Details

sample83.0ms

Algorithm

intervals

Results

64.0ms

310×

body

valid

simplify453.0ms

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize41.0ms

Local error

Found 4 expressions with local error:

9.1b	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
6.9b	(- (* b b) (* a a))
0.3b	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

761×	`times-frac`
624×	`add-sqr-sqrt`
603×	`*-un-lft-identity`
571×	`add-cube-cbrt`
508×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
89×	`div-inv`
21×	`difference-of-squares`
19×	`associate-r`
18×	`add-cbrt-cube` `add-exp-log`
14×	`fma-neg` `distribute-lft-out--`
13×	`associate-l`
8×	`add-log-exp`
7×	`flip3--` `flip--` `associate-/l/`
6×	`frac-times` `pow1` `associate-*r/`
5×	`cbrt-undiv` `div-exp` `frac-sub`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`diff-log` `associate-*l/` `associate-/r/` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 668

Calls

4 calls:

Slowest

62.0ms	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
56.0ms	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
16.0ms	(- (* b b) (* a a))
14.0ms	(- (/ 1 a) (/ 1 b))

series255.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
78.0ms	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
48.0ms	(- (* b b) (* a a))
23.0ms	(- (/ 1 a) (/ 1 b))

simplify1.8s

Counts: 1216 → 680

prune9.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
0.2b	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a))
0.1b	(/ (/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a)) (- b a))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

835×	`times-frac`
669×	`add-sqr-sqrt`
664×	`*-un-lft-identity`
594×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
96×	`div-inv`
32×	`add-cbrt-cube` `add-exp-log`
29×	`difference-of-squares`
25×	`distribute-lft-out--`
19×	`associate-r`
16×	`associate-/r/`
13×	`cbrt-undiv` `fma-neg` `div-exp` `associate-l`
11×	`associate-/l*`
9×	`associate-/r*`
8×	`distribute-lft-out` `associate-/l/`
7×	`flip3-+` `flip-+`
6×	`frac-times` `pow1` `flip3--` `prod-exp` `associate-*r/` `cbrt-unprod` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 739

Calls

4 calls:

Slowest

88.0ms	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
77.0ms	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a))
70.0ms	(/ (/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a)) (- b a))
28.0ms	(- (/ 1 a) (/ 1 b))

series316.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(/ (/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a)) (- b a))
104.0ms	(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (+ b a))
84.0ms	(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
23.0ms	(- (/ 1 a) (/ 1 b))

simplify2.0s

Counts: 1334 → 751

prune10.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

843×	`times-frac`
746×	`add-sqr-sqrt`
683×	`*-un-lft-identity`
359×	`add-cube-cbrt`
169×	`prod-diff`
147×	`difference-of-squares`
123×	`distribute-lft-out--`
101×	`associate-r`
88×	`div-inv`
58×	`associate-l`
32×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
27×	`distribute-lft-out`
13×	`cbrt-undiv` `fma-neg` `div-exp`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 635

Calls

4 calls:

Slowest

76.0ms	(/ (- (/ 1 a) (/ 1 b)) (- b a))
71.0ms	(* (/ (/ PI 2) (+ b a)) (/ (- (/ 1 a) (/ 1 b)) (- b a)))
26.0ms	(- (/ 1 a) (/ 1 b))
24.0ms	(/ (/ PI 2) (+ b a))

series311.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(* (/ (/ PI 2) (+ b a)) (/ (- (/ 1 a) (/ 1 b)) (- b a)))
95.0ms	(/ (/ PI 2) (+ b a))
42.0ms	(/ (- (/ 1 a) (/ 1 b)) (- b a))
23.0ms	(- (/ 1 a) (/ 1 b))

simplify1.3s

Counts: 984 → 647

prune7.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2) (/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a)))
0.2b	(/ (- (/ 1 a) (/ 1 b)) (+ b a))
0.1b	(/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a))
0.0b	(- (/ 1 a) (/ 1 b))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

2893×	`times-frac`
2343×	`*-un-lft-identity`
2306×	`add-sqr-sqrt`
755×	`add-cube-cbrt`
615×	`difference-of-squares`
515×	`distribute-lft-out--`
416×	`associate-r`
242×	`div-inv`
229×	`distribute-lft-out`
169×	`prod-diff`
101×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
13×	`cbrt-undiv` `fma-neg` `div-exp` `associate-l`
12×	`flip3-+` `flip-+`
9×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
3×	`div-sub`
2×	`clear-num` `frac-2neg` `frac-sub`
1×	`frac-times` `sub-neg` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1314

Calls

4 calls:

Slowest

90.0ms	(* (/ PI 2) (/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a)))
64.0ms	(/ (- (/ 1 a) (/ 1 b)) (+ b a))
55.0ms	(/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a))
15.0ms	(- (/ 1 a) (/ 1 b))

series306.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

106.0ms	(* (/ PI 2) (/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a)))
94.0ms	(/ (- (/ 1 a) (/ 1 b)) (+ b a))
78.0ms	(/ (/ (- (/ 1 a) (/ 1 b)) (+ b a)) (- b a))
27.0ms	(- (/ 1 a) (/ 1 b))

simplify2.3s

Counts: 2003 → 1326

prune14.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

9637×

body

valid