Details

Time bar (total: 3.3m)

sample399.0ms

Algorithm
intervals
Results
126.0ms256×body80valid
20.0ms256×pre80true

simplify872.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
872.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube associate-*r* prod-exp add-cube-cbrt
12×pow1
11×times-frac
8×associate-*l*
6×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
Counts
4 → 91
Calls
4 calls:
Slowest
42.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))
26.0ms
(* u2 (* 2 PI))
23.0ms
(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))
11.0ms
(pow (* -2 (log u1)) 0.5)

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
637.0ms
(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))
557.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))
362.0ms
(pow (* -2 (log u1)) 0.5)
58.0ms
(* u2 (* 2 PI))

simplify25.9s

Counts
108 → 103
Calls
108 calls:
Slowest
847.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (* (cbrt (cos (* u2 (* 2 PI)))) (cbrt (cos (* u2 (* 2 PI))))) 1))
779.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
756.0ms
(+ (* 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)
729.0ms
(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6)))
620.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (* (cbrt (cos (* u2 (* 2 PI)))) (cbrt (cos (* u2 (* 2 PI))))) (sqrt 6)))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log
34×add-sqr-sqrt associate-*r*
30×sqrt-prod
23×*-un-lft-identity add-cube-cbrt
21×add-cbrt-cube prod-exp
20×times-frac
16×pow1
12×associate-*l*
10×cbrt-unprod
7×pow-prod-down
6×unswap-sqr
5×sqrt-div
4×pow-exp associate-*r/ *-commutative insert-posit16 add-log-exp sqr-pow
2×pow-to-exp div-inv
1×frac-times unpow-prod-down associate-*l/
Counts
4 → 117
Calls
4 calls:
Slowest
41.0ms
(* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))
17.0ms
(* u2 (* 2 PI))
16.0ms
(* u2 (* 2 PI))
16.0ms
(* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
618.0ms
(* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))
596.0ms
(* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))
53.0ms
(* u2 (* 2 PI))
51.0ms
(* u2 (* 2 PI))

simplify32.0s

Counts
132 → 129
Calls
132 calls:
Slowest
1.1s
(* (* (* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))) (* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6))))
976.0ms
(* (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))))))
733.0ms
(* (* (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6)))) (* (pow (* -2 (log u1)) 0.5) (sqrt (/ (cos (* u2 (* 2 PI))) 6))))
729.0ms
(* (pow (* -2 (log u1)) 0.5) (sqrt (/ (sqrt (cos (* u2 (* 2 PI)))) 1)))
702.0ms
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (sqrt (/ (cos (* u2 (* 2 PI))) 6))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
10×*-un-lft-identity
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×div-exp
4×pow-prod-down pow-exp cbrt-unprod insert-posit16
3×pow-unpow associate-/r* times-frac associate-*r*
2×pow-to-exp cbrt-undiv pow-pow
1×+-commutative clear-num sum-log unpow-prod-down frac-2neg flip3-+ associate-*l* *-commutative flip-+ div-inv distribute-lft-out associate-/l* sqr-pow
Counts
4 → 75
Calls
4 calls:
Slowest
52.0ms
(/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6)
19.0ms
(* (* 2 u2) PI)
12.0ms
(+ 0.5 (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6))
5.0ms
(pow (* -2 (log u1)) 0.5)

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
592.0ms
(/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6)
571.0ms
(+ 0.5 (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6))
353.0ms
(pow (* -2 (log u1)) 0.5)
35.0ms
(* (* 2 u2) PI)

simplify20.2s

Counts
93 → 87
Calls
93 calls:
Slowest
1.1s
(* (* (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6) (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6)) (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6))
782.0ms
(+ (* 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)
777.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
677.0ms
(/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) (* (cbrt 6) (cbrt 6)))
642.0ms
(- (* 0.5 0.5) (* (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6) (/ (* (pow (* -2 (log u1)) 0.5) (cos (* (* 2 u2) PI))) 6)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

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-*r*
25×cbrt-unprod
11×pow1 associate-*l*
9×cbrt-undiv
8×unswap-sqr
7×associate-*r/
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-*l/ pow-sqr pow-prod-up
Counts
4 → 231
Calls
4 calls:
Slowest
81.0ms
(* (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)) (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))
25.0ms
(/ (- (* 0.5 0.5) (* (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)) (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))) (- 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))))
22.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))
18.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))

series2.9s

Counts
4 → 12
Calls
4 calls:
Slowest
982.0ms
(/ (- (* 0.5 0.5) (* (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)) (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))) (- 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))))
635.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))
630.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))
619.0ms
(* (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)) (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))

simplify1.6m

Counts
263 → 243
Calls
263 calls:
Slowest
1.0s
(+ (+ (* (+ (log -2) (log (log u1))) 0.5) (- (log (cos (* u2 (* 2 PI)))) (log 6))) (+ (* (+ (log -2) (log (log u1))) 0.5) (- (log (cos (* u2 (* 2 PI)))) (log 6))))
982.0ms
(* (* (* (* (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) (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))))
907.0ms
(+ (+ (log (pow (* -2 (log u1)) 0.5)) (- (log (cos (* u2 (* 2 PI)))) (log 6))) (+ (* (log (* -2 (log u1))) 0.5) (- (log (cos (* u2 (* 2 PI)))) (log 6))))
877.0ms
(* (* (* (* (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)) (* (* (/ (cos (* u2 (* 2 PI))) 6) (/ (cos (* u2 (* 2 PI))) 6)) (/ (cos (* u2 (* 2 PI))) 6))))
875.0ms
(log (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))

prune3.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes372.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.0s8000×body80valid
841.0ms8000×pre80true