Details

sample65.0ms

Algorithm

intervals

Results

50.0ms

303×

body

valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
5	2008
4	1503
3	361
2	95
1	33
0	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ PI 2) (+ a b))
0.2b	(/ (/ PI 2) (+ a b))
4.2b	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)
4.5b	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) b)

rewrite694.0ms

Algorithm

rewrite-expression-head

Rules

7810×	`times-frac`
4872×	`*-un-lft-identity`
3776×	`add-sqr-sqrt`
2848×	`add-cube-cbrt`
618×	`associate-/l*`
548×	`distribute-lft-out`
464×	`distribute-lft-out--` `difference-of-squares`
222×	`div-inv`
100×	`associate-/r/`
42×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
26×	`cbrt-undiv` `div-exp`
14×	`associate-/r*`
8×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`

Counts

4 → 2596

Calls

4 calls:

25.0ms	(/ (/ PI 2) (+ a b))
398.0ms	(/ (/ PI 2) (+ a b))
41.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)
45.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) b)

series426.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (/ PI 2) (+ a b))
97.0ms	(/ (/ PI 2) (+ a b))
104.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)
158.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) b)

simplify2.6s

Counts

2608 → 2608

Iterations

Iter	Nodes
done	2863
0	2863

prune38.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
0.2b	(/ (/ PI 2) (+ a b))
0.2b	(/ (/ PI 2) (+ a b))
4.2b	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

4236×	`times-frac`
2651×	`*-un-lft-identity`
2023×	`add-sqr-sqrt`
1559×	`add-cube-cbrt`
380×	`associate-/l*`
314×	`distribute-lft-out`
232×	`distribute-lft-out--` `difference-of-squares`
128×	`div-inv`
58×	`associate-/r/`
49×	`add-cbrt-cube` `add-exp-log`
28×	`cbrt-undiv` `div-exp`
24×	`flip3-+` `flip-+`
12×	`associate-/r*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`prod-exp` `cbrt-unprod`
2×	`associate-*r/`

Counts

4 → 1532

Calls

4 calls:

50.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
23.0ms	(/ (/ PI 2) (+ a b))
23.0ms	(/ (/ PI 2) (+ a b))
54.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)

series460.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
100.0ms	(/ (/ PI 2) (+ a b))
80.0ms	(/ (/ PI 2) (+ a b))
130.0ms	(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)

simplify2.4s

Counts

1544 → 1544

Iterations

Iter	Nodes
done	2001
1	2001
0	1919

prune20.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
0.2b	(/ (/ (/ PI 2) (+ a b)) (/ a (/ 1 (- b a))))
0.2b	(/ (/ PI 2) (+ a b))
0.2b	(/ (/ PI 2) (+ a b))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

16816×	`times-frac`
8939×	`*-un-lft-identity`
7037×	`add-sqr-sqrt`
5975×	`add-cube-cbrt`
951×	`distribute-lft-out`
605×	`div-inv`
562×	`associate-/r/`
531×	`distribute-lft-out--` `difference-of-squares`
178×	`flip3--` `flip--`
142×	`associate-/l*`
95×	`add-exp-log`
77×	`associate-/r*`
73×	`flip3-+` `flip-+`
71×	`add-cbrt-cube`
66×	`div-exp`
45×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`rec-exp` `1-exp` `prod-exp` `cbrt-unprod`
2×	`associate-*r/`

Counts

4 → 4432

Calls

4 calls:

23.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
42.0ms	(/ (/ (/ PI 2) (+ a b)) (/ a (/ 1 (- b a))))
12.0ms	(/ (/ PI 2) (+ a b))
12.0ms	(/ (/ PI 2) (+ a b))

series404.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
119.0ms	(/ (/ (/ PI 2) (+ a b)) (/ a (/ 1 (- b a))))
87.0ms	(/ (/ PI 2) (+ a b))
67.0ms	(/ (/ PI 2) (+ a b))

simplify5.7s

Counts

4444 → 4444

Iterations

Iter	Nodes
done	5229
0	5229

prune1.1m

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
0.2b	(/ (/ PI 2) (+ a b))
0.2b	(/ (/ PI 2) (+ a b))
0.4b	(/ 1 (/ a (/ 1 (- b a))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

1064×	`times-frac`
631×	`*-un-lft-identity`
523×	`add-sqr-sqrt`
451×	`add-cube-cbrt`
87×	`associate-/l*`
77×	`associate-/r*`
70×	`add-exp-log`
54×	`distribute-lft-out`
46×	`div-exp`
44×	`add-cbrt-cube`
40×	`div-inv`
39×	`associate-/r/`
36×	`distribute-lft-out--` `difference-of-squares`
24×	`cbrt-undiv`
13×	`flip3--` `flip--`
8×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `associate-/l/`
2×	`associate-*r/`
1×	`pow-flip` `inv-pow`

Counts

4 → 632

Calls

4 calls:

27.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
12.0ms	(/ (/ PI 2) (+ a b))
12.0ms	(/ (/ PI 2) (+ a b))
18.0ms	(/ 1 (/ a (/ 1 (- b a))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (/ (/ PI 2) (+ a b)) (* b (- b a)))
59.0ms	(/ (/ PI 2) (+ a b))
71.0ms	(/ (/ PI 2) (+ a b))
68.0ms	(/ 1 (/ a (/ 1 (- b a))))

simplify851.0ms

Counts

644 → 644

Iterations

Iter	Nodes
done	2000
1	2000
0	846

prune6.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

2.0s

9516×

body

valid