Details

sample58.0ms

Algorithm

intervals

Results

34.0ms

313×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	405
1	31	405
2	90	405
3	385	405
4	1848	405
done	5000	405

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize36.0ms

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)))
3.5b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite313.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log`

Counts

4 → 501

Calls

4 calls:

39.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
13.0ms	(- (* b b) (* a a))
194.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
50.0ms	(/ 1.0 (- (* b b) (* a a)))
37.0ms	(- (* b b) (* a a))
113.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify4.0s

Counts

513 → 513

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	886	498216
1	2914	464789
done	5000	435191

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize51.0ms

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
7.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite461.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

9.0ms	(/ 1.0 (- b a))
110.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
28.0ms	(/ (/ PI 2.0) (+ b a))
228.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1.0 (- b a))
90.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
93.0ms	(/ (/ PI 2.0) (+ b a))
141.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify4.4s

Counts

646 → 646

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	1031	545806
1	3387	511827
done	5002	479923

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

833×	`times-frac`
661×	`*-un-lft-identity`
641×	`add-sqr-sqrt`
613×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
90×	`div-inv`
43×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
13×	`fma-neg`
12×	`associate-r` `distribute-lft-out--`
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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 718

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
168.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
13.0ms	(/ (/ PI 2.0) (+ b a))
126.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (/ 1.0 a) (/ 1.0 b))
143.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
63.0ms	(/ (/ PI 2.0) (+ b a))
171.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.7s

Counts

730 → 730

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	955	579270
1	2949	529744
done	5001	487188

prune6.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

492×	`times-frac`
457×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
258×	`add-cube-cbrt`
169×	`prod-diff`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
55×	`div-inv`
47×	`add-cbrt-cube` `add-exp-log`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`fma-neg` `associate-/l*`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
3×	`distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-*l/` `frac-sub` `flip-+` `unswap-sqr`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 441

Calls

4 calls:

56.0ms	(- (/ 1.0 a) (/ 1.0 b))
189.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
157.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
30.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

series330.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (/ 1.0 a) (/ 1.0 b))
139.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
70.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
75.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

simplify1.9s

Counts

453 → 453

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	605	232235
1	1763	211030
done	5001	194512

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes259.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	15	405
1	18	405
done	18	405

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

9545×

body

valid