Details

Time bar (total: 4.1m)

sample571.0ms

Algorithm
intervals
Results
73.0ms256×body80valid
18.0ms256×pre80true

simplify527.0ms

Calls
1 calls:
Slowest
526.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

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)))

rewrite82.0ms

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
Calls
4 calls:
Slowest
40.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
19.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
13.0ms
(* u2 (* 2 PI))
5.0ms
(pow (* -2 (log u1)) 0.5)

series1.6s

Calls
4 calls:
Slowest
559.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
525.0ms
(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
462.0ms
(pow (* -2 (log u1)) 0.5)
49.0ms
(* u2 (* 2 PI))

simplify12.2s

Calls
64 calls:
Slowest
922.0ms
(+ (* 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)
791.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
601.0ms
(* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5))
566.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) (/ 0.5 2)))
541.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) (/ 0.5 2)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
0.3b
(* u2 (* 2 PI))
0.3b
(* u2 (* 2 PI))
0.2b
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))

rewrite120.0ms

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/
Calls
4 calls:
Slowest
50.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
32.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
17.0ms
(* u2 (* 2 PI))
17.0ms
(* u2 (* 2 PI))

series1.3s

Calls
4 calls:
Slowest
585.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
557.0ms
(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
60.0ms
(* u2 (* 2 PI))
53.0ms
(* u2 (* 2 PI))

simplify15.6s

Calls
94 calls:
Slowest
976.0ms
(* (sqrt (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (pow (* -2 (log u1)) (/ 0.5 2)))
893.0ms
(* (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))))))
793.0ms
(* (* (* (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)))
684.0ms
(* (sqrt (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6))) (pow (* -2 (log u1)) (/ 0.5 2)))
668.0ms
(* (sqrt (cos (* u2 (* 2 PI)))) (pow (* -2 (log u1)) 0.5))

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))))
0.5b
(* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))
0.4b
(* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2)))))
0.3b
(/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
1610×add-exp-log
1090×prod-exp
390×div-exp
326×pow-exp
163×pow-to-exp
110×add-cbrt-cube
59×times-frac
51×cbrt-unprod
38×add-sqr-sqrt
30×cbrt-undiv
27×*-un-lft-identity add-cube-cbrt
19×associate-*r*
13×associate-/r*
11×pow1
6×associate-*l* unswap-sqr
5×div-inv
4×insert-posit16 add-log-exp sqr-pow
2×associate-*r/ associate-/r/ *-commutative
1×cbrt-prod pow2 cbrt-div clear-num unpow-prod-down frac-2neg pow-plus pow1/3 swap-sqr pow-prod-down pow-sqr pow-prod-up associate-/l*
Calls
4 calls:
Slowest
175.0ms
(* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))
145.0ms
(/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))
94.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2)))))
60.0ms
(cbrt (* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))))

series2.4s

Calls
4 calls:
Slowest
753.0ms
(* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2)))))
614.0ms
(cbrt (* (pow (* -2 (log u1)) 0.5) (/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))))
508.0ms
(* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))
501.0ms
(/ (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (/ 216 (cos (* (* PI 2) u2))))

simplify2.9m

Calls
414 calls:
Slowest
2.7s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (/ (* (* (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))) (* (* (/ 216 (cos (* (* PI 2) u2))) (/ 216 (cos (* (* PI 2) u2)))) (/ 216 (cos (* (* PI 2) u2))))))
2.4s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (/ (* (* (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))) (/ (* (* 216 216) 216) (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))))))
2.3s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (/ (* (* (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))) (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)))) (* (* (/ 216 (cos (* (* PI 2) u2))) (/ 216 (cos (* (* PI 2) u2)))) (/ 216 (cos (* (* PI 2) u2))))))
2.3s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (/ (* (* (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))) (* (* (/ 216 (cos (* (* PI 2) u2))) (/ 216 (cos (* (* PI 2) u2)))) (/ 216 (cos (* (* PI 2) u2))))))
2.3s
(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (/ (* (* (* (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5)) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (cos (* (* PI 2) u2)) (pow (* -2 (log u1)) 0.5))) (* (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))) (/ (* (* 216 216) 216) (* (* (cos (* (* PI 2) u2)) (cos (* (* PI 2) u2))) (cos (* (* PI 2) u2))))))

prune7.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
99×prod-exp
40×pow-exp
29×add-sqr-sqrt
23×add-cbrt-cube
21×*-un-lft-identity add-cube-cbrt
20×pow-to-exp times-frac div-exp
17×associate-*l*
13×pow-unpow
12×pow1
11×associate-*r*
10×cbrt-unprod
5×sqr-pow
4×pow-prod-down insert-posit16 add-log-exp unswap-sqr
3×unpow-prod-down associate-*l/ *-commutative
2×cbrt-undiv pow-pow div-inv
Calls
4 calls:
Slowest
105.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))
46.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) (/ 0.5 2)))
13.0ms
(* u2 (* 2 PI))
7.0ms
(pow (* -2 (log u1)) (/ 0.5 2))

series1.5s

Calls
4 calls:
Slowest
572.0ms
(* (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))
473.0ms
(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) (/ 0.5 2)))
403.0ms
(pow (* -2 (log u1)) (/ 0.5 2))
39.0ms
(* u2 (* 2 PI))

simplify24.9s

Calls
120 calls:
Slowest
858.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.25)))
839.0ms
(* 1/6 (* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (cos (* 2 (* u2 PI)))))
754.0ms
(+ (+ (- (log (cos (* u2 (* 2 PI)))) (log 6)) (* (log (* -2 (log u1))) (/ 0.5 2))) (* (+ (log -2) (log (log u1))) (/ 0.5 2)))
711.0ms
(* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) (/ 0.5 2)))
686.0ms
(* (* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))

prune2.1s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes319.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.5s8000×body80valid
457.0ms8000×pre80true