Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample37.0ms

Algorithm

intervals

Results

20.0ms	88×	body	1280	valid
5.0ms	130×	body	80	valid
4.0ms	21×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	6×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.5b

Counts

2 → 1

localize191.0ms

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))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

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 → 65

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(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))))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4844	870
1	4844	870

prune134.0ms

Filtered

54 candidates to 77 candidates (-42.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Merged error: 16.0b

Counts

78 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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))
1.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate--r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

3.0ms	(+ 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))
4.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4937	971
1	4937	971

prune206.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	93	1	94

Merged error: 16.0b

Counts

94 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
0.0b	(/ (- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
0.0b	(pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)
1.5b	(- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`times-frac` `difference-of-squares`
26×	`sqr-pow`
21×	`add-cube-cbrt`
18×	`associate-*r/`
14×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`pow1`
11×	`unpow-prod-down`
10×	`associate-/l*`
8×	`frac-times`
6×	`frac-add` `add-log-exp`
5×	`distribute-lft-out--`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`pow-unpow` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `cube-prod` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 139

Calls

4 calls:

18.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
13.0ms	(/ (- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
8.0ms	(pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)
7.0ms	(- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3))

series167.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
82.0ms	(/ (- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
16.0ms	(pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)
36.0ms	(- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3))

simplify109.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5044	5968

prune978.0ms

Filtered

108 candidates to 151 candidates (-39.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	3	152

Merged error: 16.0b

Counts

152 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
0.0b	(/ (- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
0.5b	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))
1.5b	(- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
60×	`difference-of-squares`
56×	`unpow-prod-down`
52×	`sqr-pow`
48×	`times-frac`
41×	`*-un-lft-identity`
29×	`add-cube-cbrt`
16×	`associate-r/` `associate-/l`
15×	`add-exp-log`
12×	`flip3-+` `flip-+`
11×	`add-cbrt-cube`
9×	`pow1`
8×	`frac-times`
6×	`pow-unpow` `frac-add` `pow-exp` `add-log-exp`
5×	`distribute-lft-out--`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `prod-exp`
3×	`pow-prod-down` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`pow-to-exp` `flip3--` `associate-*l/` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 170

Calls

4 calls:

18.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
17.0ms	(/ (- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
5.0ms	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))
8.0ms	(- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5))))
159.0ms	(/ (- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))) (+ (pow 1.0 4) (* 0.5 (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) (+ 1.0 0.5)))))))
116.0ms	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3))
68.0ms	(- (pow 1.0 6) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 3)) (sqrt 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4975	8883
1	4975	8883

prune1.4s

Filtered

129 candidates to 182 candidates (-41.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	182	3	185

Merged error: 15.9b

Counts

185 → 3

regimes93.0ms

Accuracy

0% (0.0b remaining)

Error of 15.8b against oracle of 15.8b and baseline of 15.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	72
1	52	72

end0.0ms

sample1.1s

Algorithm

intervals

Results

651.0ms	2836×	body	1280	valid
165.0ms	3979×	body	80	valid
122.0ms	672×	body	640	valid
41.0ms	322×	body	320	valid
15.0ms	191×	body	160	valid

Details

analyze2.0ms

sample37.0ms

simplify19.0ms

prune5.0ms

localize191.0ms

rewrite19.0ms

series37.0ms

simplify73.0ms

prune134.0ms

localize11.0ms

rewrite14.0ms

series28.0ms

simplify64.0ms

prune206.0ms

localize29.0ms

rewrite53.0ms

series167.0ms

simplify109.0ms

prune978.0ms

localize31.0ms

rewrite55.0ms

series361.0ms

simplify96.0ms

prune1.4s

regimes93.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling