Details

Time bar (total: 4.5s)

sample51.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
7.0ms256×pre80true

simplify720.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
0487219
1487219

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.4b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* PI u2)
0.4b
(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
25×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
12×prod-exp
11×times-frac add-cbrt-cube
9×pow1
8×associate-*l*
6×pow-exp add-log-exp
5×unswap-sqr
4×div-exp sqr-pow
3×pow-to-exp pow-unpow cbrt-unprod
2×unpow-prod-down pow-pow pow-prod-down *-commutative
1×cbrt-undiv +-commutative flip3-+ associate-*r/ sum-log flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
3.0ms
(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
23.0ms
(pow (* -2.0 (log u1)) 0.5)
3.0ms
(* PI u2)
11.0ms
(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

series201.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
38.0ms
(pow (* -2.0 (log u1)) 0.5)
2.0ms
(* PI u2)
84.0ms
(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049571396
149571396

prune219.0ms

Filtered
67 candidates to 99 candidates (-47.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New891099
Fresh000
Picked101
Done000
Total9010100

Merged error: 0.0b

Counts
100 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×associate-*r*
30×add-exp-log sqrt-prod
25×add-cube-cbrt *-un-lft-identity
20×times-frac
17×prod-exp
15×add-cbrt-cube
12×associate-*l*
10×pow1
8×unswap-sqr
6×cbrt-unprod
5×sqrt-div
4×associate-*r/ pow-exp *-commutative add-log-exp sqr-pow
3×pow-prod-down
2×pow-to-exp div-inv
1×frac-times unpow-prod-down associate-*l/
Counts
4 → 113
Calls
4 calls:
3.0ms
(* PI u2)
3.0ms
(* PI u2)
12.0ms
(* (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0))) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
9.0ms
(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))

series157.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI u2)
2.0ms
(* PI u2)
75.0ms
(* (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0))) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
78.0ms
(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))

simplify38.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
049851843
149851843

prune282.0ms

Filtered
82 candidates to 125 candidates (-52.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1232125
Fresh549
Picked011
Done000
Total1287135

Merged error: 0b

Counts
135 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
21×prod-exp
18×add-sqr-sqrt add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity associate-*l*
10×pow1
9×times-frac
7×cbrt-unprod
6×log-prod
5×div-exp
4×log-div exp-prod associate-*r* pow-exp add-log-exp
3×exp-sum
2×cbrt-undiv pow-to-exp flip3-+ exp-diff pow-prod-down log-pow *-commutative flip-+
1×rem-log-exp associate-*l/ div-inv rem-exp-log unswap-sqr
Counts
4 → 87
Calls
4 calls:
3.0ms
(* PI u2)
2.0ms
(log (+ 0.5 (* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0))))
3.0ms
(exp (log (+ 0.5 (* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0)))))
9.0ms
(* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0))

series227.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI u2)
89.0ms
(log (+ 0.5 (* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0))))
69.0ms
(exp (log (+ 0.5 (* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0)))))
67.0ms
(* (/ (cos (* 2.0 (* PI u2))) 6.0) (* (pow (* -2.0 (log u1)) 0.5) 1.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049511833
149511833

prune200.0ms

Filtered
63 candidates to 99 candidates (-57.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done011
Total997106

Merged error: 0b

Counts
106 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* PI u2)
0.2b
(* PI u2)
0.3b
(* (/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0)) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
0.6b
(/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
34×add-sqr-sqrt
24×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
22×times-frac associate-*r* add-cbrt-cube
18×prod-exp
16×associate-*l*
10×pow1 div-exp
7×cbrt-unprod
6×associate-/r*
5×unswap-sqr
4×cbrt-undiv pow-exp add-log-exp
3×pow-prod-down *-commutative div-inv
2×pow-to-exp sqrt-div
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num associate-/l*
Counts
4 → 116
Calls
4 calls:
4.0ms
(* PI u2)
4.0ms
(* PI u2)
15.0ms
(* (/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0)) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
9.0ms
(/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0))

series164.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI u2)
2.0ms
(* PI u2)
79.0ms
(* (/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0)) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
81.0ms
(/ (* (pow (* -2.0 (log u1)) 0.5) (sqrt (cos (* 2.0 (* PI u2))))) (sqrt 6.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049382246
149382246

prune283.0ms

Filtered
85 candidates to 128 candidates (-50.6%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1280128
Fresh044
Picked011
Done022
Total1287135

Merged error: 0b

Counts
135 → 7

regimes328.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02730
12730

end0.0ms

sample1.2s

Algorithm
intervals
Results
789.0ms8000×body80valid
187.0ms8000×pre80true

Profiling

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