Details

sample331.0ms

Algorithm

intervals

Results

82.0ms	256×	body	80	valid
23.0ms	256×	pre	80	true

simplify237.0ms

Calls

1 calls:

Slowest

236.0ms

(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-l` `insert-posit16` `add-log-exp`
3×	`prod-exp`
2×	`pow-to-exp` `unpow-prod-down` `pow-exp` `*-commutative`
1×	`+-commutative` `pow-pow` `flip3-+` `associate-r` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

44.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
8.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
3.0ms	(pow (* -2 (log u1)) 0.5)
0.0ms	(* PI u2)

series1.8s

Calls

4 calls:

Slowest

666.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
642.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
420.0ms	(pow (* -2 (log u1)) 0.5)
37.0ms	(* PI u2)

simplify2.7s

Calls

22 calls:

Slowest

726.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
359.0ms	(- (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
287.0ms	(- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
219.0ms	(* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI)))))
192.0ms	(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)

prune805.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
0.5b	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.4b	(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
0.3b	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

441×	`add-exp-log`
423×	`prod-exp`
118×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
31×	`cbrt-unprod`
14×	`pow1`
13×	`pow-prod-down`
9×	`associate-r`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow2` `associate-l`
5×	`pow3`
4×	`pow-plus` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`unpow-prod-down` `*-commutative`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Calls

4 calls:

Slowest

270.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
192.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
21.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
15.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series3.1s

Calls

4 calls:

Slowest

933.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
909.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
661.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
618.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))

simplify1.1m

Calls

188 calls:

Slowest

1.0s	(+ (+ (+ (* (log (* -2 (log u1))) 0.5) (* (log (* -2 (log u1))) 0.5)) (* (log (* -2 (log u1))) 0.5)) (+ (+ (log (* (cos (* (* PI u2) 2)) 1/6)) (log (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
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))) (* (* (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
700.0ms	(+ (+ (+ (* (log (* -2 (log u1))) 0.5) (* (log (* -2 (log u1))) 0.5)) (log (pow (* -2 (log u1)) 0.5))) (+ (log (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
700.0ms	(+ (+ (+ (* (log (* -2 (log u1))) 0.5) (* (log (* -2 (log u1))) 0.5)) (log (pow (* -2 (log u1)) 0.5))) (+ (log (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
690.0ms	(+ (+ (+ (* (log (* -2 (log u1))) 0.5) (* (log (* -2 (log u1))) 0.5)) (log (pow (* -2 (log u1)) 0.5))) (+ (log (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
0.4b	(* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
0.3b	(pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5))
0.3b	(* PI u2)

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
18×	`prod-exp`
13×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod`
5×	`pow1` `associate-l`
4×	`pow-to-exp` `pow-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow`
2×	`unpow-prod-up` `unpow-prod-down` `*-commutative`
1×	`cbrt-prod` `pow-pow` `pow1/3` `associate-r`

Calls

4 calls:

Slowest

266.0ms	(* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
161.0ms	(cbrt (* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
4.0ms	(pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5))
0.0ms	(* PI u2)

series1.7s

Calls

4 calls:

Slowest

652.0ms	(* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6)))
621.0ms	(cbrt (* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (* (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6)) (* (cos (* (* PI u2) 2)) 1/6))))
369.0ms	(pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5))
43.0ms	(* PI u2)

simplify7.6s

Calls

37 calls:

Slowest

750.0ms	(+ (* (log (* -2 (log u1))) (+ (+ 0.5 0.5) 0.5)) (+ (log (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
657.0ms	(+ (* (log (* -2 (log u1))) (+ (+ 0.5 0.5) 0.5)) (+ (log (* (* (cos (* (* PI u2) 2)) 1/6) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
626.0ms	(- (* (cbrt 1/216) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (* 2 (* (* (pow u2 2) (* (cbrt 1/216) (pow PI 2))) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
530.0ms	(+ (* (log (* -2 (log u1))) (+ (+ 0.5 0.5) 0.5)) (+ (+ (log (* (cos (* (* PI u2) 2)) 1/6)) (log (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
507.0ms	(+ (* (log (* -2 (log u1))) (+ (+ 0.5 0.5) 0.5)) (+ (+ (log (* (cos (* (* PI u2) 2)) 1/6)) (log (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
0.3b	(exp (log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))))
0.3b	(* PI u2)
0.2b	(log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod` `add-cbrt-cube`
4×	`log-div` `exp-prod` `associate-l` `insert-posit16` `add-log-exp`
3×	`exp-sum` `prod-exp`
2×	`flip3-+` `exp-diff` `log-pow` `*-commutative` `flip-+`
1×	`pow-to-exp` `unpow-prod-down` `rem-log-exp` `associate-r` `pow-exp` `cbrt-unprod` `rem-exp-log`

Calls

4 calls:

Slowest

40.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
5.0ms	(exp (log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))))
2.0ms	(log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
0.0ms	(* PI u2)

series1.9s

Calls

4 calls:

Slowest

744.0ms	(log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
582.0ms	(exp (log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))))
529.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
32.0ms	(* PI u2)

simplify4.8s

Calls

34 calls:

Slowest

582.0ms	(exp (log (- (* 0.5 0.5) (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))))
439.0ms	(- (log (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))) (* 1/3 (* (/ (* (pow u2 2) (pow PI 2)) (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)))) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
377.0ms	(log (+ (pow 0.5 3) (pow (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) 3)))
357.0ms	(- (+ 0.5 (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))
340.0ms	(- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (* 1/3 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))))

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes467.0ms

Accuracy

0% (0.5b remaining)

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

bsearch5.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
415.0ms	8000×	pre	80	true