Details

Time bar (total: 15.4s)

sample280.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
26819
314719
439519
5129219
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 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)
0.2b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite45.0ms

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 add-log-exp
5×cbrt-unprod
4×div-exp pow-prod-down unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative flip3-+ associate-*l/ sum-log flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
19.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
3.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 2.0 PI) u2)
13.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts
4 → 12
Calls
4 calls:
450.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
265.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
692.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify699.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (174.0ms)

IterNodesCost
02031408
15061344
217921222
done50001222

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite33.0ms

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
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
18.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 2.0 PI) u2)
4.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
454.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
257.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
684.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify540.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
01951363
14371318
215291206
done50011206

prune323.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.5b
(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3))
0.7b
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
54×unpow-prod-down
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
44×cbrt-prod
38×cube-prod
26×add-exp-log
18×sqr-pow
14×add-cbrt-cube
10×pow1
9×pow-exp
8×div-exp
5×prod-exp div-inv associate-/l*
4×add-log-exp
3×pow-to-exp pow-unpow associate-*r* pow-prod-down associate-/r* cbrt-unprod
2×cbrt-undiv cube-div cube-mult unpow3 rem-cube-cbrt
1×cbrt-div pow-pow frac-2neg pow1/3 associate-*l* clear-num *-commutative rem-cbrt-cube
Counts
4 → 171
Calls
4 calls:
6.0ms
(* (* 2.0 PI) u2)
3.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
6.0ms
(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3))
10.0ms
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

series2.2s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 2.0 PI) u2)
688.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
686.0ms
(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3))
767.0ms
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

simplify756.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (259.0ms)

IterNodesCost
02613221
16432768
223742475
done50002475

prune519.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.5b
(pow (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3) 1/3)
0.7b
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
98×unpow-prod-down
75×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
38×cube-prod
36×add-exp-log
23×pow-exp
19×sqr-pow
14×add-cbrt-cube
12×div-exp
10×pow1
6×pow-to-exp pow-unpow prod-exp
5×div-inv associate-/l*
4×add-log-exp
3×associate-*r* pow-prod-down associate-/r* cbrt-unprod
2×cbrt-undiv cube-mult pow-pow unpow3 rem-cube-cbrt
1×cube-div frac-2neg unpow1/3 associate-*l* clear-num *-commutative
Counts
4 → 182
Calls
4 calls:
7.0ms
(* (* 2.0 PI) u2)
3.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
14.0ms
(pow (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3) 1/3)
6.0ms
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

series2.6s

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 2.0 PI) u2)
691.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
959.0ms
(pow (pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3) 1/3)
901.0ms
(pow (/ (pow (* -2.0 (log u1)) 0.5) 6.0) 3)

simplify1.1s

Counts
194 → 194
Iterations

Useful iterations: 2 (439.0ms)

IterNodesCost
02823493
18133044
229832597
done50002597

prune523.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes431.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01819
12419
done2419

end0.0ms

sample924.0ms

Algorithm
intervals
Results
652.0ms8000×body80valid
121.0ms8000×pre80true