Details

sample63.0ms

Algorithm

intervals

Results

34.0ms

302×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1848
3	385
2	90
1	31
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
4.4b	(- (* b b) (* a a))
7.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-cbrt-cube` `add-exp-log`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log`

Counts

4 → 501

Calls

4 calls:

40.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
20.0ms	(/ 1.0 (- (* b b) (* a a)))
16.0ms	(- (* b b) (* a a))
217.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
68.0ms	(/ 1.0 (- (* b b) (* a a)))
41.0ms	(- (* b b) (* a a))
152.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2914
0	886

prune4.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ a b))
7.6b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
61×	`add-cbrt-cube` `add-exp-log`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-l/` `associate-r/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

13.0ms	(/ 1.0 (- b a))
71.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
23.0ms	(/ (/ PI 2.0) (+ a b))
232.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- b a))
92.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
60.0ms	(/ (/ PI 2.0) (+ a b))
115.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.1s

Counts

646 → 646

Iterations

Iter	Nodes
done	5000
1	3394
0	1032

prune5.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ a b)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.2b	(/ (/ PI 2.0) (+ a b))
0.3b	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite750.0ms

Algorithm

rewrite-expression-head

Rules

1630×	`times-frac`
1285×	`*-un-lft-identity`
1240×	`add-sqr-sqrt`
1209×	`add-cube-cbrt`
1014×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
171×	`div-inv`
79×	`associate-l`
52×	`add-cbrt-cube` `add-exp-log`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 1314

Calls

4 calls:

9.0ms	(/ 1.0 (- b a))
306.0ms	(* (/ (/ PI 2.0) (+ a b)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
20.0ms	(/ (/ PI 2.0) (+ a b))
183.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 1.0 (- b a))
142.0ms	(* (/ (/ PI 2.0) (+ a b)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
63.0ms	(/ (/ PI 2.0) (+ a b))
96.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.0s

Counts

1326 → 1326

Iterations

Iter	Nodes
done	5001
0	1768

prune10.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (* a b)))
0.2b	(/ (/ PI 2.0) (+ a b))
0.6b	(/ 1.0 (* a b))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
152×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
58×	`associate-l`
49×	`add-cbrt-cube` `add-exp-log`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod` `div-inv`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 211

Calls

3 calls:

72.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (* a b)))
21.0ms	(/ (/ PI 2.0) (+ a b))
17.0ms	(/ 1.0 (* a b))

series227.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (* a b)))
89.0ms	(/ (/ PI 2.0) (+ a b))
35.0ms	(/ 1.0 (* a b))

simplify2.0s

Counts

220 → 220

Iterations

Iter	Nodes
done	5000
2	4558
1	880
0	291

prune909.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

9578×

body

valid