Details

sample78.0ms

Algorithm

intervals

Results

63.0ms

310×

body

valid

simplify453.0ms

Calls

1 calls:

Slowest

453.0ms

(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize26.0ms

Local error

Found 4 expressions with local error:

10.3b	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
3.6b	(- (* b b) (* a a))
0.5b	(/ PI (- (* b b) (* a a)))
0.2b	(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

43×	`associate-/r/`
42×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`div-inv`
21×	`add-cube-cbrt`
19×	`associate-/r*`
18×	`flip3--` `flip--`
8×	`frac-sub`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`pow1` `insert-posit16` `distribute-lft-out--`
3×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`

Calls

4 calls:

Slowest

5.0ms	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
2.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))
2.0ms	(- (* b b) (* a a))
1.0ms	(/ PI (- (* b b) (* a a)))

series132.0ms

Calls

4 calls:

Slowest

60.0ms	(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
34.0ms	(/ PI (- (* b b) (* a a)))
19.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))
19.0ms	(- (* b b) (* a a))

simplify19.6s

Calls

130 calls:

Slowest

747.0ms	(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
617.0ms	(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
531.0ms	(/ (/ 1 (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
445.0ms	(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))
418.0ms	(/ (/ PI (- (* b b) (* a a))) (+ (* (/ 1 a) (/ 1 a)) (+ (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.1b

localize14.0ms

Local error

Found 4 expressions with local error:

10.3b	(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
0.3b	(/ PI (+ b a))
0.2b	(/ 2 (- (/ 1 a) (/ 1 b)))
0.1b	(/ (/ PI (+ b a)) (- b a))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
155×	`associate-/r/`
126×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
69×	`div-inv`
35×	`flip3--` `flip--`
30×	`associate-/l*`
29×	`flip3-+` `flip-+`
26×	`frac-sub`
21×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `distribute-lft-out--` `add-log-exp`
2×	`associate-/l/`
1×	`difference-of-squares`

Calls

4 calls:

Slowest

22.0ms	(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
4.0ms	(/ (/ PI (+ b a)) (- b a))
3.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))
1.0ms	(/ PI (+ b a))

series228.0ms

Calls

4 calls:

Slowest

92.0ms	(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
66.0ms	(/ (/ PI (+ b a)) (- b a))
49.0ms	(/ PI (+ b a))
21.0ms	(/ 2 (- (/ 1 a) (/ 1 b)))

simplify1.3m

Calls

447 calls:

Slowest

941.0ms	(/ (/ (* (cbrt (/ PI (+ b a))) (cbrt (/ PI (+ b a)))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
881.0ms	(/ (/ (/ PI (+ (pow b 3) (pow a 3))) (sqrt (- b a))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
809.0ms	(/ (/ (sqrt (/ PI (+ b a))) (cbrt (- b a))) (/ 1 (- (/ 1 a) (/ 1 b))))
775.0ms	(/ (/ (/ PI (+ (pow b 3) (pow a 3))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
629.0ms	(/ (/ (* (cbrt (/ PI (+ b a))) (cbrt (/ PI (+ b a)))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a))
0.2b	(/ (/ 1 a) b)
0.2b	(* (/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a)) (/ (/ 1 a) b))
0.2b	(* (+ b a) (/ 2 (- b a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
41×	`associate-/r/`
36×	`associate-l`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`frac-times` `associate-*l/`
16×	`flip3-+` `flip-+`
13×	`add-cbrt-cube` `add-exp-log` `div-inv` `associate-/l*`
10×	`associate-r`
9×	`associate-*r/`
8×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `*-commutative` `associate-/l/`

Calls

4 calls:

Slowest

12.0ms	(/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a))
10.0ms	(* (/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a)) (/ (/ 1 a) b))
6.0ms	(/ (/ 1 a) b)
4.0ms	(* (+ b a) (/ 2 (- b a)))

series183.0ms

Calls

4 calls:

Slowest

81.0ms	(* (/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a)) (/ (/ 1 a) b))
63.0ms	(/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a))
31.0ms	(* (+ b a) (/ 2 (- b a)))
8.0ms	(/ (/ 1 a) b)

simplify21.6s

Calls

144 calls:

Slowest

672.0ms	(* (/ (* (* (/ PI (* (+ b a) (/ 2 (- b a)))) (/ PI (* (+ b a) (/ 2 (- b a))))) (/ PI (* (+ b a) (/ 2 (- b a))))) (* (* (- b a) (- b a)) (- b a))) (* (* (/ (/ 1 a) b) (/ (/ 1 a) b)) (/ (/ 1 a) b)))
660.0ms	(* (/ (/ PI (* (+ b a) (/ 2 (- b a)))) (- b a)) (/ (/ 1 a) b))
534.0ms	(* (+ (* b b) (- (* a a) (* b a))) (- b a))
479.0ms	(/ (/ PI (* (- (* b b) (* a a)) (/ 2 (- b a)))) (* (cbrt (- b a)) (cbrt (- b a))))
466.0ms	(* (/ PI (* (+ b a) (/ 2 (- b a)))) (/ (/ 1 a) b))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ PI (* (+ b a) 2))
0.2b	(/ (/ (/ PI (* (+ b a) 2)) 1) (* a b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `-un-lft-identity` `times-frac` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `div-inv` `associate-/l`
2×	`pow1` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-/r/` `insert-posit16` `add-log-exp`
1×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l/`

Calls

2 calls:

Slowest

15.0ms	(/ (/ (/ PI (* (+ b a) 2)) 1) (* a b))
2.0ms	(/ PI (* (+ b a) 2))

series139.0ms

Calls

2 calls:

Slowest

71.0ms	(/ (/ (/ PI (* (+ b a) 2)) 1) (* a b))
68.0ms	(/ PI (* (+ b a) 2))

simplify1.2s

Calls

22 calls:

Slowest

265.0ms	(/ (* (* (/ (/ PI (* (+ b a) 2)) 1) (/ (/ PI (* (+ b a) 2)) 1)) (/ (/ PI (* (+ b a) 2)) 1)) (* (* (* a b) (* a b)) (* a b)))
262.0ms	(- (log (/ (/ PI (* (+ b a) 2)) 1)) (log (* a b)))
129.0ms	(/ (/ (/ PI (* (+ b a) 2)) 1) b)
91.0ms	(/ (/ PI (* (+ b a) 2)) a)
63.0ms	(/ (* (cbrt (/ (/ PI (* (+ b a) 2)) 1)) (cbrt (/ (/ PI (* (+ b a) 2)) 1))) a)

prune342.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.5s

9635×

body

valid