Details

sample41.0ms

Algorithm

intervals

Results

24.0ms

316×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
6.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite351.0ms

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:

74.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
20.0ms	(/ 1.0 (- (* b b) (* a a)))
13.0ms	(- (* b b) (* a a))
182.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
66.0ms	(/ 1.0 (- (* b b) (* a a)))
45.0ms	(- (* b b) (* a a))
153.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.9s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2914
0	886

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ a b))
6.5b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite621.0ms

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:

12.0ms	(/ 1.0 (- b a))
94.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
14.0ms	(/ (/ PI 2.0) (+ a b))
446.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1.0 (- b a))
102.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
81.0ms	(/ (/ PI 2.0) (+ a b))
138.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.2s

Counts

646 → 646

Iterations

Iter	Nodes
done	5000
1	3394
0	1032

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite571.0ms

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:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
206.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
28.0ms	(/ (/ PI 2.0) (+ a b))
217.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (/ 1.0 a) (/ 1.0 b))
125.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
67.0ms	(/ (/ PI 2.0) (+ a b))
172.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.6s

Counts

730 → 730

Iterations

Iter	Nodes
done	5000
1	2955
0	956

prune5.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

757×	`times-frac`
609×	`add-sqr-sqrt`
569×	`*-un-lft-identity`
331×	`add-cube-cbrt`
169×	`prod-diff`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
71×	`div-inv`
43×	`add-cbrt-cube` `add-exp-log`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
13×	`fma-neg`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `frac-sub` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 556

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
125.0ms	(/ (* (/ (/ PI 2.0) (+ a b)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
15.0ms	(/ (/ PI 2.0) (+ a b))

series341.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
78.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
128.0ms	(/ (* (/ (/ PI 2.0) (+ a b)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
96.0ms	(/ (/ PI 2.0) (+ a b))

simplify2.0s

Counts

568 → 568

Iterations

Iter	Nodes
done	5002
1	2220
0	796

prune3.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes170.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

9576×

body

valid