Details

sample87.0ms

Algorithm

intervals

Results

67.0ms

300×

body

valid

simplify2.5s

Counts: 1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.9b

localize40.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* (- b a) 2)))
0.3b	(/ PI b)
0.3b	(/ PI a)
0.0b	(- (/ PI a) (/ PI b))

rewrite135.0ms

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-*l/` `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-*r/` `frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 323

Calls

4 calls:

Slowest

101.0ms	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* (- b a) 2)))
13.0ms	(- (/ PI a) (/ PI b))
4.0ms	(/ PI b)
4.0ms	(/ PI a)

series241.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(/ (- (/ PI a) (/ PI b)) (* (+ a b) (* (- b a) 2)))
47.0ms	(/ PI b)
40.0ms	(/ PI a)
32.0ms	(- (/ PI a) (/ PI b))

simplify1.6s

Counts: 335 → 335

prune4.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
0.3b	(/ PI (+ a b))
0.2b	(* (/ PI (+ a b)) (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
323×	`add-sqr-sqrt`
300×	`*-un-lft-identity`
222×	`add-cube-cbrt`
169×	`prod-diff`
47×	`div-inv`
36×	`difference-of-squares`
32×	`add-cbrt-cube` `add-exp-log`
28×	`distribute-lft-out--`
25×	`associate-r`
22×	`associate-/l*`
18×	`associate-l`
13×	`fma-neg`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`distribute-lft-out`
6×	`pow1` `add-log-exp`
5×	`associate-/r` `associate-l/`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `frac-sub` `flip-+` `unswap-sqr`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 384

Calls

4 calls:

Slowest

133.0ms	(* (/ PI (+ a b)) (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
39.0ms	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
14.0ms	(- (/ 1 a) (/ 1 b))
8.0ms	(/ PI (+ a b))

series225.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(* (/ PI (+ a b)) (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
57.0ms	(/ PI (+ a b))
53.0ms	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
15.0ms	(- (/ 1 a) (/ 1 b))

simplify620.0ms

Counts: 396 → 396

prune6.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
0.3b	(* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
0.2b	(/ (* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))) (+ a b))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

357×	`times-frac`
306×	`add-sqr-sqrt`
276×	`*-un-lft-identity`
208×	`add-cube-cbrt`
169×	`prod-diff`
46×	`div-inv`
36×	`difference-of-squares`
32×	`add-cbrt-cube` `add-exp-log`
28×	`distribute-lft-out--`
25×	`associate-r`
20×	`associate-/l*`
13×	`fma-neg`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3--` `associate-*l/` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
3×	`associate-l`
2×	`clear-num` `frac-2neg` `associate-*r/` `frac-sub` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 357

Calls

4 calls:

Slowest

79.0ms	(* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
77.0ms	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
54.0ms	(/ (* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))) (+ a b))
14.0ms	(- (/ 1 a) (/ 1 b))

series275.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(/ (* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))) (+ a b))
66.0ms	(/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2))
64.0ms	(* PI (/ (- (/ 1 a) (/ 1 b)) (* (- b a) 2)))
15.0ms	(- (/ 1 a) (/ 1 b))

simplify1.7s

Counts: 369 → 369

prune5.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ PI (* a b))
0.2b	(/ (* 1/2 (/ PI (* a b))) (+ a b))
0.0b	(* 1/2 (/ PI (* a b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `times-frac` `div-exp` `add-cube-cbrt`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr` `associate-/l/`

Counts

3 → 87

Calls

3 calls:

Slowest

33.0ms	(* 1/2 (/ PI (* a b)))
29.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
11.0ms	(/ PI (* a b))

series178.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

100.0ms	(/ (* 1/2 (/ PI (* a b))) (+ a b))
40.0ms	(* 1/2 (/ PI (* a b)))
36.0ms	(/ PI (* a b))

simplify3.9s

Counts: 96 → 96

prune979.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes173.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s

9589×

body

valid