Details

analyze1.0ms

Algorithm

Search

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

sample62.0ms

Algorithm

intervals

Results

22.0ms	89×	body	1280	valid
5.0ms	131×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	8×	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: 16.2b

Counts

2 → 1

localize9.0ms

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))
16.1b	(- 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	(+ 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))))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
17.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4844	870
1	4844	870

prune145.0ms

Filtered

54 candidates to 77 candidates (-42.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Merged error: 15.7b

Counts

78 → 4

localize13.0ms

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 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
15.7b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

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

series27.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(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

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5000	919

prune221.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	92	4	96

Merged error: 15.6b

Counts

96 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (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)
0.1b	(/ (- (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)))))))
15.7b	(- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

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

series156.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (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))))))
15.0ms	(pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)
81.0ms	(/ (- (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)))))))
41.0ms	(- (pow 1.0 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5220	5404

prune840.0ms

Filtered

98 candidates to 133 candidates (-35.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	133	4	137

Merged error: 15.6b

Counts

137 → 4

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)
0.1b	(pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6)
0.1b	(/ (- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)) (* (+ (pow 1.0 12) (* (pow 1.0 6) (+ (pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)))) (+ (pow 1.0 4) (* 0.5 (* 1.0 (* (+ 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
15.7b	(- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-sqr-sqrt`
164×	`unpow-prod-down`
144×	`difference-of-squares`
130×	`sqr-pow`
124×	`cube-prod`
57×	`times-frac` `associate-/l*`
43×	`*-un-lft-identity`
15×	`distribute-lft-out--`
14×	`add-exp-log`
11×	`add-cube-cbrt`
10×	`add-cbrt-cube`
8×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow-unpow` `add-log-exp`
5×	`pow1`
4×	`cube-div` `frac-times` `associate-*r/`
3×	`difference-cubes` `cube-mult` `pow-to-exp` `unpow3`
2×	`cbrt-undiv` `flip3--` `pow-pow` `div-exp` `associate-*l/` `prod-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 261

Calls

4 calls:

5.0ms	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)
9.0ms	(pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6)
40.0ms	(/ (- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)) (* (+ (pow 1.0 12) (* (pow 1.0 6) (+ (pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)))) (+ (pow 1.0 4) (* 0.5 (* 1.0 (* (+ 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
26.0ms	(- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3))

series874.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)
18.0ms	(pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6)
649.0ms	(/ (- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3)) (* (+ (pow 1.0 12) (* (pow 1.0 6) (+ (pow (+ 0.5 (/ 0.5 (hypot 1.0 x))) 6) (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3)))) (+ (pow 1.0 4) (* 0.5 (* 1.0 (* (+ 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
176.0ms	(- (pow (pow 1.0 6) 3) (pow (pow (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 3) 3))

simplify136.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4962	15843
1	4962	15843

prune2.5s

Filtered

134 candidates to 273 candidates (-103.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	271	2	273
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	273	4	277

Merged error: 15.6b

Counts

277 → 4

regimes327.0ms

Accuracy

0% (0.0b remaining)

Error of 15.2b against oracle of 15.2b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	114
1	90	114

end0.0ms

sample1.6s

Algorithm

intervals

Results

726.0ms	2895×	body	1280	valid
145.0ms	3983×	body	80	valid
105.0ms	620×	body	640	valid
39.0ms	329×	body	320	valid
13.0ms	173×	body	160	valid

Details

analyze1.0ms

sample62.0ms

simplify19.0ms

prune5.0ms

localize9.0ms

rewrite20.0ms

series39.0ms

simplify77.0ms

prune145.0ms

localize13.0ms

rewrite19.0ms

series27.0ms

simplify50.0ms

prune221.0ms

localize33.0ms

rewrite41.0ms

series156.0ms

simplify77.0ms

prune840.0ms

localize43.0ms

rewrite95.0ms

series874.0ms

simplify136.0ms

prune2.5s

regimes327.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling