Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	206×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
3.0ms	9×	body	2560	valid
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	48
4	48
3	46
2	40
1	28
0	14

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.0b	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
1.5b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
15.9b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `div-inv` `distribute-lft-out`

Counts

4 → 88

Calls

4 calls:

14.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
5.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
1.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
83.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
101.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
91.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify3.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
4	4580
3	1393
2	523
1	230
0	128

prune619.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) 0.5))
0.2b	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
15.9b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-l`
2×	`flip3-+` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

6.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) 0.5))
18.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
9.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
1.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) 0.5))
62.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
88.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
72.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.8s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	2295
2	895
1	333
0	150

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize38.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (* (cbrt (fma p (* 4.0 p) (* x x))) (cbrt (fma p (* 4.0 p) (* x x)))))
16.7b	(cbrt (fma p (* 4.0 p) (* x x)))
16.7b	(cbrt (fma p (* 4.0 p) (* x x)))
16.7b	(cbrt (fma p (* 4.0 p) (* x x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (* (cbrt (fma p (* 4.0 p) (* x x))) (cbrt (fma p (* 4.0 p) (* x x)))))
1.0ms	(cbrt (fma p (* 4.0 p) (* x x)))
1.0ms	(cbrt (fma p (* 4.0 p) (* x x)))
1.0ms	(cbrt (fma p (* 4.0 p) (* x x)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(sqrt (* (cbrt (fma p (* 4.0 p) (* x x))) (cbrt (fma p (* 4.0 p) (* x x)))))
155.0ms	(cbrt (fma p (* 4.0 p) (* x x)))
152.0ms	(cbrt (fma p (* 4.0 p) (* x x)))
157.0ms	(cbrt (fma p (* 4.0 p) (* x x)))

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
5	4343
4	1352
3	514
2	240
1	122
0	69

prune443.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.7b

localize47.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ x (fma (* p 4.0) p (* x x)))
4.8b	(/ (* x x) (fma (* p 4.0) p (* x x)))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))
15.9b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

4.0ms	(/ x (fma (* p 4.0) p (* x x)))
13.0ms	(/ (* x x) (fma (* p 4.0) p (* x x)))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))
1.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (fma (* p 4.0) p (* x x)))
56.0ms	(/ (* x x) (fma (* p 4.0) p (* x x)))
67.0ms	(sqrt (fma (* p 4.0) p (* x x)))
65.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify2.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5023
3	4624
2	794
1	210
0	97

prune554.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.6b

regimes197.0ms

Accuracy

0% (0.6b remaining)

Error of 13.4b against oracle of 12.8b and baseline of 13.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

302.0ms	6035×	body	80	valid
280.0ms	151×	body	320	valid
240.0ms	764×	body	2560	valid
235.0ms	8000×	pre	80	true
224.0ms	596×	body	1280	valid
57.0ms	310×	body	640	valid
22.0ms	63×	body	5120	valid
7.0ms	81×	body	160	valid