Details

sample60.0ms

Algorithm

intervals

Results

34.0ms

302×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	385	21
4	1860	21
done	5001	21

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.1b	(/ 1.0 (- (* b b) (* a a)))
3.4b	(- (* b b) (* a a))
9.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite499.0ms

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:

98.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
25.0ms	(/ 1.0 (- (* b b) (* a a)))
17.0ms	(- (* b b) (* a a))
279.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
77.0ms	(/ 1.0 (- (* b b) (* a a)))
54.0ms	(- (* b b) (* a a))
159.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.7s

Counts

513 → 513

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	886	27857
1	2914	25859
done	5002	23272

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
9.7b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite626.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

20.0ms	(/ 1.0 (- b a))
141.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
32.0ms	(/ (/ PI 2.0) (+ b a))
334.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1.0 (- b a))
134.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
111.0ms	(/ (/ PI 2.0) (+ b a))
187.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.6s

Counts

646 → 646

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	1031	29916
1	3387	27807
done	5001	25121

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.2b	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite758.0ms

Algorithm

rewrite-expression-head

Rules

525×	`times-frac`
437×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
399×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-exp-log` `add-cbrt-cube`
58×	`div-inv`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`associate-/r*`
8×	`frac-sub`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `frac-2neg` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 541

Calls

4 calls:

22.0ms	(/ 1.0 (- b a))
307.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
252.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
75.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1.0 (- b a))
199.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
116.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify3.4s

Counts

553 → 553

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	930	25655
1	3059	23601
done	5000	20887

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))) (+ b a))
0.2b	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`times-frac`
23×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
16×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
9×	`associate-/r*`
6×	`associate-/r/` `associate-/l/`
5×	`pow1` `associate-*r/`
4×	`div-inv`
3×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `distribute-lft-out` `associate-/l` `unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `frac-sub` `flip-+`

Counts

3 → 124

Calls

3 calls:

178.0ms	(/ (* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))) (+ b a))
666.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
210.0ms	(* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))

series374.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(/ (* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))) (+ b a))
82.0ms	(/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a))
122.0ms	(* (/ PI 2.0) (/ (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (- b a)))

simplify3.2s

Counts

133 → 133

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	213	3012
1	679	2945
2	4385	2351
done	5000	2341

prune800.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes249.0ms

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

sample2.0s

Algorithm

intervals

Results

1.5s

9585×

body

valid