Details

sample46.0ms

Algorithm

intervals

Results

25.0ms

300×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	384	21
4	1663	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.2b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
10.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite304.0ms

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-exp-log` `add-cbrt-cube`
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-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

49.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
185.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
67.0ms	(/ 1.0 (- (* b b) (* a a)))
51.0ms	(- (* b b) (* a a))
115.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.8s

Counts

513 → 513

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	886	27857
1	2290	25797
done	5000	22403

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
10.6b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

1061×	`times-frac`
851×	`*-un-lft-identity`
814×	`add-sqr-sqrt`
695×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
97×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`associate-/l*`
14×	`frac-times` `associate-l`
13×	`fma-neg`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 875

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
118.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
48.0ms	(/ (/ 1.0 (+ b a)) (- b a))
293.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
83.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
75.0ms	(/ (/ 1.0 (+ b a)) (- b a))
138.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts

887 → 887

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1082	39230
1	2927	35734
done	5000	30775

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite697.0ms

Algorithm

rewrite-expression-head

Rules

745×	`times-frac`
600×	`add-sqr-sqrt`
593×	`*-un-lft-identity`
571×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
85×	`div-inv`
50×	`add-exp-log` `add-cbrt-cube`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`fma-neg`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `distribute-lft-out`
2×	`associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 665

Calls

4 calls:

68.0ms	(- (/ 1.0 a) (/ 1.0 b))
252.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
219.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms	(* PI (/ 1.0 (+ b a)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (/ 1.0 a) (/ 1.0 b))
109.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
112.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
73.0ms	(* PI (/ 1.0 (+ b a)))

simplify1.9s

Counts

677 → 677

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	857	30871
1	2222	27696
done	5001	22785

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

753×	`times-frac`
592×	`add-sqr-sqrt` `*-un-lft-identity`
568×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
87×	`div-inv`
50×	`add-exp-log` `add-cbrt-cube`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
13×	`fma-neg`
12×	`associate-r`
11×	`associate-/l*`
10×	`distribute-lft-out--`
9×	`pow1`
8×	`associate-*r/` `associate-/r/` `difference-of-squares`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/` `distribute-lft-out`
3×	`sub-neg` `flip3-+` `pow-prod-down` `frac-sub` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 664

Calls

4 calls:

70.0ms	(- (/ 1.0 a) (/ 1.0 b))
112.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
133.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
123.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (/ 1.0 a) (/ 1.0 b))
128.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
155.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
107.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts

676 → 676

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	862	28434
1	2189	25255
done	5000	20318

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes89.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	17	19
done	17	19

end0.0ms

sample965.0ms

Algorithm

intervals

Results

622.0ms

9518×

body

valid