Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	196×	body	80	valid
8.0ms	20×	body	2560	valid
8.0ms	24×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
0.8b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
15.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

22×	`fma-def`
19×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `times-frac`
17×	`add-cube-cbrt`
13×	`sqrt-prod`
7×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `div-inv` `distribute-lft-out`

Counts

3 → 66

Calls

3 calls:

34.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
42.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series527.0ms

Counts

3 → 9

Calls

3 calls:

308.0ms	(sqrt (* (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0) 0.5))
118.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
100.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.9s

Counts

75 → 75

Iterations

Useful iterations: 3 (184.0ms)

Iter	Nodes	Cost
0	79	835
1	149	781
2	339	734
3	868	690
4	2605	690
done	5000	690

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
0.8b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.2b	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
15.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `fma-def`
21×	`add-cube-cbrt`
18×	`times-frac`
12×	`sqrt-prod`
8×	`log-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `exp-prod` `exp-sum` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `distribute-lft-out`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `div-inv` `rem-exp-log`

Counts

4 → 88

Calls

4 calls:

29.0ms	(exp (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
40.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
26.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(exp (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
105.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
199.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
69.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.8s

Counts

100 → 100

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	103	1383
1	195	1294
2	444	1159
3	1240	1092
4	4249	1086
done	5000	1086

prune752.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)) 3))
0.8b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.2b	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
15.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `fma-def`
18×	`times-frac`
14×	`cbrt-prod`
12×	`sqrt-prod`
8×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `unpow-prod-down` `log-prod` `cube-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-pow`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `rem-log-exp` `sum-log` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

3.0ms	(cbrt (pow (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)) 3))
31.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
23.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series707.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (pow (log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)) 3))
115.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
243.0ms	(log (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0))
97.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	110	1648
1	232	1449
2	896	1315
done	5000	1293

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
7.3b	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
15.0b	(sqrt (fma (* 4.0 p) p (* x x)))
15.0b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
52×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
7×	`fma-def`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

32.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
49.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
83.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
65.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
69.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.3s

Counts

140 → 140

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	116	3008
1	249	1718
2	1152	1576
done	5002	1544

prune730.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.5b

regimes201.0ms

Accuracy

0% (3.6b remaining)

Error of 13.4b against oracle of 9.8b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	21
1	21	21
done	21	21

end0.0ms

sample1.8s

Algorithm

intervals

Results

634.0ms	769×	body	2560	valid
362.0ms	6019×	body	80	valid
222.0ms	641×	body	1280	valid
134.0ms	8000×	pre	80	true
121.0ms	293×	body	640	valid
55.0ms	158×	body	320	valid
20.0ms	49×	body	5120	valid
7.0ms	71×	body	160	valid