Details

sample33.0ms

Algorithm

intervals

Results

17.0ms	103×	body	1280	valid
4.0ms	121×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
70.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
83.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune167.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 14.9b

Counts

79 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.9b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-*r/`
6×	`add-log-exp`
4×	`pow1` `flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 110

Calls

4 calls:

11.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
35.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify51.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	407	1275
1	1594	1181
2	5001	1177

prune311.0ms

Filtered

122 candidates to 88 candidates (72.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Merged error: 14.8b

Counts

127 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.8b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
28×	`associate-l`
26×	`*-un-lft-identity`
16×	`add-cube-cbrt` `difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `sqr-pow`
6×	`associate-r/` `associate-r` `associate-l/` `add-log-exp`
5×	`distribute-lft-out--`
4×	`flip3--` `frac-sub` `flip--`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`difference-cubes` `cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 109

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
17.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
9.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
17.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
21.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
40.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify95.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	563	1053
1	2945	974
2	5003	974

prune493.0ms

Filtered

121 candidates to 83 candidates (68.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 14.7b

Counts

126 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.8b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
3.3b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
28×	`associate-l`
26×	`*-un-lft-identity`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`log-pow`
13×	`exp-prod`
12×	`unpow-prod-down` `cube-prod`
9×	`pow1` `times-frac`
8×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
6×	`associate-r/` `associate-r` `associate-l/` `add-log-exp`
5×	`distribute-lft-out--`
4×	`flip3--` `frac-sub` `flip--`
3×	`log-prod` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`difference-cubes` `sub-neg` `diff-log` `rem-log-exp` `div-inv`

Counts

4 → 107

Calls

4 calls:

17.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
12.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
17.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
5.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
24.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
35.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
6.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	574	1035
1	2822	950
2	5001	950

prune497.0ms

Filtered

119 candidates to 83 candidates (69.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 14.7b

Counts

126 → 6

regimes137.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample820.0ms

Algorithm

intervals

Results

474.0ms	2872×	body	1280	valid
125.0ms	4069×	body	80	valid
76.0ms	590×	body	640	valid
27.0ms	302×	body	320	valid
10.0ms	167×	body	160	valid