Details

Time bar (total: 2.1m)

sample163.0ms

Algorithm
intervals
Results
101.0ms256×body80valid
15.0ms256×pre80true

simplify537.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
536.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
0.3b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)
0.0b
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity add-cbrt-cube prod-exp add-cube-cbrt
12×pow1
11×times-frac
6×associate-*r* pow-exp add-log-exp
5×cbrt-unprod
4×div-exp pow-prod-down insert-posit16 unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative sum-log flip3-+ associate-*l/ flip-+ div-inv
Counts
4 → 91
Calls
4 calls:
Slowest
24.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
16.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
12.0ms
(* u2 (* 2 PI))
9.0ms
(pow (* -2 (log u1)) 0.5)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
532.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
527.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
366.0ms
(pow (* -2 (log u1)) 0.5)
56.0ms
(* u2 (* 2 PI))

simplify12.6s

Counts
64 → 103
Calls
64 calls:
Slowest
974.0ms
(+ (* 1/6 (* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
864.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
725.0ms
(* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5))
709.0ms
(* (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6)) (sqrt (pow (* -2 (log u1)) 0.5)))
642.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) (/ 0.5 2)))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
0.3b
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
0.3b
(* u2 (* 2 PI))
0.3b
(* u2 (* 2 PI))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
38×associate-*l*
36×add-exp-log
34×add-sqr-sqrt
30×sqrt-prod
23×*-un-lft-identity add-cube-cbrt
21×add-cbrt-cube prod-exp
20×times-frac
16×pow1
10×cbrt-unprod
8×associate-*r*
7×pow-prod-down
6×unswap-sqr
5×sqrt-div
4×associate-*l/ pow-exp *-commutative insert-posit16 add-log-exp sqr-pow
2×pow-to-exp div-inv
1×frac-times unpow-prod-down associate-*r/
Counts
4 → 117
Calls
4 calls:
Slowest
59.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
26.0ms
(* u2 (* 2 PI))
25.0ms
(* u2 (* 2 PI))
24.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
632.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
587.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
44.0ms
(* u2 (* 2 PI))
40.0ms
(* u2 (* 2 PI))

simplify14.6s

Counts
94 → 129
Calls
94 calls:
Slowest
921.0ms
(* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (* (sqrt 1/6) (sqrt (cos (* 2 (* u2 PI))))))
668.0ms
(* (* (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
598.0ms
(* (sqrt (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (pow (* -2 (log u1)) (/ 0.5 2)))
598.0ms
(* (sqrt (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6))) (pow (* -2 (log u1)) (/ 0.5 2)))
597.0ms
(* (sqrt (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6))) (pow (* -2 (log u1)) (/ 0.5 2)))

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6))
0.3b
(* (* PI 2) u2)
0.1b
(pow (* (log u1) -2) 0.5)
0.0b
(+ 0.5 (pow (* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6)) 1))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
16×*-un-lft-identity associate-*r*
14×add-cbrt-cube prod-exp add-cube-cbrt
12×pow1
11×times-frac
6×associate-*l* pow-exp add-log-exp
5×cbrt-unprod
4×div-exp pow-prod-down insert-posit16 unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative sum-log flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
Counts
4 → 92
Calls
4 calls:
Slowest
33.0ms
(* (* PI 2) u2)
30.0ms
(* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6))
9.0ms
(pow (* (log u1) -2) 0.5)
8.0ms
(+ 0.5 (pow (* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6)) 1))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
604.0ms
(+ 0.5 (pow (* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6)) 1))
592.0ms
(* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6))
442.0ms
(pow (* (log u1) -2) 0.5)
39.0ms
(* (* PI 2) u2)

simplify11.1s

Counts
64 → 104
Calls
64 calls:
Slowest
902.0ms
(+ (* 1/6 (* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
853.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
516.0ms
(+ 0.5 (pow (* (pow (* (log u1) -2) 0.5) (/ (cos (* (* PI 2) u2)) 6)) 1))
493.0ms
(+ (log (pow (* (log u1) -2) 0.5)) (log (/ (cos (* (* PI 2) u2)) 6)))
479.0ms
(+ (log (pow (* (log u1) -2) 0.5)) (- (log (cos (* (* PI 2) u2))) (log 6)))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))
0.5b
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.3b
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)))
0.3b
(/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216)

rewrite556.0ms

Algorithm
rewrite-expression-head
Rules
506×add-exp-log
386×prod-exp
212×pow-exp
106×pow-to-exp
69×div-exp
20×add-cbrt-cube
16×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
10×associate-*l* sqr-pow
7×cbrt-unprod
6×associate-*r* unswap-sqr
5×unpow-prod-down swap-sqr
4×pow1 pow-prod-up insert-posit16 add-log-exp
3×cbrt-undiv cbrt-div associate-/r* times-frac pow-prod-down associate-*l/
2×pow-sqr cos-mult *-commutative
1×cbrt-prod pow2 frac-times clear-num frac-2neg pow1/3 cube-unmult associate-*r/ div-inv associate-/l*
Counts
4 → 243
Calls
4 calls:
Slowest
422.0ms
(cbrt (* (/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))
62.0ms
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)))
35.0ms
(/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216)
24.0ms
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series3.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216)
951.0ms
(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
894.0ms
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)))
603.0ms
(cbrt (* (/ (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) 216) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))

simplify1.1m

Counts
230 → 255
Calls
230 calls:
Slowest
1.0s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))) (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))))
918.0ms
(* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (* (cbrt 1/216) (cos (* 2 (* u2 PI)))))
900.0ms
(pow (pow (pow (pow (pow (pow (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0)
880.0ms
(+ (log (pow (* -2 (log u1)) 0.5)) (+ (* (log (* -2 (log u1))) 0.5) (log (pow (* -2 (log u1)) 0.5))))
767.0ms
(* (* (cbrt (pow (* -2 (log u1)) 0.5)) (cbrt (pow (* -2 (log u1)) 0.5))) (* (cbrt (pow (* -2 (log u1)) 0.5)) (cbrt (pow (* -2 (log u1)) 0.5))))

prune4.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes458.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.1s8000×body80valid
330.0ms8000×pre80true