Details

sample60.0ms

Algorithm

intervals

Results

32.0ms	97×	body	1280	valid
8.0ms	130×	body	80	valid
5.0ms	18×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify8.0ms

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 (100.0%)

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: 14.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1984	411
3	5001	411

prune127.0ms

Filtered

73 candidates to 52 candidates (28.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 13.6b

Counts

74 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ (- (* 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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
30.0ms	(/ (- (* 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)))))))
13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	423	1277
1	1641	1179
2	5001	1174

prune264.0ms

Filtered

107 candidates to 77 candidates (28.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Merged error: 13.6b

Counts

111 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.3b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

271×	`associate-*r/`
104×	`frac-add`
74×	`flip3--` `associate-/r/` `flip--`
68×	`frac-times`
39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`times-frac`
26×	`associate-*l/`
21×	`sqr-pow`
20×	`difference-of-squares`
19×	`add-cube-cbrt`
18×	`flip3-+` `flip-+`
12×	`add-exp-log` `add-cbrt-cube`
9×	`cube-div` `associate-/l*`
8×	`add-log-exp`
7×	`pow1`
5×	`difference-cubes` `distribute-lft-out--`
4×	`frac-sub` `associate-/l/`
3×	`pow-unpow` `pow-exp` `associate-/r*` `rem-cube-cbrt`
2×	`cbrt-undiv` `pow-pow` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `diff-log` `unpow3` `div-sub` `cube-prod` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 187

Calls

4 calls:

29.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
10.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series90.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
12.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
14.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1925	6433
1	5001	6292

prune2.0s

Filtered

199 candidates to 150 candidates (24.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	197	5	202

Merged error: 13.3b

Counts

202 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.3b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
1.3b	(log (exp (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-exp-log` `log-pow` `add-cbrt-cube`
9×	`exp-prod` `sqr-pow`
8×	`pow1` `add-log-exp` `difference-of-squares`
7×	`add-cube-cbrt`
5×	`cube-div` `log-prod` `associate-*r/`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`difference-cubes` `sub-neg` `flip3--` `pow-pow` `exp-sum` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `unpow-prod-down` `log-div` `flip3-+` `exp-diff` `diff-log` `unpow3` `cube-prod` `div-exp` `rem-log-exp` `pow-prod-down` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
8.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
8.0ms	(log (exp (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
18.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
15.0ms	(log (exp (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))))

simplify60.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	408	850
1	1654	783
2	5002	782

prune423.0ms

Filtered

93 candidates to 66 candidates (29.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 13.3b

Counts

98 → 5

regimes150.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample1.1s

Algorithm

intervals

Results

607.0ms	2867×	body	1280	valid
154.0ms	4003×	body	80	valid
111.0ms	658×	body	640	valid
38.0ms	309×	body	320	valid
14.0ms	163×	body	160	valid

Details

sample60.0ms

simplify8.0ms

prune2.0ms

localize8.0ms

rewrite14.0ms

series33.0ms

simplify56.0ms

prune127.0ms

localize13.0ms

rewrite25.0ms

series55.0ms

simplify52.0ms

prune264.0ms

localize22.0ms

rewrite62.0ms

series90.0ms

simplify97.0ms

prune2.0s

localize28.0ms

rewrite26.0ms

series55.0ms

simplify60.0ms

prune423.0ms

regimes150.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling