Details

sample291.0ms

Algorithm

intervals

Results

68.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify919.0ms

Calls

1 calls:

Slowest

918.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

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

rewrite31.0ms

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

24.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
4.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
2.0ms	(pow (* -2 (log u1)) 0.5)
0.0ms	(* PI u2)

series1.4s

Calls

4 calls:

Slowest

535.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
455.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
419.0ms	(pow (* -2 (log u1)) 0.5)
34.0ms	(* PI u2)

simplify2.4s

Calls

22 calls:

Slowest

467.0ms	(* (* (* (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)))
323.0ms	(- (+ 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))))
281.0ms	(- (* 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))))
220.0ms	(+ (log (pow (* -2 (log u1)) 0.5)) (log (* (cos (* (* PI u2) 2)) 1/6)))
192.0ms	(+ (* (log (* -2 (log u1))) 0.5) (log (* (cos (* (* PI u2) 2)) 1/6)))

prune733.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `prod-exp` `add-cube-cbrt`
4×	`exp-prod` `rem-log-exp` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `log-prod` `pow-exp` `log-pow` `*-commutative`
1×	`unpow-prod-down` `associate-r` `exp-sum` `cbrt-unprod` `rem-exp-log`

Calls

4 calls:

Slowest

47.0ms	(exp (log (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
38.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
23.0ms	(log (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
0.0ms	(* PI u2)

series1.5s

Calls

4 calls:

Slowest

545.0ms	(log (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
488.0ms	(exp (log (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
465.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
43.0ms	(* PI u2)

simplify3.6s

Calls

30 calls:

Slowest

416.0ms	(- (log (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) (* 2 (* (pow u2 2) (pow PI 2))))
372.0ms	(* (* (* (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)))
300.0ms	(- (* 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))))
286.0ms	(- (* 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))))
256.0ms	(log (* 1/6 (* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (cos (* 2 (* u2 PI))))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.5b	(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))))
0.4b	(* (* (* (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))

rewrite532.0ms

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

281.0ms	(* (* (* (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)))
214.0ms	(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))))
17.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
8.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series2.8s

Calls

4 calls:

Slowest

909.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
873.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
503.0ms	(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))))
490.0ms	(* (* (* (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

1.1s	(* (* (* (* (* (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))))
994.0ms	(+ (+ (+ (* (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) (* (cos (* (* PI u2) 2)) 1/6))) (log (* (cos (* (* PI u2) 2)) 1/6))))
705.0ms	(+ (+ (+ (* (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))))
688.0ms	(+ (+ (+ (* (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))))
683.0ms	(* (* (* (* (* (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))))

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))
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	(* PI u2)

rewrite399.0ms

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

227.0ms	(* (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)))
167.0ms	(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)

series1.4s

Calls

4 calls:

Slowest

508.0ms	(* (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)))
463.0ms	(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))))
337.0ms	(pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5))
47.0ms	(* PI u2)

simplify7.8s

Calls

37 calls:

Slowest

707.0ms	(+ (* (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))))
619.0ms	(+ (* (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))))
615.0ms	(+ (* (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))))
584.0ms	(- (* (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))))
574.0ms	(* (* (* (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5)) (pow (* -2 (log u1)) (+ (+ 0.5 0.5) 0.5))) (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) (* (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))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch7.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.5s	8000×	body	80	valid
464.0ms	8000×	pre	80	true