Details

sample40.0ms

Algorithm

intervals

Results

22.0ms

310×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	377	21
4	1644	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
6.0b	(- (* b b) (* a a))
7.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite695.0ms

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:

80.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
14.0ms	(/ 1.0 (- (* b b) (* a a)))
11.0ms	(- (* b b) (* a a))
583.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
77.0ms	(/ 1.0 (- (* b b) (* a a)))
49.0ms	(- (* b b) (* a a))
126.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.4s

Counts

165 → 165

Iterations

Useful iterations: 2 (734.0ms)

Iter	Nodes	Cost
0	258	3239
1	776	3164
2	3267	2690
done	5000	2690

prune577.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

281×	`add-sqr-sqrt`
267×	`times-frac`
239×	`*-un-lft-identity`
87×	`add-cube-cbrt`
80×	`distribute-lft-out--`
79×	`associate-l`
69×	`difference-of-squares`
61×	`add-exp-log` `add-cbrt-cube`
27×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp` `associate-r`
15×	`associate-/l*`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-/r/`
7×	`distribute-lft-out`
6×	`frac-times` `associate-*r/`
4×	`pow-prod-down` `associate-*l/` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`div-sub` `frac-sub`

Counts

4 → 287

Calls

4 calls:

20.0ms	(/ 1.0 (+ b a))
203.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
179.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
115.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series409.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1.0 (+ b a))
167.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
124.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
69.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify2.4s

Counts

299 → 299

Iterations

Useful iterations: 2 (883.0ms)

Iter	Nodes	Cost
0	388	6222
1	1153	6055
2	3515	5355
done	5000	5355

prune951.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite507.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
59×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
49×	`times-frac`
33×	`add-cube-cbrt`
29×	`frac-times`
25×	`associate-l`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `associate-r/` `div-exp` `associate-r*`
17×	`associate-*l/`
15×	`associate-/l/`
11×	`pow1` `flip3--` `flip--`
10×	`frac-sub`
9×	`associate-/r*`
7×	`distribute-lft-out` `distribute-lft-out--`
6×	`associate-/r/` `div-inv` `difference-of-squares`
4×	`pow-prod-down` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 188

Calls

4 calls:

22.0ms	(/ 1.0 (+ b a))
174.0ms	(/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a)))) (- b a))
133.0ms	(* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a))))
160.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (+ b a))
120.0ms	(/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a)))) (- b a))
146.0ms	(* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a))))
143.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (+ b a)))

simplify2.0s

Counts

200 → 200

Iterations

Useful iterations: 2 (780.0ms)

Iter	Nodes	Cost
0	306	3974
1	876	3859
2	3767	3185
done	5000	3185

prune696.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite479.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
73×	`*-un-lft-identity`
58×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
22×	`cbrt-undiv` `div-exp`
18×	`prod-exp` `cbrt-unprod`
16×	`associate-/r/`
14×	`associate-*l/`
13×	`associate-l`
11×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
9×	`associate-/r*` `div-inv`
8×	`pow1` `associate-/l/` `distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`frac-times` `associate-*r/`
5×	`flip3--` `flip--`
4×	`frac-sub`
3×	`pow-prod-down` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-r` `*-commutative`

Counts

3 → 167

Calls

3 calls:

125.0ms	(/ (/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (+ b a)) (- b a))
163.0ms	(/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (+ b a))
183.0ms	(* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

series311.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (+ b a)) (- b a))
116.0ms	(/ (* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (+ b a))
86.0ms	(* (/ PI 2.0) (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

simplify1.8s

Counts

176 → 176

Iterations

Useful iterations: 2 (689.0ms)

Iter	Nodes	Cost
0	290	4663
1	851	4503
2	3644	3867
done	5002	3867

prune600.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes92.0ms

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	15	21
1	18	21
done	18	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.5s

9654×

body

valid