Details

analyze1.0ms

Algorithm

Search

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

sample39.0ms

Algorithm

intervals

Results

18.0ms	85×	body	1280	valid
7.0ms	19×	body	640	valid
5.0ms	132×	body	80	valid
2.0ms	14×	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: 16.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 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))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4844	870
1	4844	870

prune148.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 15.6b

Counts

78 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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*`
6×	`add-log-exp`
4×	`pow1` `distribute-lft-out`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 103

Calls

4 calls:

7.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 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))
4.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 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)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5252	1942

prune294.0ms

Filtered

86 candidates to 115 candidates (-33.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Merged error: 15.6b

Counts

121 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
1.6b	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
7×	`flip3-+` `flip-+`
6×	`add-log-exp` `difference-of-squares` `sqr-pow`
4×	`frac-times` `associate-r/` `associate-l*`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `associate-/r` `associate-/l`
2×	`cube-div` `pow-pow` `pow-prod-down` `associate-*l/` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `div-exp` `clear-num` `*-commutative` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
7.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series70.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(* (+ 1.0 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
16.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
36.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4988	1968
1	4988	1968

prune490.0ms

Filtered

79 candidates to 110 candidates (-39.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 15.6b

Counts

114 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
0.0b	(pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)
0.5b	(cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))
1.6b	(- (pow 1.0 6) (cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
37×	`add-sqr-sqrt`
34×	`unpow-prod-down`
27×	`cube-prod`
23×	`sqr-pow`
21×	`difference-of-squares`
13×	`*-un-lft-identity`
11×	`add-exp-log` `add-cube-cbrt`
10×	`cube-div`
8×	`pow-exp` `add-cbrt-cube`
7×	`pow1` `cube-mult` `unpow3`
6×	`pow-unpow` `associate-*r/` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `flip3-+` `flip-+` `rem-cube-cbrt`
2×	`cbrt-div` `prod-exp`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `pow-prod-down` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 128

Calls

4 calls:

8.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
5.0ms	(pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)
4.0ms	(cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))
15.0ms	(- (pow 1.0 6) (cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
30.0ms	(pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)
21.0ms	(cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))
34.0ms	(- (pow 1.0 6) (cbrt (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3)))

simplify39.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5371	2588

prune410.0ms

Filtered

68 candidates to 140 candidates (-105.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	141	3	144

Merged error: 15.6b

Counts

144 → 3

regimes190.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	62
1	44	62

end0.0ms

sample1.0s

Algorithm

intervals

Results

601.0ms	2823×	body	1280	valid
164.0ms	4079×	body	80	valid
102.0ms	595×	body	640	valid
40.0ms	338×	body	320	valid
13.0ms	165×	body	160	valid

Details

analyze1.0ms

sample39.0ms

simplify19.0ms

prune5.0ms

localize8.0ms

rewrite20.0ms

series40.0ms

simplify74.0ms

prune148.0ms

localize14.0ms

rewrite19.0ms

series47.0ms

simplify50.0ms

prune294.0ms

localize22.0ms

rewrite32.0ms

series70.0ms

simplify64.0ms

prune490.0ms

localize25.0ms

rewrite37.0ms

series101.0ms

simplify39.0ms

prune410.0ms

regimes190.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling