Details

sample49.0ms

Algorithm

intervals

Results

29.0ms

320×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
3.0b	(- (* b b) (* a a))
9.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite431.0ms

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:

47.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
24.0ms	(/ 1.0 (- (* b b) (* a a)))
20.0ms	(- (* b b) (* a a))
279.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
51.0ms	(/ 1.0 (- (* b b) (* a a)))
47.0ms	(- (* b b) (* a a))
148.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.0s

Counts

513 → 513

Iterations

Useful iterations: done (1.9s)

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

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (- b a))
0.1b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.4b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
9.7b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite796.0ms

Algorithm

rewrite-expression-head

Rules

578×	`times-frac`
486×	`add-sqr-sqrt`
475×	`*-un-lft-identity`
429×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-exp-log` `add-cbrt-cube`
78×	`associate-r`
58×	`div-inv`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times` `sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
18×	`distribute-lft-out--`
17×	`difference-of-squares`
15×	`associate-l`
10×	`flip3--` `pow-prod-down` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `distribute-lft-out` `associate-/l*` `unswap-sqr`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 625

Calls

4 calls:

26.0ms	(/ (sqrt 1.0) (- b a))
106.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
45.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
545.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (sqrt 1.0) (- b a))
313.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
221.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
390.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.2s

Counts

637 → 637

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	1023	33844
1	2775	31117
done	5001	27713

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))
0.3b	(* (/ (* PI 1.0) (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 665

Calls

4 calls:

43.0ms	(- (/ 1.0 a) (/ 1.0 b))
183.0ms	(/ (* (/ (* PI 1.0) (- b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
19.0ms	(/ (* PI 1.0) (- b a))
215.0ms	(* (/ (* PI 1.0) (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (/ 1.0 a) (/ 1.0 b))
154.0ms	(/ (* (/ (* PI 1.0) (- b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
72.0ms	(/ (* PI 1.0) (- b a))
103.0ms	(* (/ (* PI 1.0) (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts

677 → 677

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	856	30947
1	2224	27783
done	5001	22870

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.5b	(/ PI (* a b))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
3×	`associate-*r/`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 57

Calls

2 calls:

56.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
24.0ms	(/ PI (* a b))

series148.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
37.0ms	(/ PI (* a b))

simplify1.5s

Counts

63 → 63

Iterations

Useful iterations: 2 (396.0ms)

Iter	Nodes	Cost
0	122	941
1	367	902
2	1935	650
done	5000	650

prune152.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes135.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

9591×

body

valid