Details

sample58.0ms

Algorithm

intervals

Results

35.0ms

302×

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	378	21
4	1789	21
done	5000	21

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
5.7b	(- (* b b) (* a a))
8.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite297.0ms

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:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
19.0ms	(/ 1.0 (- (* b b) (* a a)))
16.0ms	(- (* b b) (* a a))
200.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
67.0ms	(/ 1.0 (- (* b b) (* a a)))
58.0ms	(- (* b b) (* a a))
127.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify542.0ms

Counts

165 → 165

Iterations

Useful iterations: done (532.0ms)

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

prune710.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.9b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

43.0ms	(- (/ 1.0 a) (/ 1.0 b))
88.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
18.0ms	(/ (/ PI 2.0) (+ b a))
158.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
95.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
57.0ms	(/ (/ PI 2.0) (+ b a))
127.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify697.0ms

Counts

285 → 285

Iterations

Useful iterations: done (688.0ms)

Iter	Nodes	Cost
0	405	5259
1	1335	5084
done	5001	4552

prune978.0ms

Pruning

9 alts after pruning (9 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 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite639.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `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`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
128.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
18.0ms	(/ (/ PI 2.0) (+ b a))
457.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
104.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
58.0ms	(/ (/ PI 2.0) (+ b a))
112.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify572.0ms

Counts

202 → 202

Iterations

Useful iterations: done (562.0ms)

Iter	Nodes	Cost
0	336	3777
1	964	3626
done	5001	3190

prune754.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite628.0ms

Algorithm

rewrite-expression-head

Rules

217×	`times-frac`
216×	`add-exp-log` `add-cbrt-cube`
173×	`*-un-lft-identity`
119×	`add-sqr-sqrt`
107×	`add-cube-cbrt`
89×	`prod-exp` `cbrt-unprod`
82×	`cbrt-undiv` `div-exp`
58×	`associate-r`
27×	`distribute-lft-out`
19×	`div-inv` `associate-/l*`
10×	`associate-r/` `associate-/r`
9×	`pow1` `associate-*l/`
7×	`associate-/l/`
6×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`flip3-+` `flip-+`
1×	`associate-l` `*-commutative`

Counts

4 → 304

Calls

4 calls:

245.0ms	(/ (/ (* (* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a))) 1.0) (* a b)) (- b a))
19.0ms	(/ (/ PI 2.0) (+ b a))
90.0ms	(* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a)))
247.0ms	(/ (* (* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a))) 1.0) (* a b))

series438.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (/ (* (* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a))) 1.0) (* a b)) (- b a))
70.0ms	(/ (/ PI 2.0) (+ b a))
123.0ms	(* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a)))
164.0ms	(/ (* (* (* 1.0 (- b a)) (/ (/ PI 2.0) (+ b a))) 1.0) (* a b))

simplify883.0ms

Counts

316 → 316

Iterations

Useful iterations: done (872.0ms)

Iter	Nodes	Cost
0	439	7867
1	1491	7436
done	5000	6130

prune1.1s

Pruning

10 alts after pruning (9 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	15	23
1	20	23
done	20	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

953.0ms

9582×

body

valid