Details

sample78.0ms

Algorithm

intervals

Results

17.0ms	195×	body	80	valid
13.0ms	28×	body	1280	valid
12.0ms	21×	body	2560	valid
7.0ms	256×	pre	80	true
2.0ms	6×	body	320	valid
1.0ms	4×	body	640	valid
1.0ms	2×	body	5120	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.0b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

25.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
47.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
7.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
142.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
94.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
80.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.6s

Counts

119 → 119

Iterations

Useful iterations: 2 (126.0ms)

Iter	Nodes	Cost
0	128	1655
1	230	1507
2	581	1405
3	2050	1405
done	5000	1405

prune584.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.7b

localize51.0ms

Local error

Found 4 expressions with local error:

1.4b	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
3.5b	(/ (* x x) (fma (* 4.0 p) p (* x x)))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
70×	`add-cube-cbrt`
66×	`prod-diff`
59×	`times-frac`
34×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l*` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

37.0ms	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
22.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
4.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
14.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
58.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
74.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
85.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.9s

Counts

152 → 152

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	260	7025
1	655	6171
2	3091	4676
done	5002	4294

prune777.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize31.0ms

Local error

Found 4 expressions with local error:

10.2b	(+ (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
67×	`fma-def`
50×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
42×	`cbrt-prod`
30×	`sqrt-prod`
10×	`div-inv`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 126

Calls

4 calls:

128.0ms	(+ (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ (/ (/ x (* (cbrt (sqrt (fma (* 4.0 p) p (* x x)))) (cbrt (sqrt (fma (* 4.0 p) p (* x x)))))) (cbrt (sqrt (fma (* 4.0 p) p (* x x))))) 1.0)
86.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
85.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
108.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.2s

Counts

138 → 138

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	57	1365
1	125	1286
2	330	756
3	1245	746
done	5000	710

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.0b	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
13.4b	(sqrt (fma (* 4.0 p) p (* x x)))
14.5b	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
16×	`sqrt-prod`
10×	`pow1`
8×	`add-exp-log`
6×	`associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `pow1/2` `associate-/l*`
2×	`div-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 85

Calls

4 calls:

6.0ms	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
9.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
0.0ms	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)

series795.0ms

Counts

4 → 12

Calls

4 calls:

419.0ms	(sqrt (* (fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
120.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
125.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
130.0ms	(fma x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)

simplify3.6s

Counts

97 → 97

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	110	1492
1	167	1307
2	505	1205
3	2657	1205
done	5000	1205

prune406.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.7b

regimes199.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	48
1	23	48
done	23	48

end0.0ms

sample2.2s

Algorithm

intervals

Results

617.0ms	8000×	pre	80	true
448.0ms	5996×	body	80	valid
435.0ms	745×	body	2560	valid
228.0ms	608×	body	1280	valid
113.0ms	334×	body	640	valid
31.0ms	178×	body	320	valid
31.0ms	59×	body	5120	valid
9.0ms	80×	body	160	valid