Details

sample71.0ms

Algorithm

intervals

Results

48.0ms

306×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.2b	(/ 1.0 (- (* b b) (* a a)))
4.1b	(- (* b b) (* a a))
9.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite324.0ms

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:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
20.0ms	(/ 1.0 (- (* b b) (* a a)))
14.0ms	(- (* b b) (* a a))
199.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms	(/ 1.0 (- (* b b) (* a a)))
54.0ms	(- (* b b) (* a a))
141.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2914
0	886

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize28.0ms

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 (- b a)))
0.3b	(/ (/ PI 2.0) (+ a b))
9.6b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-cbrt-cube` `associate-l` `add-exp-log`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-l/` `associate-r/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
78.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
14.0ms	(/ (/ PI 2.0) (+ a b))
212.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
88.0ms	(/ (/ PI 2.0) (+ a b))
137.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.9s

Counts

813 → 813

Iterations

Iter	Nodes
done	5001
1	3375
0	1025

prune6.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(/ (/ PI 2.0) (+ a b))
0.3b	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite525.0ms

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:

57.0ms	(- (/ 1.0 a) (/ 1.0 b))
217.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
14.0ms	(/ (/ PI 2.0) (+ a b))
167.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ 1.0 a) (/ 1.0 b))
139.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
75.0ms	(/ (/ PI 2.0) (+ a b))
184.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

730 → 730

Iterations

Iter	Nodes
done	5000
1	2955
0	956

prune6.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite394.0ms

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:

55.0ms	(- (/ 1.0 a) (/ 1.0 b))
170.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
91.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
19.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

series393.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (/ 1.0 a) (/ 1.0 b))
155.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
92.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
90.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

simplify1.5s

Counts

453 → 453

Iterations

Iter	Nodes
done	5000
1	1770
0	606

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

9607×

body

valid