Details

Time bar (total: 46.2s)

sample241.0ms

Algorithm
intervals
Results
59.0ms256×body80valid
9.0ms256×pre80true

simplify6.8s

Counts
1 → 1
Iterations
IterNodes
done5002
51427
4387
3148
272
135
018

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* u2 (* PI 2.0))
0.4b
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
12×pow1
11×add-sqr-sqrt add-cbrt-cube
9×prod-exp
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow sqr-pow
2×pow-to-exp unpow-prod-down pow-pow *-commutative unswap-sqr
1×fma-udef
Counts
4 → 74
Calls
4 calls:
85.0ms
(* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))
13.0ms
(pow (* -2.0 (log u1)) 0.5)
33.0ms
(* u2 (* PI 2.0))
4.0ms
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

series2.1s

Counts
4 → 12
Calls
4 calls:
739.0ms
(* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))
514.0ms
(pow (* -2.0 (log u1)) 0.5)
78.0ms
(* u2 (* PI 2.0))
767.0ms
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

simplify6.0s

Counts
86 → 86
Iterations
IterNodes
done5000
34574
21195
1407
0164

prune926.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
783×add-exp-log
710×prod-exp
172×pow-exp
86×pow-to-exp
57×add-cbrt-cube
39×cbrt-unprod
30×pow1
7×pow-plus pow-prod-up
4×add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity pow-prod-down log1p-expm1-u add-log-exp
3×pow2 pow-sqr
2×associate-*r* associate-*l* pow3 *-commutative
1×cbrt-prod pow1/3 swap-sqr rem-cbrt-cube fma-udef
Counts
4 → 232
Calls
4 calls:
719.0ms
(* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))
0.0ms
(fma (/ 1.0 6.0) (cbrt (* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))) 0.5)
275.0ms
(* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))
503.0ms
(cbrt (* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))))

series2.9s

Counts
4 → 12
Calls
4 calls:
769.0ms
(* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))
697.0ms
(fma (/ 1.0 6.0) (cbrt (* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))) 0.5)
657.0ms
(* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)))
772.0ms
(cbrt (* (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5))))

simplify4.9s

Counts
244 → 244
Iterations
IterNodes
done5000
21860
1675
0263

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5))
0.3b
(* u2 (* PI 2.0))
0.4b
(exp (log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)))
0.4b
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×log-prod
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×associate-*l* exp-sum pow-prod-down prod-exp cbrt-unprod
2×log-pow
1×rem-log-exp associate-*r* *-commutative fma-udef rem-exp-log
Counts
4 → 61
Calls
4 calls:
3.0ms
(log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5))
35.0ms
(* u2 (* PI 2.0))
20.0ms
(exp (log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)))
1.0ms
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

series2.4s

Counts
4 → 12
Calls
4 calls:
856.0ms
(log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5))
67.0ms
(* u2 (* PI 2.0))
715.0ms
(exp (log (fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)))
716.0ms
(fma (/ 1.0 6.0) (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) 0.5)) 0.5)

simplify4.8s

Counts
73 → 73
Iterations
IterNodes
done5005
33336
2823
1284
0134

prune938.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.3b
(* u2 (* PI 2.0))
0.4b
(fma (/ 1.0 6.0) (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) 0.5)
0.6b
(* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
49×prod-exp
20×pow-exp
14×add-cbrt-cube
13×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
12×pow1
10×pow-to-exp
9×times-frac
6×associate-*r* cbrt-unprod
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
2×unpow-prod-down pow-pow *-commutative sqr-pow
1×fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
16.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
28.0ms
(* u2 (* PI 2.0))
0.0ms
(fma (/ 1.0 6.0) (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) 0.5)
187.0ms
(* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series2.6s

Counts
4 → 12
Calls
4 calls:
542.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
73.0ms
(* u2 (* PI 2.0))
1.3s
(fma (/ 1.0 6.0) (* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) 0.5)
715.0ms
(* (* (cos (* u2 (* PI 2.0))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify3.7s

Counts
109 → 109
Iterations
IterNodes
done5000
21680
1539
0204

prune985.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes975.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done24
124
018

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.0s8000×body80valid
299.0ms8000×pre80true