Details

sample92.0ms

Algorithm

intervals

Results

73.0ms

306×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
5	4980
4	1403
3	361
2	93
1	31
0	15

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
15×	`associate-/l*`
12×	`associate-*l/` `associate-/r/`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`flip3-+` `flip-+`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

4 → 122

Calls

4 calls:

0.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
23.0ms	(/ (/ PI (* (+ a b) 2)) a)
9.0ms	(/ PI (* (+ a b) 2))
9.0ms	(/ PI (* (+ a b) 2))

series400.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
99.0ms	(/ (/ PI (* (+ a b) 2)) a)
91.0ms	(/ PI (* (+ a b) 2))
68.0ms	(/ PI (* (+ a b) 2))

simplify3.1s

Counts

134 → 134

Iterations

Iter	Nodes
3	6133
2	1258
1	419
0	176

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
20×	`add-cbrt-cube` `add-exp-log`
18×	`add-cube-cbrt`
9×	`associate-/l*`
7×	`associate-/r*`
6×	`cbrt-undiv` `div-exp` `associate-/r/`
4×	`expm1-log1p-u` `pow1` `associate-*l/` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`clear-num` `frac-2neg` `div-inv`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`flip3--` `fma-udef` `flip--`

Counts

4 → 105

Calls

4 calls:

8.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
0.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
15.0ms	(/ PI (* (+ a b) 2))
39.0ms	(/ PI (* a (* (+ a b) 2)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
180.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
95.0ms	(/ PI (* (+ a b) 2))
111.0ms	(/ PI (* a (* (+ a b) 2)))

simplify3.3s

Counts

117 → 117

Iterations

Iter	Nodes
3	7034
2	1387
1	415
0	185

prune976.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ 1 (/ (* a (* (+ a b) 2)) PI)))
0.2b	(/ (* a (* (+ a b) 2)) PI)
0.3b	(/ PI (* (+ a b) 2))
0.4b	(/ 1 (/ (* a (* (+ a b) 2)) PI))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
39×	`times-frac`
32×	`add-cbrt-cube`
24×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`div-exp`
13×	`prod-exp`
12×	`cbrt-undiv`
11×	`associate-/r*`
7×	`cbrt-unprod` `div-inv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/`
1×	`fma-udef` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

1.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ 1 (/ (* a (* (+ a b) 2)) PI)))
36.0ms	(/ (* a (* (+ a b) 2)) PI)
9.0ms	(/ PI (* (+ a b) 2))
52.0ms	(/ 1 (/ (* a (* (+ a b) 2)) PI))

series457.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ 1 (/ (* a (* (+ a b) 2)) PI)))
129.0ms	(/ (* a (* (+ a b) 2)) PI)
83.0ms	(/ PI (* (+ a b) 2))
93.0ms	(/ 1 (/ (* a (* (+ a b) 2)) PI))

simplify1.4s

Counts

140 → 140

Iterations

Iter	Nodes
2	2293
1	511
0	208

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
44×	`add-exp-log`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube`
21×	`div-exp`
16×	`associate-/l*`
14×	`cbrt-undiv` `associate-/r*`
12×	`associate-*l/` `div-inv`
11×	`associate-/r/`
6×	`flip3-+` `prod-exp` `flip-+`
5×	`pow1`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 170

Calls

4 calls:

21.0ms	(/ (/ PI (* (+ a b) 2)) a)
20.0ms	(/ (* (+ a b) 2) PI)
9.0ms	(/ PI (* (+ a b) 2))
17.0ms	(/ 1 (/ (* (+ a b) 2) PI))

series354.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (/ PI (* (+ a b) 2)) a)
83.0ms	(/ (* (+ a b) 2) PI)
105.0ms	(/ PI (* (+ a b) 2))
68.0ms	(/ 1 (/ (* (+ a b) 2) PI))

simplify2.8s

Counts

182 → 182

Iterations

Iter	Nodes
2	2559
1	668
0	258

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes200.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

2.1s

9641×

body

valid