Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	28×	body	2560	valid
7.0ms	192×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
2.0ms	13×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ (* (* 4.0 p) p) (* x x))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
36.0ms	(+ (* (* 4.0 p) p) (* x x))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

75 → 75

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	108	1196
1	259	1034
2	807	952
3	2455	920
done	5000	915

prune300.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
3.4b	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

50×	`fma-def`
45×	`*-un-lft-identity`
39×	`times-frac`
37×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
26×	`unpow-prod-down` `cube-prod`
24×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `div-inv`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`+-commutative` `cube-mult` `frac-2neg` `flip3-+` `unpow3` `prod-exp` `clear-num` `sum-log` `sum-cubes` `cbrt-unprod` `flip-+` `associate-/l*` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

93.0ms	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
9.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (pow (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))) 3) (pow 1.0 3))
52.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
65.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
61.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify2.2s

Counts

134 → 134

Iterations

Useful iterations: 3 (869.0ms)

Iter	Nodes	Cost
0	101	1310
1	239	1213
2	836	1076
3	4348	1074
done	5000	1074

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

Local error

Found 4 expressions with local error:

15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite7.0ms

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:

1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
65.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
64.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	28	780
1	47	680
2	78	652
3	116	652
4	156	652
5	187	652
6	247	652
7	453	652
8	1281	652
done	5001	652

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
0.6b	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
0.6b	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
15.2b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

51.0ms	(exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
15.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
53.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2))))))
82.0ms	(+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
81.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
58.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify2.9s

Counts

79 → 79

Iterations

Useful iterations: 4 (446.0ms)

Iter	Nodes	Cost
0	87	1116
1	163	1031
2	367	931
3	800	920
4	1937	919
5	4781	919
done	5000	919

prune258.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.6b

regimes167.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	21
1	21	21
done	21	21

end0.0ms

sample855.0ms

Algorithm

intervals

Results

213.0ms	6097×	body	80	valid
179.0ms	793×	body	2560	valid
98.0ms	8000×	pre	80	true
95.0ms	540×	body	1280	valid
47.0ms	340×	body	640	valid
15.0ms	142×	body	320	valid
6.0ms	88×	body	160	valid