Details

sample66.0ms

Algorithm

intervals

Results

50.0ms

308×

body

valid

simplify2.6s

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize24.0ms

Local error

Found 4 expressions with local error:

9.4b	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
5.5b	(- (* b b) (* a a))
0.3b	(/ PI b)
0.3b	(/ PI a)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

536×	`times-frac`
379×	`add-sqr-sqrt`
311×	`*-un-lft-identity`
175×	`add-cube-cbrt`
108×	`difference-of-squares`
85×	`distribute-lft-out--`
50×	`div-inv`
22×	`associate-/r*`
18×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `associate-/r/` `frac-sub`

Counts

4 → 320

Calls

4 calls:

Slowest

39.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
12.0ms	(- (* b b) (* a a))
5.0ms	(/ PI a)
4.0ms	(/ PI b)

series210.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

106.0ms	(/ (- (/ PI a) (/ PI b)) (/ (- (* b b) (* a a)) 1/2))
38.0ms	(- (* b b) (* a a))
34.0ms	(/ PI a)
32.0ms	(/ PI b)

simplify804.0ms

Counts: 332 → 332

prune3.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

2303×	`times-frac`
1896×	`add-sqr-sqrt`
1569×	`*-un-lft-identity`
681×	`add-cube-cbrt`
477×	`difference-of-squares`
397×	`distribute-lft-out--`
366×	`associate-r`
230×	`div-inv`
169×	`prod-diff`
32×	`add-cbrt-cube` `add-exp-log`
23×	`associate-/r*`
22×	`associate-/l*`
18×	`associate-l`
13×	`cbrt-undiv` `fma-neg` `div-exp`
7×	`distribute-lft-out`
6×	`pow1` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `frac-sub` `flip-+` `flip--`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1088

Calls

4 calls:

Slowest

76.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2))
73.0ms	(* (/ PI (+ a b)) (/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2)))
16.0ms	(/ PI (+ a b))
14.0ms	(- (/ 1 a) (/ 1 b))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(* (/ PI (+ a b)) (/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2)))
74.0ms	(/ PI (+ a b))
64.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2))
14.0ms	(- (/ 1 a) (/ 1 b))

simplify2.3s

Counts: 1100 → 1100

prune13.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))
0.3b	(/ PI (+ a b))
0.1b	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (/ (- b a) 1/2))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

821×	`times-frac`
662×	`add-sqr-sqrt`
655×	`*-un-lft-identity`
597×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
92×	`div-inv`
32×	`add-cbrt-cube` `add-exp-log`
24×	`difference-of-squares`
23×	`associate-/r*`
20×	`distribute-lft-out--`
19×	`associate-r`
18×	`associate-l`
13×	`cbrt-undiv` `fma-neg` `div-exp`
7×	`distribute-lft-out` `associate-/l/`
6×	`frac-times` `pow1` `prod-exp` `associate-*r/` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `associate-/r/` `frac-sub` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`sub-neg`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-*l/` `flip-+` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 726

Calls

4 calls:

Slowest

73.0ms	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))
56.0ms	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (/ (- b a) 1/2))
18.0ms	(- (/ 1 a) (/ 1 b))
12.0ms	(/ PI (+ a b))

series340.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))
132.0ms	(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (/ (- b a) 1/2))
46.0ms	(/ PI (+ a b))
29.0ms	(- (/ 1 a) (/ 1 b))

simplify1.8s

Counts: 738 → 738

prune8.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

2234×	`times-frac`
1799×	`add-sqr-sqrt`
1486×	`*-un-lft-identity`
572×	`add-cube-cbrt`
468×	`difference-of-squares`
390×	`distribute-lft-out--`
366×	`associate-r`
207×	`div-inv`
100×	`add-exp-log`
53×	`div-exp` `associate-l`
52×	`add-cbrt-cube`
38×	`associate-/r*`
26×	`associate-/l*`
25×	`cbrt-undiv` `distribute-lft-out`
21×	`prod-exp`
15×	`unswap-sqr`
9×	`cbrt-unprod`
8×	`rec-exp` `1-exp`
7×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `flip3-+` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `frac-sub` `flip-+` `pow-flip` `flip--` `inv-pow`

Counts

4 → 1027

Calls

4 calls:

Slowest

108.0ms	(* (/ 1 (/ (+ a b) PI)) (/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2)))
55.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2))
28.0ms	(/ (+ a b) PI)
15.0ms	(/ 1 (/ (+ a b) PI))

series671.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

427.0ms	(/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2))
117.0ms	(* (/ 1 (/ (+ a b) PI)) (/ (- (/ 1 a) (/ 1 b)) (/ (- b a) 1/2)))
82.0ms	(/ (+ a b) PI)
46.0ms	(/ 1 (/ (+ a b) PI))

simplify2.9s

Counts: 1039 → 1039

prune11.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

2.1s

9636×

body

valid