Details

Time bar (total: 10.4s)

sample284.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03410
17110
215410
346910
4181210
5500110

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))

rewrite120.0ms

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:
58.0ms
(+ (* (* (/ 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)
26.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.3s

Counts
4 → 12
Calls
4 calls:
415.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
240.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
653.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0507728
12155656
25001656

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

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
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.2b
(* (* 2.0 PI) u2)

rewrite83.0ms

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:
49.0ms
(+ (* (* 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)
9.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
17.0ms
(* (* 2.0 PI) u2)

series1.3s

Counts
4 → 12
Calls
4 calls:
426.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
245.0ms
(pow (* -2.0 (log u1)) 0.5)
647.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
30.0ms
(* (* 2.0 PI) u2)

simplify54.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0438710
11838655
25001655

prune308.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
324×add-exp-log
223×prod-exp
128×pow1
96×add-cbrt-cube
72×pow-prod-down
62×cbrt-unprod
57×div-exp
28×pow-exp
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow-to-exp
12×times-frac
9×cbrt-undiv pow-sqr pow-prod-up
7×associate-*r*
5×associate-*r/ associate-*l/
4×associate-/l* add-log-exp difference-of-squares
3×pow-plus associate-*l* associate-/r* *-commutative
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow2 frac-times frac-2neg div-sub swap-sqr clear-num div-inv
Counts
4 → 182
Calls
4 calls:
17.0ms
(* (* 2.0 PI) u2)
17.0ms
(* (* 2.0 PI) u2)
729.0ms
(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
303.0ms
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* 2.0 PI) u2)
30.0ms
(* (* 2.0 PI) u2)
716.0ms
(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
426.0ms
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

simplify123.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
09453662
143512732
250032666

prune410.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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×associate-*l/ 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 → 112
Calls
4 calls:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
59.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
28.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts
4 → 12
Calls
4 calls:
253.0ms
(pow (* -2.0 (log u1)) 0.5)
30.0ms
(* (* 2.0 PI) u2)
703.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
673.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify54.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0447924
11791827
25002823

prune408.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes311.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample944.0ms

Algorithm
intervals
Results
640.0ms8000×body80valid
109.0ms8000×pre80true