Details

sample56.0ms

Algorithm

intervals

Results

14.0ms	184×	body	80	valid
12.0ms	31×	body	2560	valid
6.0ms	19×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	10×	body	320	valid
2.0ms	6×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (* 4.0 p) p) (* x x))
60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.9b	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
15.7b	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

47.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
42.0ms	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
20.0ms	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

series460.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))
34.0ms	(+ (* (* 4.0 p) p) (* x x))
81.0ms	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
61.0ms	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

simplify128.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	266	590
1	1021	535
2	4631	519
3	5001	519

prune233.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1)))))))
0.7b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))))
0.9b	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
15.7b	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `sqrt-prod`
8×	`exp-prod`
7×	`add-log-exp`
5×	`pow1` `log-pow`
4×	`add-exp-log` `unpow-prod-down` `add-cbrt-cube`
3×	`rem-sqrt-square` `log-prod`
2×	`sqr-pow`
1×	`+-commutative` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `sum-log` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 59

Calls

4 calls:

2.0ms	(exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1)))))))
1.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))))
44.0ms	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
20.0ms	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

672.0ms	(exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1)))))))
295.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))))))
80.0ms	(+ 1.0 (/ x (sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))))
56.0ms	(sqrt (pow (+ (* (* 4.0 p) p) (* x x)) 1))

simplify61.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	706
1	521	616
2	1863	614
3	5001	614

prune273.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.9b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `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` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

14.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
59.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	367	1201
1	1656	1080
2	5001	1018

prune461.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.1b

regimes148.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.8b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	22	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

444.0ms	6075×	body	80	valid
287.0ms	739×	body	2560	valid
193.0ms	592×	body	1280	valid
141.0ms	8000×	pre	80	true
79.0ms	308×	body	640	valid
32.0ms	169×	body	320	valid
25.0ms	54×	body	5120	valid
10.0ms	63×	body	160	valid