Details

Time bar (total: 3.5m)

sample570.0ms

Algorithm
intervals
Results
235.0ms256×body80valid
55.0ms256×pre80true

simplify413.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
413.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

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

rewrite61.0ms

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
23.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
12.0ms
(* u2 (* 2 PI))
12.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
10.0ms
(pow (* -2 (log u1)) 0.5)

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
886.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
536.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
370.0ms
(pow (* -2 (log u1)) 0.5)
41.0ms
(* u2 (* 2 PI))

simplify12.4s

Counts
64 → 103
Calls
64 calls:
Slowest
939.0ms
(+ (* 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)
861.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
673.0ms
(+ (log (/ (cos (* u2 (* 2 PI))) 6)) (* (log (* -2 (log u1))) 0.5))
609.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) (/ 0.5 2)))
549.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) (/ 0.5 2)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2)))))
0.3b
(* PI (* u2 2))
0.1b
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
0.1b
(+ 0.5 (* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2))))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
66×prod-exp
48×pow-exp
21×pow-to-exp
14×add-cbrt-cube
10×pow1
8×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-unprod add-log-exp
4×pow-prod-down insert-posit16
3×pow-unpow
2×unpow-prod-down pow-pow associate-*r* *-commutative sqr-pow
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 98
Calls
4 calls:
Slowest
136.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2)))))
17.0ms
(* PI (* u2 2))
16.0ms
(+ 0.5 (* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2))))))
7.0ms
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)

series2.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
641.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2)))))
605.0ms
(+ 0.5 (* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) (* 1/6 (cos (* PI (* u2 2))))))
56.0ms
(* PI (* u2 2))

simplify15.2s

Counts
67 → 110
Calls
67 calls:
Slowest
927.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
749.0ms
(+ (* 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)
654.0ms
(* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI)))))
537.0ms
(pow (pow (pow (pow (pow (pow (pow (pow (pow (pow (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 0.5)
491.0ms
(+ (* (+ (log (pow (log u1) 1.0)) (* (log -2) 1.0)) 0.5) (log (* 1/6 (cos (* PI (* u2 2))))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
424×add-exp-log
281×prod-exp
81×div-exp
80×pow-exp
52×add-cbrt-cube
45×add-sqr-sqrt
40×pow-to-exp
34×times-frac
29×*-un-lft-identity add-cube-cbrt
27×associate-*l*
25×cbrt-unprod
11×pow1 associate-*r*
9×cbrt-undiv
8×unswap-sqr
7×associate-*l/
6×sqr-pow
4×insert-posit16 associate-/l* add-log-exp difference-of-squares
3×associate-/r* *-commutative div-inv
2×unpow-prod-down flip3-- associate-/r/ flip-- associate-/l/
1×pow2 frac-times clear-num frac-2neg pow-plus div-sub swap-sqr pow-prod-down associate-*r/ pow-sqr pow-prod-up
Counts
4 → 231
Calls
4 calls:
Slowest
102.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
25.0ms
(/ (- (* 0.5 0.5) (* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))) (- 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))))
21.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
21.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
814.0ms
(/ (- (* 0.5 0.5) (* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))) (- 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))))
454.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
391.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
378.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))

simplify1.3m

Counts
224 → 243
Calls
224 calls:
Slowest
1.3s
(* (* (* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))) (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
1.1s
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
1.0s
(+ (+ (- (log (cos (* u2 (* 2 PI)))) (log 6)) (log (pow (* -2 (log u1)) 0.5))) (+ (log (/ (cos (* u2 (* 2 PI))) 6)) (* (log (* -2 (log u1))) 0.5)))
1.0s
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))))
998.0ms
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (/ (cos (* u2 (* 2 PI))) 6) (/ (cos (* u2 (* 2 PI))) 6)) (/ (cos (* u2 (* 2 PI))) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

prune4.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
442×add-exp-log
291×prod-exp
84×div-exp pow-exp
55×add-cbrt-cube
52×add-sqr-sqrt
42×pow-to-exp
40×associate-*l*
33×times-frac
28×*-un-lft-identity add-cube-cbrt
27×cbrt-unprod
16×associate-*r*
12×unswap-sqr
11×pow1
9×cbrt-undiv sqr-pow
8×associate-*l/
4×*-commutative insert-posit16 add-log-exp
3×unpow-prod-down div-inv
1×pow2 frac-times pow-plus swap-sqr pow-prod-down associate-*r/ pow-sqr pow-prod-up
Counts
4 → 236
Calls
4 calls:
Slowest
116.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
43.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
27.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
21.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
540.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
533.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
523.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
498.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))

simplify1.3m

Counts
223 → 248
Calls
223 calls:
Slowest
1.4s
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))) (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))))
1.1s
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
946.0ms
(* (* (/ (* (* (cos (* u2 (* 2 PI))) (cos (* u2 (* 2 PI)))) (cos (* u2 (* 2 PI)))) (* (* 6 6) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (/ (cos (* u2 (* 2 PI))) 6) (/ (cos (* u2 (* 2 PI))) 6)) (/ (cos (* u2 (* 2 PI))) 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
938.0ms
(* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5))
930.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))

prune4.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes593.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.6s8000×body80valid
399.0ms8000×pre80true