Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	198×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	12×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

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: 11.3b

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))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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:

9.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (* 4.0 p) p) (* x x))
58.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(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

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

13.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506

prune455.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

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:

8.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	367	1199
1	1642	1080
2	5001	1018

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.6b	(+ 1.0 (* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`prod-exp`
15×	`sqrt-prod` `add-cbrt-cube`
12×	`pow1`
7×	`1-exp`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`cbrt-unprod`
4×	`sqrt-div`
3×	`rec-exp` `pow-flip` `flip3-+` `associate-r/` `associate-l` `pow-prod-down` `un-div-inv` `flip-+` `associate-/l`
2×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r` `clear-num` `sum-log` `*-commutative` `div-inv` `inv-pow`

Counts

4 → 102

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
3.0ms	(+ 1.0 (* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms	(* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
77.0ms	(+ 1.0 (* x (* 1 (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify96.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	367	1024
1	1295	894
2	3201	856
3	5001	852

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

regimes155.0ms

Accuracy

0% (0.6b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample823.0ms

Algorithm

intervals

Results

218.0ms	6045×	body	80	valid
172.0ms	775×	body	2560	valid
108.0ms	617×	body	1280	valid
104.0ms	8000×	pre	80	true
43.0ms	317×	body	640	valid
17.0ms	157×	body	320	valid
6.0ms	89×	body	160	valid