36.0ms
(* (* PI 2) u2)
25.0ms
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)
1.0ms
(expm1 (fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5))
0.0ms
(fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5)

series3.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)
926.0ms
(expm1 (fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5))
740.0ms
(fma (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* (* PI 2) u2))) 0.5)
42.0ms
(* (* PI 2) u2)

simplify2.6s

Counts
84 → 84

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))
1.0b
(expm1 (log1p (expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))))
0.3b
(fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5)
0.2b
(* u2 PI)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×expm1-log1p expm1-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 56
Calls
4 calls:
Slowest
13.0ms
(* u2 PI)
0.0ms
(expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))
0.0ms
(fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5)
0.0ms
(expm1 (log1p (expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))))

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
804.0ms
(expm1 (log1p (expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))))
793.0ms
(expm1 (fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5))
655.0ms
(fma (* (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5) (cos (* 2 (* u2 PI)))) 1/6 0.5)
34.0ms
(* u2 PI)

simplify1.1s

Counts
68 → 68

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes660.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.3s8000×body80valid
369.0ms8000×pre80true