Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	190×	body	80	valid
6.0ms	19×	body	2560	valid
5.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify64.0ms

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: 14.5b

localize15.0ms

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	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

114.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
99.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
44.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

485.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
88.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
126.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
93.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

104 → 104

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	145	1890
1	298	1592
2	764	1504
3	1877	1491
done	5000	1484

prune595.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
0.2b	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
3.2b	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
13.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
22×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 127

Calls

4 calls:

22.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
11.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
114.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
132.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
103.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify3.1s

Counts

139 → 139

Iterations

Useful iterations: 3 (488.0ms)

Iter	Nodes	Cost
0	147	2235
1	308	1821
2	634	1689
3	1467	1686
4	3662	1686
done	5000	1686

prune520.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.9b	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
1.3b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
13.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

6.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
3.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
14.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
303.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x))))) 0.5))))
87.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
68.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.6s

Counts

103 → 103

Iterations

Useful iterations: 4 (585.0ms)

Iter	Nodes	Cost
0	142	1759
1	240	1589
2	473	1485
3	905	1485
4	2222	1484
done	5001	1484

prune409.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
2.9b	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))) 0.5))))
3.2b	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
13.1b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1` `add-exp-log`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`log-prod` `pow-flip` `fma-def` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-exp`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `rem-log-exp` `clear-num` `sum-log` `flip-+` `div-inv` `inv-pow`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
3.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))) 0.5))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (sqrt (fma (* 4.0 p) p (* x x))))
364.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))) 0.5))))
86.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
68.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify2.9s

Counts

108 → 108

Iterations

Useful iterations: 3 (312.0ms)

Iter	Nodes	Cost
0	143	1863
1	250	1648
2	524	1444
3	1354	1441
4	3543	1441
done	5000	1441

prune325.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.1b

regimes159.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	20	20
done	20	20

end0.0ms

sample2.1s

Algorithm

intervals

Results

590.0ms	627×	body	1280	valid
440.0ms	6042×	body	80	valid
400.0ms	731×	body	2560	valid
147.0ms	8000×	pre	80	true
120.0ms	330×	body	640	valid
28.0ms	63×	body	5120	valid
25.0ms	142×	body	320	valid
7.0ms	65×	body	160	valid