Details

sample82.0ms

Algorithm

intervals

Results

65.0ms

310×

body

valid

simplify412.0ms

Calls

1 calls:

Slowest

412.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize22.0ms

Local error

Found 4 expressions with local error:

5.8b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
4.6b	(/ (/ PI (- (* b b) (* a a))) a)
3.6b	(- (* b b) (* a a))
3.6b	(- (* b b) (* a a))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
6×	`associate-/l*`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `div-inv` `difference-of-squares`
1×	`clear-num` `frac-2neg` `fma-udef` `associate-/l/`

Calls

4 calls:

Slowest

4.0ms	(/ (/ PI (- (* b b) (* a a))) a)
3.0ms	(- (* b b) (* a a))
3.0ms	(- (* b b) (* a a))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series194.0ms

Calls

4 calls:

Slowest

78.0ms	(/ (/ PI (- (* b b) (* a a))) a)
65.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
27.0ms	(- (* b b) (* a a))
24.0ms	(- (* b b) (* a a))

simplify1.2s

Calls

26 calls:

Slowest

341.0ms	(/ PI (- (pow (* b b) 3) (pow (* a a) 3)))
272.0ms	(/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a))))
167.0ms	(sqrt (/ PI (- (* b b) (* a a))))
138.0ms	(* (cbrt (/ PI (- (* b b) (* a a)))) (cbrt (/ PI (- (* b b) (* a a)))))
59.0ms	(/ (exp (* b b)) (exp (* a a)))

prune931.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.7b

localize28.0ms

Local error

Found 4 expressions with local error:

5.8b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ PI (/ a (/ 1 (- (* b b) (* a a))))))
4.6b	(/ a (/ 1 (- (* b b) (* a a))))
3.6b	(- (* b b) (* a a))
3.6b	(- (* b b) (* a a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
6×	`associate-/r*`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-/r/` `flip--`
2×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `difference-of-squares`
1×	`clear-num` `frac-2neg` `fma-udef`

Calls

4 calls:

Slowest

5.0ms	(- (* b b) (* a a))
5.0ms	(- (* b b) (* a a))
2.0ms	(/ a (/ 1 (- (* b b) (* a a))))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ PI (/ a (/ 1 (- (* b b) (* a a))))))

series170.0ms

Calls

4 calls:

Slowest

73.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ PI (/ a (/ 1 (- (* b b) (* a a))))))
42.0ms	(/ a (/ 1 (- (* b b) (* a a))))
28.0ms	(- (* b b) (* a a))
27.0ms	(- (* b b) (* a a))

simplify1.3s

Calls

29 calls:

Slowest

180.0ms	(cbrt (/ 1 (- (* b b) (* a a))))
161.0ms	(/ 1 (- (* b b) (* a a)))
146.0ms	(/ 1 (- (* b b) (* a a)))
143.0ms	(sqrt (/ 1 (- (* b b) (* a a))))
138.0ms	(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))

prune955.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.7b

localize29.0ms

Local error

Found 4 expressions with local error:

10.3b	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
3.6b	(- (* b b) (* a a))
0.4b	(/ 1 (- (* b b) (* a a)))
0.2b	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

33×	`prod-diff`
28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
23×	`div-inv`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`frac-times` `add-exp-log`
14×	`associate-r`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-*l/`
8×	`flip3--` `associate-*r/` `flip--`
7×	`prod-exp`
6×	`add-log-exp`
5×	`associate-l` `un-div-inv` `frac-sub`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`rec-exp` `sub-neg` `difference-of-squares`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `pow-flip` `inv-pow`

Calls

4 calls:

Slowest

37.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
5.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
4.0ms	(- (* b b) (* a a))
2.0ms	(/ 1 (- (* b b) (* a a)))

series242.0ms

Calls

4 calls:

Slowest

96.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
86.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
32.0ms	(/ 1 (- (* b b) (* a a)))
28.0ms	(- (* b b) (* a a))

simplify30.5s

Calls

124 calls:

Slowest

1.0s	(* (* 2 (- (* b b) (* a a))) (+ (/ 1 a) (/ 1 b)))
846.0ms	(* (fma (- (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))))) (* (/ PI 2) (/ 1 (- (* b b) (* a a)))))
633.0ms	(* (* PI (/ 1 (- (* b b) (* a a)))) (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
632.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))))))
626.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`times-frac` `associate-/r/` `associate-/l*`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `div-inv`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `div-exp` `associate-/l/`

Calls

2 calls:

Slowest

8.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
1.0ms	(/ PI (+ b a))

series120.0ms

Calls

2 calls:

Slowest

76.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
44.0ms	(/ PI (+ b a))

simplify1.8s

Calls

30 calls:

Slowest

352.0ms	(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
293.0ms	(- (log (/ PI (+ b a))) (log (* 2 (* a b))))
280.0ms	(/ (/ PI (- (* b b) (* a a))) 2)
270.0ms	(/ (+ (* b b) (- (* a a) (* b a))) (* a b))
117.0ms	(/ PI (- (* b b) (* a a)))

prune410.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.9s

9635×

body

valid