Details

Time bar (total: 31.5s)

sample169.0ms

Algorithm
intervals
Results
38.0ms256×body80valid
7.0ms256×pre80true

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5000
53177
4483
3159
272
135
018

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* 2.0 (* PI u2))) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
0.3b
(* PI u2)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
119×times-frac
65×add-sqr-sqrt
63×*-un-lft-identity add-cube-cbrt
29×add-exp-log
15×unpow-prod-down sqr-pow
13×associate-/r*
12×div-exp
11×add-cbrt-cube
9×pow1
7×div-inv
6×pow-exp
5×associate-/l*
4×expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-*r* associate-*l*
2×pow-pow pow-prod-down
1×clear-num frac-2neg associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 155
Calls
4 calls:
0.0ms
(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* 2.0 (* PI u2))) 0.5)
5.0ms
(pow (* -2.0 (log u1)) 0.5)
10.0ms
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
8.0ms
(* PI u2)

series2.1s

Counts
4 → 12
Calls
4 calls:
647.0ms
(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* 2.0 (* PI u2))) 0.5)
385.0ms
(pow (* -2.0 (log u1)) 0.5)
984.0ms
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
49.0ms
(* PI u2)

simplify2.3s

Counts
167 → 167
Iterations
IterNodes
done5000
23876
1811
0322

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
59×pow-exp
58×prod-exp
29×pow-to-exp
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt
5×add-cbrt-cube
3×expm1-log1p-u pow-unpow associate-*r* associate-*l* pow-prod-down log1p-expm1-u add-log-exp
2×pow-pow
1×unpow-prod-down *-commutative cbrt-unprod fma-udef unswap-sqr sqr-pow
Counts
3 → 78
Calls
3 calls:
33.0ms
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
0.0ms
(fma (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* u2 PI) 2.0))) 0.5)
6.0ms
(* u2 PI)

series2.7s

Counts
3 → 9
Calls
3 calls:
1.8s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
923.0ms
(fma (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* u2 PI) 2.0))) 0.5)
33.0ms
(* u2 PI)

simplify2.3s

Counts
87 → 87
Iterations
IterNodes
done5001
21435
1481
0191

prune537.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (pow (- (log u1)) 1.0) 0.5)
0.2b
(fma (* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5)) (* 0.16666666666666666 (cos (* (* u2 PI) 2.0))) 0.5)
0.3b
(* u2 PI)
0.4b
(* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
132×pow-exp
114×add-exp-log
106×prod-exp
65×unpow-prod-down
61×pow-to-exp
30×add-sqr-sqrt
23×associate-*r*
17×*-un-lft-identity add-cube-cbrt
14×sqr-pow
11×unswap-sqr
10×pow1
8×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube associate-*l*
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×pow-unpow
2×neg-mul-1 pow-prod-down *-commutative cbrt-unprod
1×pow-pow fma-udef
Counts
4 → 171
Calls
4 calls:
9.0ms
(pow (pow (- (log u1)) 1.0) 0.5)
0.0ms
(fma (* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5)) (* 0.16666666666666666 (cos (* (* u2 PI) 2.0))) 0.5)
7.0ms
(* u2 PI)
76.0ms
(* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5))

series3.3s

Counts
4 → 12
Calls
4 calls:
681.0ms
(pow (pow (- (log u1)) 1.0) 0.5)
838.0ms
(fma (* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5)) (* 0.16666666666666666 (cos (* (* u2 PI) 2.0))) 0.5)
43.0ms
(* u2 PI)
1.7s
(* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5))

simplify2.0s

Counts
183 → 183
Iterations
IterNodes
done5001
22538
1613
0257

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
0.3b
(* PI u2)
0.4b
(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
119×times-frac
64×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
26×add-exp-log
14×unpow-prod-down sqr-pow
13×associate-/r*
12×div-exp
11×add-cbrt-cube
7×div-inv
6×pow1
5×expm1-log1p-u associate-/l*
4×pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*r* associate-*l* prod-exp
2×pow-to-exp
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 associate-/r/ *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 148
Calls
4 calls:
1.0ms
(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
22.0ms
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
10.0ms
(* PI u2)
0.0ms
(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

series3.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
39.0ms
(* PI u2)
1.4s
(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

simplify2.2s

Counts
160 → 160
Iterations
IterNodes
done5000
23386
1715
0304

prune1.4s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes481.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s8000×body80valid
166.0ms8000×pre80true