Details

sample82.0ms

Algorithm

intervals

Results

65.0ms

300×

body

valid

simplify2.4s

Counts: 1 → 1

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize45.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* 2 (- b a))))
0.3b	(/ PI a)
0.2b	(/ PI b)
0.0b	(- (/ PI a) (/ PI b))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

303×	`times-frac`
253×	`add-sqr-sqrt`
241×	`*-un-lft-identity`
217×	`add-cube-cbrt`
169×	`prod-diff`
36×	`div-inv`
18×	`associate-/l*`
17×	`add-cbrt-cube` `add-exp-log`
15×	`distribute-lft-out--`
13×	`fma-neg`
12×	`difference-of-squares`
8×	`associate-*r/` `associate-/r/`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`expm1-log1p-u` `frac-times` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
2×	`associate-*l/` `frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 323

Calls

4 calls:

Slowest

81.0ms	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* 2 (- b a))))
16.0ms	(- (/ PI a) (/ PI b))
4.0ms	(/ PI b)
4.0ms	(/ PI a)

series214.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

103.0ms	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* 2 (- b a))))
53.0ms	(- (/ PI a) (/ PI b))
33.0ms	(/ PI b)
25.0ms	(/ PI a)

simplify1.6s

Counts: 335 → 335

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

346×	`times-frac`
276×	`*-un-lft-identity`
254×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
72×	`associate-/l*`
65×	`distribute-lft-out--`
52×	`difference-of-squares`
37×	`distribute-lft-out`
32×	`div-inv`
22×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
8×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`flip3-+` `div-sub` `flip-+`
2×	`flip3--` `prod-exp` `associate-*r/` `cbrt-unprod` `flip--`
1×	`frac-sub`

Counts

4 → 279

Calls

4 calls:

Slowest

62.0ms	(/ (/ (- (/ PI a) (/ PI b)) (+ a b)) (* 2 (- b a)))
44.0ms	(/ (- (/ PI a) (/ PI b)) (+ a b))
8.0ms	(/ PI b)
8.0ms	(/ PI a)

series343.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(/ (- (/ PI a) (/ PI b)) (+ a b))
130.0ms	(/ (/ (- (/ PI a) (/ PI b)) (+ a b)) (* 2 (- b a)))
38.0ms	(/ PI b)
26.0ms	(/ PI a)

simplify1.2s

Counts: 291 → 291

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI a)
0.2b	(/ PI b)
0.2b	(/ (- (/ PI a) (/ PI b)) (+ a b))
0.2b	(/ (/ (- (/ PI a) (/ PI b)) (+ a b)) (- b a))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

914×	`times-frac`
765×	`*-un-lft-identity`
711×	`add-sqr-sqrt`
253×	`add-cube-cbrt`
200×	`distribute-lft-out--`
171×	`difference-of-squares`
85×	`distribute-lft-out`
72×	`associate-/l*`
68×	`div-inv`
16×	`associate-/r/`
15×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
7×	`flip3-+` `flip-+`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`div-sub`
2×	`flip3--` `flip--`
1×	`frac-sub`

Counts

4 → 495

Calls

4 calls:

Slowest

76.0ms	(/ (- (/ PI a) (/ PI b)) (+ a b))
73.0ms	(/ (/ (- (/ PI a) (/ PI b)) (+ a b)) (- b a))
8.0ms	(/ PI a)
7.0ms	(/ PI b)

series313.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(/ (- (/ PI a) (/ PI b)) (+ a b))
91.0ms	(/ (/ (- (/ PI a) (/ PI b)) (+ a b)) (- b a))
46.0ms	(/ PI a)
44.0ms	(/ PI b)

simplify699.0ms

Counts: 507 → 507

prune5.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b))))
0.2b	(/ (+ a b) (- (/ 1 a) (/ 1 b)))
0.2b	(/ (/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b)))) (- b a))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

6696×	`times-frac`
4667×	`*-un-lft-identity`
4543×	`add-sqr-sqrt`
1777×	`add-cube-cbrt`
1101×	`difference-of-squares`
913×	`distribute-lft-out--`
438×	`distribute-lft-out`
434×	`div-inv`
261×	`associate-/l*`
169×	`prod-diff`
107×	`associate-/r*`
78×	`associate-/r/`
25×	`flip3--` `flip--`
24×	`frac-sub`
20×	`add-cbrt-cube` `add-exp-log`
13×	`fma-neg`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 2237

Calls

4 calls:

Slowest

42.0ms	(/ (/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b)))) (- b a))
28.0ms	(/ (+ a b) (- (/ 1 a) (/ 1 b)))
22.0ms	(/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b))))
17.0ms	(- (/ 1 a) (/ 1 b))

series376.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b))))
107.0ms	(/ (/ PI (/ (+ a b) (- (/ 1 a) (/ 1 b)))) (- b a))
107.0ms	(/ (+ a b) (- (/ 1 a) (/ 1 b)))
14.0ms	(- (/ 1 a) (/ 1 b))

simplify7.0s

Counts: 2249 → 2249

prune29.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.1s

9597×

body

valid