Details

sample168.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
51.0ms	256×	pre	80	true

simplify201.0ms

Calls

1 calls:

Slowest

200.0ms

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
0.2b	(* PI u2)
0.1b	(pow (* -2 (log u1)) 0.5)
0.0b	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))

rewrite68.0ms

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

43.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
19.0ms	(+ 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)

series1.4s

Calls

4 calls:

Slowest

514.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
502.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
355.0ms	(pow (* -2 (log u1)) 0.5)
55.0ms	(* PI u2)

simplify2.3s

Calls

22 calls:

Slowest

393.0ms	(* (* (* (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)))
315.0ms	(- (+ 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))))
273.0ms	(- (* 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))))
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)
166.0ms	(+ (* (log (* -2 (log u1))) 0.5) (log (* (cos (* (* PI u2) 2)) 1/6)))

prune886.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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

26.0ms	(* (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)))))
1.0ms	(log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
0.0ms	(* PI u2)

series1.6s

Calls

4 calls:

Slowest

572.0ms	(log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
503.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))
478.0ms	(exp (log (+ 0.5 (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))))
56.0ms	(* PI u2)

simplify5.0s

Calls

34 calls:

Slowest

441.0ms	(exp (log (+ (pow 0.5 3) (pow (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) 3))))
428.0ms	(- (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))))
371.0ms	(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))))))
364.0ms	(log (+ (pow 0.5 3) (pow (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) 3)))
348.0ms	(* (* (* (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)))

prune1.2s

Pruning

10 alts after pruning (9 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) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
0.5b	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
0.4b	(* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
0.3b	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))

rewrite690.0ms

Algorithm

rewrite-expression-head

Rules

355×	`add-exp-log`
322×	`prod-exp`
59×	`add-cbrt-cube`
58×	`pow-to-exp` `pow-exp`
40×	`cbrt-unprod`
23×	`pow1`
6×	`pow-plus` `associate-l` `pow-prod-up`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow2` `associate-r` `*-commutative`
2×	`pow3`
1×	`cbrt-prod` `unpow-prod-down` `pow1/3` `rem-cbrt-cube`

Calls

4 calls:

Slowest

264.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
238.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
162.0ms	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
20.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))

series2.1s

Calls

4 calls:

Slowest

587.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
525.0ms	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
506.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))
468.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))

simplify52.3s

Calls

139 calls:

Slowest

1.2s	(* (* (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (* (* (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)))) (* (* (* (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))))
988.0ms	(* (* (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))) (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))) (* (* (* (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))))
927.0ms	(* (* (* (* (* (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))) (* (* (* (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)))) (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
921.0ms	(* (* (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (* (* (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)))) (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))
845.0ms	(* (* (* (* (* (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))) (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)))) (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* PI u2) 2)) 1/6))))

prune2.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (log u1) 3.0)
0.6b	(cbrt (* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
0.5b	(* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216))
0.2b	(* (* 2 PI) u2)

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

237.0ms	(* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216))
155.0ms	(cbrt (* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
3.0ms	(* (* 2 PI) u2)
2.0ms	(pow (log u1) 3.0)

series1.6s

Calls

4 calls:

Slowest

586.0ms	(cbrt (* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
483.0ms	(* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216))
400.0ms	(pow (log u1) 3.0)
85.0ms	(* (* 2 PI) u2)

simplify5.3s

Calls

32 calls:

Slowest

732.0ms	(- (* (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))))
374.0ms	(* (* (* (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5) (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5)) (pow (* (pow (log u1) 3.0) (pow -2 3.0)) 0.5)) (* (* (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)) (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
350.0ms	(+ (* (+ (log (pow (log u1) 3.0)) (log (pow -2 3.0))) 0.5) (log (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
344.0ms	(+ (* (+ (* (log (log u1)) 3.0) (log (pow -2 3.0))) 0.5) (log (* (* (cos (* (* 2 PI) u2)) (* (cos (* (* 2 PI) u2)) (cos (* (* 2 PI) u2)))) 1/216)))
323.0ms	(- (* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5)) (* 1/36 (* (* (pow u2 2) (pow PI 2)) (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5))))

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes603.0ms

Accuracy

0% (0.6b remaining)

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

bsearch4.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
380.0ms	8000×	pre	80	true