Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	185×	body	80	valid
8.0ms	23×	body	2560	valid
7.0ms	28×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0b	(fma (* 4.0 p) p (* x x))
0.4b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`fma-def`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`div-inv`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `clear-num` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0ms	(fma (* 4.0 p) p (* x x))
53.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
55.0ms	(fma (* 4.0 p) p (* x x))
140.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
111.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: 3 (627.0ms)

Iter	Nodes	Cost
0	117	1452
1	225	1328
2	665	1266
3	2837	1244
done	5001	1244

prune659.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
9.9b	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

564×	`sqrt-prod`
549×	`times-frac`
295×	`add-sqr-sqrt` `*-un-lft-identity`
293×	`add-cube-cbrt`
283×	`fma-def`
11×	`div-inv`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 380

Calls

4 calls:

8.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
229.0ms	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
98.0ms	(+ (/ (/ x (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
82.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
99.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.7s

Counts

392 → 392

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	150	2157
1	300	1714
2	925	1634
3	4758	1618
done	5000	1618

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.7b

localize32.0ms

Local error

Found 4 expressions with local error:

13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
94.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
122.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
87.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	28	780
1	42	680
2	67	652
3	98	652
4	134	652
5	174	652
6	259	652
7	441	652
8	1215	652
done	5000	652

prune576.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.7b

localize66.0ms

Local error

Found 4 expressions with local error:

13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
13.5b	(sqrt (fma (* 4.0 p) p (* x x)))
17.0b	(fma (/ (/ (* (cbrt x) (cbrt x)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) (/ (/ (cbrt x) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(fma (/ (/ (* (cbrt x) (cbrt x)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) (/ (/ (cbrt x) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)

series778.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
107.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
99.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
465.0ms	(fma (/ (/ (* (cbrt x) (cbrt x)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))))) (/ (/ (cbrt x) (sqrt (sqrt (fma (* 4.0 p) p (* x x))))) (sqrt (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)

simplify1.4s

Counts

67 → 67

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	82	1432
1	159	1185
2	453	1045
3	2148	1040
done	5000	995

prune490.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.7b

regimes373.0ms

Accuracy

89.9% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 15.8b

bsearch81.0ms

Steps

Iters	Range		Point
8	-7.520258622712412e-124	-4.624638329525608e-127	-1.409903055203331e-126

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	54
1	33	54
done	33	54

end0.0ms

sample2.1s

Algorithm

intervals

Results

630.0ms	8000×	pre	80	true
408.0ms	778×	body	2560	valid
388.0ms	5975×	body	80	valid
218.0ms	671×	body	1280	valid
68.0ms	316×	body	640	valid
24.0ms	54×	body	5120	valid
22.0ms	139×	body	320	valid
7.0ms	67×	body	160	valid