Details

sample56.0ms

Algorithm

intervals

Results

34.0ms

300×

body

valid

simplify2.4s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite279.0ms

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:

75.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
11.0ms	(- (* b b) (* a a))
167.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
64.0ms	(/ 1.0 (- (* b b) (* a a)))
52.0ms	(- (* b b) (* a a))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.6s

Counts

165 → 165

Iterations

Useful iterations: 2 (776.0ms)

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

prune647.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
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))

rewrite664.0ms

Algorithm

rewrite-expression-head

Rules

286×	`add-sqr-sqrt`
265×	`times-frac`
232×	`*-un-lft-identity`
85×	`distribute-lft-out--`
80×	`add-cube-cbrt`
79×	`associate-l`
73×	`difference-of-squares`
59×	`add-exp-log` `add-cbrt-cube`
28×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
19×	`associate-r`
18×	`cbrt-undiv` `div-exp`
12×	`associate-/l*`
11×	`pow1`
6×	`frac-times` `associate-*r/` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `unswap-sqr`
3×	`associate-/l/` `distribute-lft-out`
2×	`*-commutative` `frac-sub`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `clear-num` `flip-+`

Counts

4 → 276

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
182.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
247.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
157.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series379.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (/ 1.0 a) (/ 1.0 b))
149.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
113.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
75.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify2.2s

Counts

288 → 288

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	388	6213
1	1181	6052
2	3636	5342
done	5001	5342

prune928.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
143×	`times-frac`
132×	`*-un-lft-identity`
56×	`add-exp-log` `add-cbrt-cube`
48×	`distribute-lft-out--`
46×	`add-cube-cbrt`
41×	`difference-of-squares`
20×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
17×	`div-inv`
13×	`associate-l` `associate-/l*`
9×	`pow1` `associate-/r*`
6×	`associate-*l/` `associate-/l/` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `frac-sub` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `*-commutative` `flip-+`

Counts

4 → 194

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
184.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
94.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
153.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series334.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1.0 a) (/ 1.0 b))
130.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
55.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
106.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.4s

Counts

206 → 206

Iterations

Useful iterations: 2 (621.0ms)

Iter	Nodes	Cost
0	325	4481
1	879	4338
2	2844	3698
done	5000	3698

prune674.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.7b	(/ PI (* a b))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`cbrt-undiv` `div-exp`
7×	`times-frac`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`prod-exp` `associate-/r*` `cbrt-unprod`
4×	`associate-/l*`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r/` `div-inv` `distribute-lft-out` `add-log-exp`
1×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/`

Counts

2 → 51

Calls

2 calls:

46.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
8.0ms	(/ PI (* a b))

series131.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
35.0ms	(/ PI (* a b))

simplify963.0ms

Counts

57 → 57

Iterations

Useful iterations: 2 (210.0ms)

Iter	Nodes	Cost
0	107	688
1	284	659
2	1174	527
done	5000	527

prune106.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes54.0ms

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	11	13
1	16	13
done	16	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

9496×

body

valid