Details

sample64.0ms

Algorithm

intervals

Results

43.0ms

298×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	378	21
4	1789	21
done	5000	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
3.7b	(- (* b b) (* a a))
7.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
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×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

89.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
204.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
82.0ms	(/ 1.0 (- (* b b) (* a a)))
44.0ms	(- (* b b) (* a a))
130.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify493.0ms

Counts

165 → 165

Iterations

Useful iterations: done (488.0ms)

Iter	Nodes	Cost
0	258	3239
1	873	3170
done	5000	2752

prune702.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
7.9b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite678.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log` `add-cbrt-cube`
103×	`add-sqr-sqrt`
90×	`times-frac`
88×	`*-un-lft-identity`
78×	`associate-r`
51×	`prod-exp` `cbrt-unprod`
48×	`add-cube-cbrt`
47×	`frac-times`
33×	`associate-*l/`
30×	`cbrt-undiv` `div-exp`
29×	`sqrt-prod`
20×	`pow1`
19×	`associate-*r/`
16×	`distribute-lft-out--`
15×	`associate-l`
14×	`difference-of-squares`
10×	`flip3--` `pow-prod-down` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`flip3-+` `diff-log` `flip-+`

Counts

4 → 246

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
55.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
447.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series987.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ 1.0 a) (/ 1.0 b))
254.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
201.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
471.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify840.0ms

Counts

258 → 258

Iterations

Useful iterations: done (828.0ms)

Iter	Nodes	Cost
0	392	6141
1	1432	5825
done	5000	4891

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
74×	`add-exp-log` `add-cbrt-cube`
65×	`*-un-lft-identity` `times-frac`
42×	`associate-r`
39×	`associate-*l/`
34×	`prod-exp` `cbrt-unprod`
33×	`add-cube-cbrt`
27×	`frac-times`
19×	`cbrt-undiv` `div-exp`
15×	`pow1` `associate-*r/` `associate-/l/`
14×	`associate-l` `sqrt-prod`
12×	`distribute-lft-out--`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
7×	`pow-prod-down` `div-inv`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`associate-/r*`
4×	`associate-/r/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 198

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
387.0ms	(/ (* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
500.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
71.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (/ 1.0 a) (/ 1.0 b))
429.0ms	(/ (* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
517.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
208.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))

simplify913.0ms

Counts

210 → 210

Iterations

Useful iterations: done (898.0ms)

Iter	Nodes	Cost
0	348	4671
1	1184	4436
done	5000	3734

prune962.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(/ (* PI (sqrt 1.0)) (* 2.0 (+ b a)))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-exp-log` `add-cbrt-cube`
39×	`add-sqr-sqrt`
34×	`prod-exp` `cbrt-unprod`
31×	`*-un-lft-identity`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
12×	`associate-r` `distribute-lft-out--`
11×	`add-cube-cbrt`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1`
8×	`associate-*r/`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-/r*` `flip--` `div-inv` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/l*`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
247.0ms	(/ (* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
301.0ms	(* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
35.0ms	(/ (* PI (sqrt 1.0)) (* 2.0 (+ b a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (/ 1.0 a) (/ 1.0 b))
374.0ms	(/ (* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
524.0ms	(* (* (/ (* PI (sqrt 1.0)) (* 2.0 (+ b a))) (sqrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
213.0ms	(/ (* PI (sqrt 1.0)) (* 2.0 (+ b a)))

simplify480.0ms

Counts

147 → 147

Iterations

Useful iterations: done (472.0ms)

Iter	Nodes	Cost
0	255	3655
1	879	3486
done	5000	2518

prune563.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes103.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	22	25
done	22	25

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

9581×

body

valid