Details

Time bar (total: 55.1s)

sample283.0ms

Algorithm
intervals
Results
60.0ms256×body80valid
14.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Calls
1 calls:
Slowest
1.0s
(+ (* (* (/ 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

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
12×pow1
11×add-sqr-sqrt add-cbrt-cube
9×prod-exp
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×pow-prod-down pow-exp cbrt-unprod insert-posit16
3×pow-unpow sqr-pow
2×pow-to-exp unpow-prod-down pow-pow *-commutative unswap-sqr
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 73
Calls
4 calls:
Slowest
19.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
18.0ms
(* PI (* 2 u2))
12.0ms
(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* PI (* 2 u2)))))
5.0ms
(pow (* -2 (log u1)) 0.5)

series2.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* PI (* 2 u2)))))
972.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
411.0ms
(pow (* -2 (log u1)) 0.5)
42.0ms
(* PI (* 2 u2))

simplify6.4s

Counts
44 → 85
Calls
44 calls:
Slowest
864.0ms
(+ (* 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)
794.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
563.0ms
(* (exp 0.5) (exp (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* PI (* 2 u2))))))
397.0ms
(* (* (* PI PI) PI) (* (* (* 2 u2) (* 2 u2)) (* 2 u2)))
360.0ms
(* (* (* PI PI) PI) (* (* (* 2 2) 2) (* (* u2 u2) u2)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
0.3b
(* PI (* 2 u2))
0.2b
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.1b
(pow (* -2 (log u1)) 0.5)

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
19×prod-exp
17×add-sqr-sqrt
16×add-cbrt-cube
15×associate-*l*
14×pow1
11×*-un-lft-identity add-cube-cbrt
8×sqrt-prod
7×associate-*r* cbrt-unprod
6×pow-exp
5×pow-prod-down
4×insert-posit16 add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow
Counts
4 → 90
Calls
4 calls:
Slowest
51.0ms
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
31.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
25.0ms
(* PI (* 2 u2))
5.0ms
(pow (* -2 (log u1)) 0.5)

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
995.0ms
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
905.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
397.0ms
(pow (* -2 (log u1)) 0.5)
55.0ms
(* PI (* 2 u2))

simplify11.0s

Counts
64 → 102
Calls
64 calls:
Slowest
905.0ms
(* (* (* (sqrt 1/6) (sqrt 1/6)) (sqrt 1/6)) (* (* (* (sqrt 1/6) (sqrt 1/6)) (sqrt 1/6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
725.0ms
(* (pow (sqrt 1/6) 2) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
713.0ms
(* (sqrt 1/6) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
659.0ms
(* (sqrt (sqrt 1/6)) (pow (* -2 (log u1)) (/ 0.5 2)))
637.0ms
(* (sqrt (sqrt 1/6)) (pow (* -2 (log u1)) (/ 0.5 2)))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
18×prod-exp
14×add-cbrt-cube
12×pow1
8×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
7×add-log-exp
6×pow-exp cbrt-unprod
4×pow-prod-down insert-posit16
3×pow-to-exp pow-unpow exp-prod
2×unpow-prod-down pow-pow associate-*r* *-commutative sqr-pow rem-exp-log
1×sum-log exp-sum
Counts
4 → 76
Calls
4 calls:
Slowest
175.0ms
(exp (+ (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))) 0.5))
91.0ms
(* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))
12.0ms
(* PI (* 2 u2))
5.0ms
(pow (* -2 (log u1)) 0.5)

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
669.0ms
(exp (+ (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))) 0.5))
597.0ms
(* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))
421.0ms
(pow (* -2 (log u1)) 0.5)
42.0ms
(* PI (* 2 u2))

simplify8.3s

Counts
48 → 88
Calls
48 calls:
Slowest
871.0ms
(exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))
865.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
451.0ms
(exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))
400.0ms
(* (* (* PI PI) PI) (* (* (* 2 u2) (* 2 u2)) (* 2 u2)))
390.0ms
(exp (* (cbrt (+ (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))) 0.5)) (cbrt (+ (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))) 0.5))))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.9b
(exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))
0.4b
(* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))
0.3b
(* (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))) (exp 0.5))
0.3b
(* PI (* 2 u2))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
18×prod-exp
16×add-cbrt-cube
11×pow1 associate-*l*
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×cbrt-unprod
6×add-log-exp
5×associate-*r*
4×pow-prod-down pow-exp insert-posit16
3×*-commutative
2×pow-to-exp
1×exp-prod unpow-prod-down exp-to-pow unswap-sqr sqr-pow rem-exp-log
Counts
4 → 74
Calls
4 calls:
Slowest
207.0ms
(* (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))) (exp 0.5))
99.0ms
(* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))
90.0ms
(exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))
25.0ms
(* PI (* 2 u2))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
752.0ms
(* (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))) (exp 0.5))
679.0ms
(exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))
600.0ms
(* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))
59.0ms
(* PI (* 2 u2))

simplify10.0s

Counts
48 → 86
Calls
48 calls:
Slowest
641.0ms
(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
633.0ms
(* (* (* (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))) (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))) (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))) (* (* (exp 0.5) (exp 0.5)) (exp 0.5)))
568.0ms
(* (sqrt (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))) (sqrt (exp 0.5)))
557.0ms
(* (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2)))))) (exp 0.5))
527.0ms
(* (sqrt (exp (* (pow (* -2 (log u1)) 0.5) (* 1/6 (cos (* PI (* 2 u2))))))) (sqrt (exp 0.5)))

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes371.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch7.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.7s8000×body80valid
397.0ms8000×pre80true