Details

Time bar (total: 27.3s)

sample111.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
5.0ms256×pre80true

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
01819
13518
27218
315918
448318
5314018
done500118

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b
(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))

rewrite62.0ms

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)
26.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
630.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
421.0ms
(pow (* -2.0 (log u1)) 0.5)
55.0ms
(* (* 2.0 PI) u2)
978.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01971340
14941292
223001170
done50001151

prune525.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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 log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
0.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
19.0ms
(* (* 2.0 PI) u2)
19.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.2s

Counts
4 → 12
Calls
4 calls:
705.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
399.0ms
(pow (* -2.0 (log u1)) 0.5)
63.0ms
(* (* 2.0 PI) u2)
1.0s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify1.4s

Counts
101 → 101
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01891291
14271249
217991152
done50001131

prune685.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.0b
(expm1 (fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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 add-log-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv expm1-log1p frac-2neg associate-*l* clear-num *-commutative div-inv expm1-udef
Counts
4 → 90
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
36.0ms
(* (* 2.0 PI) u2)
19.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.0ms
(expm1 (fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5))

series2.6s

Counts
4 → 12
Calls
4 calls:
451.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
1.2s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
852.0ms
(expm1 (fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5))

simplify1.7s

Counts
102 → 102
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01971330
14511281
218761176
done50001165

prune632.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)
1.0b
(expm1 (fma (* 1.0 (* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)) (cos (* (* 2.0 PI) u2)) 0.5))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
163×add-exp-log
150×prod-exp
118×pow-exp
58×pow-to-exp
11×add-sqr-sqrt add-cbrt-cube
10×pow1
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
5×pow-prod-down log1p-expm1-u
4×expm1-log1p-u cbrt-unprod add-log-exp
3×pow-unpow sqr-pow
2×unpow-prod-down pow-pow *-commutative unswap-sqr
1×expm1-log1p expm1-udef
Counts
4 → 133
Calls
4 calls:
51.0ms
(pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5)
20.0ms
(* (* 2.0 PI) u2)
79.0ms
(* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)
1.0ms
(expm1 (fma (* 1.0 (* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)) (cos (* (* 2.0 PI) u2)) 0.5))

series4.6s

Counts
4 → 12
Calls
4 calls:
1.9s
(pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5)
36.0ms
(* (* 2.0 PI) u2)
1.7s
(* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)
1.0s
(expm1 (fma (* 1.0 (* (pow (* (pow -1 1.0) (* (pow (- (log u1)) 1.0) (pow -2.0 1.0))) 0.5) 0.16666666666666666)) (cos (* (* 2.0 PI) u2)) 0.5))

simplify1.8s

Counts
145 → 145
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02482865
16462633
223342411
done50002367

prune743.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes499.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01920
12320
done2320

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.0s8000×body80valid
261.0ms8000×pre80true