Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample27.0ms

Algorithm

intervals

Results

8.0ms	63×	body	640	valid
6.0ms	36×	body	1280	valid
5.0ms	132×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	12×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

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: 15.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.3b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
29.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ 1.0 (sqrt x))
12.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify32.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5076	1839

prune249.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 15.1b

Counts

145 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.2b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
3.3b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
16.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
7.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series49.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
30.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5212	1577

prune186.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 0.2b

Counts

115 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative`

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
19.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
35.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5523	2087

prune253.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 0.0b

Counts

143 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
55×	`sqrt-prod`
48×	`add-cube-cbrt`
23×	`distribute-lft-out`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r` `associate-/l`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

3.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	4295
1	4975	4295

prune343.0ms

Filtered

129 candidates to 188 candidates (-45.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	188	11	199

Merged error: 0b

Counts

199 → 11

regimes61.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms

sample784.0ms

Algorithm

intervals

Results

263.0ms	1866×	body	640	valid
204.0ms	1142×	body	1280	valid
148.0ms	4095×	body	80	valid
62.0ms	607×	body	320	valid
20.0ms	290×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify11.0ms

prune5.0ms

localize10.0ms

rewrite46.0ms

series31.0ms

simplify32.0ms

prune249.0ms

localize8.0ms

rewrite37.0ms

series49.0ms

simplify36.0ms

prune186.0ms

localize12.0ms

rewrite50.0ms

series55.0ms

simplify61.0ms

prune253.0ms

localize11.0ms

rewrite37.0ms

series45.0ms

simplify86.0ms

prune343.0ms

regimes61.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample784.0ms

Profiling