Details

Time bar (total: 18.1s)

sample338.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
5.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* prod-exp add-cbrt-cube
12×pow1
11×times-frac
8×associate-*r*
6×pow-exp
5×cbrt-unprod
4×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv associate-*l/ fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
0.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
29.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts
4 → 12
Calls
4 calls:
453.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
257.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
679.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.1s

Counts
104 → 104
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01971340
14471286
214391166
done50001147

prune357.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-sqr-sqrt
33×associate-*l*
30×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
20×times-frac
19×prod-exp
16×add-cbrt-cube
14×pow1
9×associate-*r*
7×cbrt-unprod
6×pow-exp unswap-sqr
5×sqrt-div pow-prod-down sqr-pow
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow div-inv
1×frac-times associate-*r/
Counts
4 → 120
Calls
4 calls:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
60.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
17.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts
4 → 12
Calls
4 calls:
261.0ms
(pow (* -2.0 (log u1)) 0.5)
715.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
32.0ms
(* (* 2.0 PI) u2)
701.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.2s

Counts
132 → 132
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02081857
14501623
214281494
done50011485

prune485.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0)
0.3b
(* (* 2.0 PI) u2)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×div-exp
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×unpow-prod-down frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv associate-/l* sqr-pow
Counts
4 → 75
Calls
4 calls:
0.0ms
(fma (/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0)
17.0ms
(* (* 2.0 PI) u2)

series1.4s

Counts
4 → 12
Calls
4 calls:
455.0ms
(fma (/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
262.0ms
(pow (* -2.0 (log u1)) 0.5)
680.0ms
(/ (* (pow (* -2.0 (log u1)) 0.5) 1.0) 6.0)
32.0ms
(* (* 2.0 PI) u2)

simplify1.1s

Counts
87 → 87
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01781095
13981048
21345931
done5000906

prune274.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0b
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* prod-exp add-cbrt-cube
12×pow1
11×times-frac
8×associate-*r*
6×pow-exp
5×cbrt-unprod log1p-expm1-u
4×expm1-log1p-u div-exp pow-prod-down add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv expm1-log1p associate-*l/ div-inv expm1-udef
Counts
4 → 93
Calls
4 calls:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
16.0ms
(* (* 2.0 PI) u2)
23.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.0ms
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

series1.7s

Counts
4 → 12
Calls
4 calls:
260.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
682.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
718.0ms
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify2.4s

Counts
105 → 105
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01851218
14131159
212971053
346891044
done50001044

prune347.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes361.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
12118
done2118

end0.0ms

sample1.1s

Algorithm
intervals
Results
714.0ms8000×body80valid
124.0ms8000×pre80true