Details

sample66.0ms

Algorithm

intervals

Results

51.0ms

296×

body

valid

simplify448.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

448.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize53.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (/ PI (- (* b b) (* a a))) a)
3.4b	(- (* b b) (* a a))
3.4b	(- (* b b) (* a a))
2.9b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

Slowest

22.0ms	(/ (/ PI (- (* b b) (* a a))) a)
14.0ms	(- (* b b) (* a a))
8.0ms	(- (* b b) (* a a))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series322.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(/ (/ PI (- (* b b) (* a a))) a)
108.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
47.0ms	(- (* b b) (* a a))
38.0ms	(- (* b b) (* a a))

simplify21.0s

Counts

152 → 152

Calls

152 calls:

Slowest

715.0ms	(/ (+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a)))) (sqrt a))
568.0ms	(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
440.0ms	(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
429.0ms	(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
346.0ms	(- (log (/ PI (- (* b b) (* a a)))) (log a))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize52.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* b b) (* a a))
2.9b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
1.1b	(/ PI (- (* b b) (* a a)))
0.3b	(/ PI (- b a))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

Slowest

10.0ms	(/ PI (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
7.0ms	(/ PI (- b a))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
60.0ms	(- (* b b) (* a a))
59.0ms	(/ PI (- (* b b) (* a a)))
52.0ms	(/ PI (- b a))

simplify4.2s

Counts

92 → 117

Calls

92 calls:

Slowest

249.0ms	(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
182.0ms	(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
180.0ms	(/ (sqrt PI) (cbrt (- (* b b) (* a a))))
176.0ms	(/ 1 (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
176.0ms	(/ (* (cbrt PI) (cbrt PI)) (sqrt (- (* b b) (* a a))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.8b

localize61.0ms

Local error

Found 4 expressions with local error:

2.9b	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.3b	(/ PI (- b a))
0.3b	(/ PI (+ b a))
0.2b	(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
136×	`add-sqr-sqrt`
123×	`*-un-lft-identity`
80×	`add-cube-cbrt`
67×	`associate-r`
47×	`add-exp-log`
29×	`add-cbrt-cube`
20×	`div-exp`
18×	`associate-l`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`prod-exp` `associate-/r/`
11×	`cbrt-undiv`
9×	`associate-/r*` `unswap-sqr`
7×	`div-inv` `distribute-lft-out`
6×	`pow1` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 214

Calls

4 calls:

Slowest

54.0ms	(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
13.0ms	(/ PI (- b a))
8.0ms	(/ PI (+ b a))
0.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
99.0ms	(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
69.0ms	(/ PI (+ b a))
60.0ms	(/ PI (- b a))

simplify14.0s

Counts

210 → 226

Calls

210 calls:

Slowest

602.0ms	(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
540.0ms	(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
514.0ms	(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* a a) a)))
427.0ms	(+ (- 0 (log (+ b a))) (- (log (/ PI (- b a))) (log a)))
406.0ms	(+ (log (/ 1 (+ b a))) (log (/ (/ PI (- b a)) a)))

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize52.0ms

Local error

Found 4 expressions with local error:

2.9b	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (* a (- b a))) (+ b a)))
0.9b	(/ PI (* a (- b a)))
0.3b	(/ PI (+ b a))
0.2b	(/ (/ PI (* a (- b a))) (+ b a))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
63×	`*-un-lft-identity`
35×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r/`
15×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-*r/`
9×	`associate-/r*`
8×	`cbrt-undiv` `div-exp` `div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
1×	`fma-udef` `associate-/l/`

Counts

4 → 144

Calls

4 calls:

Slowest

33.0ms	(/ (/ PI (* a (- b a))) (+ b a))
9.0ms	(/ PI (* a (- b a)))
7.0ms	(/ PI (+ b a))
0.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (* a (- b a))) (+ b a)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (* a (- b a))) (+ b a)))
110.0ms	(/ (/ PI (* a (- b a))) (+ b a))
68.0ms	(/ PI (* a (- b a)))
63.0ms	(/ PI (+ b a))

simplify12.5s

Counts

152 → 156

Calls

152 calls:

Slowest

674.0ms	(- (- (log PI) (log (* a (- b a)))) (log (+ b a)))
505.0ms	(/ (/ (* (* PI PI) PI) (* (* (* a (- b a)) (* a (- b a))) (* a (- b a)))) (* (* (+ b a) (+ b a)) (+ b a)))
484.0ms	(/ (/ (* (* PI PI) PI) (* (* (* a a) a) (* (* (- b a) (- b a)) (- b a)))) (* (* (+ b a) (+ b a)) (+ b a)))
445.0ms	(/ (/ 1 (* a (- b a))) (+ b a))
442.0ms	(/ (/ 1 (* a (- b a))) (+ b a))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

regimes164.0ms

Accuracy

0% (0.2b remaining)

Error of 4.7b against oracle of 4.5b and baseline of 4.7b

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.9s

9562×

body

valid