Details

sample47.0ms

Algorithm

intervals

Results

35.0ms

305×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	4631
4	1378
3	361
2	95
1	33
0	15

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

352×	`*-un-lft-identity`
333×	`times-frac`
160×	`add-sqr-sqrt`
110×	`add-cube-cbrt`
80×	`distribute-lft-out`
67×	`associate-/l*`
60×	`distribute-rgt-neg-in`
25×	`distribute-lft-out--` `difference-of-squares`
22×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-neg-in` `associate-/r*` `div-sub`
9×	`cbrt-undiv` `div-exp`
8×	`associate-/r/`
6×	`div-inv`
5×	`distribute-frac-neg`
4×	`expm1-log1p-u` `pow1` `clear-num` `neg-mul-1` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`neg-sub0` `flip3--` `flip--`
2×	`associate-+r-` `flip3-+` `unsub-neg` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+`
1×	`frac-add`

Counts

4 → 286

Calls

4 calls:

52.0ms	(/ (/ (+ (/ PI a) (/ (- PI) b)) (- b a)) (* (+ a b) 2))
45.0ms	(/ (+ (/ PI a) (/ (- PI) b)) (- b a))
5.0ms	(/ (- PI) b)
5.0ms	(/ PI a)

series296.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (/ (+ (/ PI a) (/ (- PI) b)) (- b a)) (* (+ a b) 2))
79.0ms	(/ (+ (/ PI a) (/ (- PI) b)) (- b a))
35.0ms	(/ (- PI) b)
31.0ms	(/ PI a)

simplify792.0ms

Counts

298 → 298

Iterations

Iter	Nodes
2	2372
1	853
0	377

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ PI (* a b)) (* (+ a b) 2))
0.7b	(/ PI (* a b))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-cbrt-cube` `add-exp-log`
16×	`times-frac`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/l*`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
4×	`div-inv`
2×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 67

Calls

2 calls:

33.0ms	(/ (/ PI (* a b)) (* (+ a b) 2))
19.0ms	(/ PI (* a b))

series144.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(/ (/ PI (* a b)) (* (+ a b) 2))
39.0ms	(/ PI (* a b))

simplify3.2s

Counts

73 → 73

Iterations

Iter	Nodes
3	7680
2	1161
1	334
0	123

prune737.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ PI (+ a b)) (/ 1/2 (* b a)))
0.3b	(/ PI (+ a b))
0.5b	(/ 1/2 (* b a))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
31×	`times-frac` `add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `distribute-lft-out`
6×	`associate-/l*`
5×	`pow1` `associate-/r*`
4×	`associate-/r/` `div-inv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 114

Calls

3 calls:

58.0ms	(* (/ PI (+ a b)) (/ 1/2 (* b a)))
16.0ms	(/ PI (+ a b))
18.0ms	(/ 1/2 (* b a))

series193.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(* (/ PI (+ a b)) (/ 1/2 (* b a)))
75.0ms	(/ PI (+ a b))
34.0ms	(/ 1/2 (* b a))

simplify4.3s

Counts

123 → 123

Iterations

Iter	Nodes
3	9295
2	1737
1	432
0	162

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
61×	`times-frac`
46×	`add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
21×	`associate-r`
18×	`associate-l`
10×	`associate-/r*`
9×	`associate-/l*`
7×	`cbrt-undiv` `div-exp` `distribute-lft-out`
6×	`pow1` `associate-/r/`
5×	`div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `distribute-lft-out--` `difference-of-squares`
2×	`flip3-+` `flip-+`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 162

Calls

4 calls:

62.0ms	(* (/ (fma (/ PI b) -1 (/ PI a)) (+ b a)) (/ 1/2 (- b a)))
14.0ms	(/ (fma (/ PI b) -1 (/ PI a)) (+ b a))
4.0ms	(/ PI b)
4.0ms	(/ PI a)

series400.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (fma (/ PI b) -1 (/ PI a)) (+ b a)) (/ 1/2 (- b a)))
157.0ms	(/ (fma (/ PI b) -1 (/ PI a)) (+ b a))
46.0ms	(/ PI b)
47.0ms	(/ PI a)

simplify3.0s

Counts

174 → 174

Iterations

Iter	Nodes
3	6558
2	1930
1	620
0	251

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

2.0s

9629×

body

valid