Details

sample288.0ms

Algorithm

intervals

Results

174.0ms	256×	body	80	valid
52.0ms	256×	pre	80	true

simplify191.0ms

Calls

1 calls:

Slowest

190.0ms

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
0.2b	(* (* 2 PI) u2)
0.1b	(pow (* -2 (log u1)) 0.5)
0.0b	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

44.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
14.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
5.0ms	(* (* 2 PI) u2)
3.0ms	(pow (* -2 (log u1)) 0.5)

series2.4s

Calls

4 calls:

Slowest

1.5s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
514.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
375.0ms	(pow (* -2 (log u1)) 0.5)
37.0ms	(* (* 2 PI) u2)

simplify1.7s

Calls

26 calls:

Slowest

336.0ms	(- (+ 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))))
172.0ms	(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
169.0ms	(pow (* -2 (- (log -1) (log (/ -1 u1)))) 0.5)
150.0ms	(+ (log (/ 1 6)) (* (log (* -2 (log u1))) 0.5))
144.0ms	(+ (log (/ 1 6)) (* (log (* -2 (log u1))) 0.5))

prune825.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (* (log u1) -2) 0.5) 6)
0.2b	(* (* 2 PI) u2)
0.1b	(pow (* (log u1) -2) 0.5)
0.0b	(+ (* (/ (pow (* (log u1) -2) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`add-cbrt-cube` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`unpow-prod-down`
1×	`pow-to-exp` `+-commutative` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+` `div-inv`

Calls

4 calls:

Slowest

13.0ms	(+ (* (/ (pow (* (log u1) -2) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)
5.0ms	(/ (pow (* (log u1) -2) 0.5) 6)
3.0ms	(pow (* (log u1) -2) 0.5)
3.0ms	(* (* 2 PI) u2)

series2.0s

Calls

4 calls:

Slowest

896.0ms	(/ (pow (* (log u1) -2) 0.5) 6)
596.0ms	(+ (* (/ (pow (* (log u1) -2) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)
416.0ms	(pow (* (log u1) -2) 0.5)
44.0ms	(* (* 2 PI) u2)

simplify1.2s

Calls

18 calls:

Slowest

361.0ms	(- (+ 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))))
142.0ms	(+ (* 1/6 (* (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
136.0ms	(pow (* -2 (- (log -1) (log (/ -1 u1)))) 0.5)
124.0ms	(* 1/6 (pow (* (pow (- (log -1) (log (/ -1 u1))) 1.0) (pow -2 1.0)) 0.5))
122.0ms	(+ (* 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)

prune762.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-exp-log`
101×	`prod-exp`
46×	`add-cbrt-cube`
31×	`pow1`
29×	`cbrt-unprod`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`pow-prod-down`
12×	`pow-to-exp` `times-frac` `pow-exp`
11×	`associate-*l/`
9×	`associate-r` `associate-l`
4×	`pow-prod-up` `insert-posit16` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `-commutative` `div-inv`
2×	`unpow-prod-down` `pow-plus` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-*r/`

Calls

4 calls:

Slowest

390.0ms	(/ (- (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
137.0ms	(* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))))
6.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
6.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series3.7s

Calls

4 calls:

Slowest

1.1s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
1.0s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
966.0ms	(/ (- (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
623.0ms	(* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))))

simplify35.1s

Calls

124 calls:

Slowest

1.2s	(* (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))) (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))))
846.0ms	(* (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (* (* (/ 1 6) (/ 1 6)) (/ 1 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))
812.0ms	(* (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))
799.0ms	(* (* (* (* (* (/ 1 6) (/ 1 6)) (/ 1 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))) (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (/ 1 6) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))))
779.0ms	(* (* (* (* (* (/ 1 6) (/ 1 6)) (/ 1 6)) (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))) (* (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2))) (cos (* (* 2 PI) u2)))) (* (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))))

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0)) (* 0.5 0.5)) (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
0.4b	(* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0))
0.4b	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
0.2b	(* (* 2 PI) u2)

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
48×	`prod-exp`
22×	`pow-exp`
19×	`pow-to-exp`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`associate-l`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-l/` `-commutative` `associate-/l`
2×	`unpow-prod-down` `flip3--` `associate-/r/` `cbrt-unprod` `div-inv` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `cos-mult`

Calls

4 calls:

Slowest

185.0ms	(/ (- (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0)) (* 0.5 0.5)) (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
74.0ms	(* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0))
7.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
3.0ms	(* (* 2 PI) u2)

series2.6s

Calls

4 calls:

Slowest

939.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
902.0ms	(/ (- (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0)) (* 0.5 0.5)) (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
754.0ms	(* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0))
39.0ms	(* (* 2 PI) u2)

simplify17.8s

Calls

78 calls:

Slowest

648.0ms	(- (* 2/9 (/ (* (pow u2 2) (* (pow PI 2) (log u1))) (- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5))) (+ (* 0.25 (/ 1 (- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5))) (+ (* 0.08333333333333333 (* (/ (* (pow u2 2) (pow PI 2)) (pow (- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5) 2)) (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))) (+ (* 1/18 (/ (log u1) (- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5))) (* 1/54 (* (/ (* (pow u2 2) (pow PI 2)) (pow (- (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5) 2)) (pow (* (pow -2 1.0) (pow (log u1) 3.0)) 0.5)))))))
570.0ms	(- (* (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0)) (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0))) (* (* 0.5 0.5) (* 0.5 0.5)))
555.0ms	(+ (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (+ (* 0.5 0.5) (* (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)))
463.0ms	(/ (- (* (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36) (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 1.0)) (* 0.5 0.5)) (cbrt (- (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)))
456.0ms	(+ (log (* (* (cos (* u2 (* PI 2))) (cos (* u2 (* PI 2)))) 1/36)) (* (+ (log (pow (- (log u1)) 1.0)) (log (* (pow -2 1.0) (pow -1 1.0)))) 1.0))

prune2.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes919.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.4s	8000×	body	80	valid
383.0ms	8000×	pre	80	true