Details

analyze1.0ms

Algorithm

Search

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

sample37.0ms

Algorithm

intervals

Results

21.0ms	99×	body	1280	valid
5.0ms	121×	body	80	valid
2.0ms	11×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify18.0ms

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: 18.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
3.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
18.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5028	716

prune129.0ms

Filtered

52 candidates to 71 candidates (-36.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 17.9b

Counts

72 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(/ 0.5 (hypot 1.0 x))
2.9b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
9×	`add-log-exp`
7×	`associate-/l*`
4×	`pow1` `cbrt-undiv` `flip3--` `associate-*r/` `div-exp` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`frac-2neg` `diff-log` `clear-num` `div-inv` `distribute-lft-out--`
2×	`sub-neg` `sqrt-prod` `associate-/r/` `difference-of-squares`
1×	`associate--l-` `flip3-+` `prod-exp` `associate--l+` `cbrt-unprod` `flip-+`

Counts

4 → 105

Calls

4 calls:

17.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
3.0ms	(/ 0.5 (hypot 1.0 x))
3.0ms	(/ 0.5 (hypot 1.0 x))
10.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
4.0ms	(/ 0.5 (hypot 1.0 x))
5.0ms	(/ 0.5 (hypot 1.0 x))
6.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4974	1689
1	4974	1689

prune279.0ms

Filtered

87 candidates to 117 candidates (-34.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Merged error: 17.5b

Counts

121 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
0.2b	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
0.5b	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
3.0b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
28×	`associate-*r/`
22×	`flip3-+` `associate-*l/` `flip-+`
13×	`prod-exp` `cbrt-unprod`
12×	`frac-times`
11×	`pow1` `*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`associate-/r/` `frac-sub`
7×	`add-cube-cbrt` `associate-l`
6×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `flip--` `associate-/l/` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow-prod-down`
3×	`distribute-lft-out`
2×	`*-commutative`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `sqrt-prod` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

20.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
9.0ms	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
9.0ms	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
8.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))

series84.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
21.0ms	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
21.0ms	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
3.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))

simplify63.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4987	3672
1	4987	3672

prune458.0ms

Filtered

87 candidates to 127 candidates (-46.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 17.5b

Counts

131 → 6

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5)))))))
0.2b	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
0.5b	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
3.0b	(- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

334×	`associate-*r/`
162×	`flip3-+` `flip-+`
140×	`frac-times`
128×	`frac-sub`
70×	`associate-*l/`
66×	`associate-/l/`
50×	`flip3--` `flip--`
16×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-rgt-in` `*-un-lft-identity` `distribute-lft-in`
12×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `associate--l+` `associate--r+`
3×	`times-frac` `distribute-lft-out` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `*-commutative`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv` `unswap-sqr`

Counts

4 → 240

Calls

4 calls:

44.0ms	(/ (- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5)))))))
9.0ms	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
8.0ms	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
22.0ms	(- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5)))))))
20.0ms	(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
23.0ms	(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
4.0ms	(- (* (hypot 1.0 x) (* (- (pow 1.0 6) (pow 0.5 6)) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* 0.5 (* (+ (pow 1.0 4) (+ (pow 0.5 4) (* 1.0 (* 1.0 (* 0.5 0.5))))) (+ (pow 1.0 3) (pow 0.5 3)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5081	19591

prune8.0s

Filtered

220 candidates to 252 candidates (-14.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	249	3	252
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	252	6	258

Merged error: 17.5b

Counts

258 → 6

regimes160.0ms

Accuracy

0% (0.6b remaining)

Error of 15.4b against oracle of 14.8b and baseline of 15.4b

bsearch0.0ms

simplify33.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	1471	224
1	1471	224

end0.0ms

sample1.0s

Algorithm

intervals

Results

620.0ms	2825×	body	1280	valid
158.0ms	4053×	body	80	valid
111.0ms	631×	body	640	valid
40.0ms	333×	body	320	valid
12.0ms	158×	body	160	valid

Details

analyze1.0ms

sample37.0ms

simplify18.0ms

prune5.0ms

localize8.0ms

rewrite14.0ms

series28.0ms

simplify65.0ms

prune129.0ms

localize12.0ms

rewrite35.0ms

series50.0ms

simplify49.0ms

prune279.0ms

localize22.0ms

rewrite50.0ms

series84.0ms

simplify63.0ms

prune458.0ms

localize43.0ms

rewrite105.0ms

series54.0ms

simplify135.0ms

prune8.0s

regimes160.0ms

bsearch0.0ms

simplify33.0ms

end0.0ms

sample1.0s

Profiling