Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	183×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	26×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify100.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize28.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

60.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
3.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series243.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
103.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	56	492
1	119	463
2	267	430
3	563	408
4	1469	408
5	3726	408
done	5000	408

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.4b	(log (exp (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
0.4b	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

112.0ms	(log (exp (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
47.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series360.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(log (exp (+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)))
123.0ms	(+ (/ x (sqrt (fma (* 4.0 p) p (* x x)))) 1.0)
105.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.5s

Counts

79 → 79

Iterations

Useful iterations: 3 (185.0ms)

Iter	Nodes	Cost
0	81	868
1	148	798
2	302	725
3	607	703
4	1532	703
5	3897	703
done	5000	703

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.1b

localize17.0ms

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)))))
8.6b	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite85.0ms

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:

27.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
50.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (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)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))
105.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (sqrt (fma (* 4.0 p) p (* x x)))))) 1.0)
86.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
88.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify1.8s

Counts

140 → 140

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	116	3008
1	217	1706
2	549	1576
3	1793	1512
done	5000	1470

prune374.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.1b

localize25.0ms

Local error

Found 4 expressions with local error:

8.6b	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (* (fabs (cbrt (fma (* 4.0 p) p (* x x)))) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))))) 1.0)
15.2b	(sqrt (fma (* 4.0 p) p (* x x)))
15.9b	(cbrt (fma (* 4.0 p) p (* x x)))
15.9b	(cbrt (fma (* 4.0 p) p (* x x)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

77.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (* (fabs (cbrt (fma (* 4.0 p) p (* x x)))) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))))) 1.0)
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
1.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(+ (/ x (* (sqrt (sqrt (fma (* 4.0 p) p (* x x)))) (sqrt (* (fabs (cbrt (fma (* 4.0 p) p (* x x)))) (sqrt (cbrt (fma (* 4.0 p) p (* x x)))))))) 1.0)
70.0ms	(sqrt (fma (* 4.0 p) p (* x x)))
155.0ms	(cbrt (fma (* 4.0 p) p (* x x)))
158.0ms	(cbrt (fma (* 4.0 p) p (* x x)))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	122	1538
1	267	1494
2	688	1355
3	2116	1290
done	5000	1239

prune401.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.1b

regimes80.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	18	18
done	18	18

end0.0ms

sample1.9s

Algorithm

intervals

Results

500.0ms	627×	body	1280	valid
445.0ms	6044×	body	80	valid
236.0ms	740×	body	2560	valid
235.0ms	8000×	pre	80	true
60.0ms	286×	body	640	valid
53.0ms	59×	body	5120	valid
43.0ms	91×	body	160	valid
23.0ms	153×	body	320	valid