Details

analyze267.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample56.0ms

Algorithm

intervals

Results

18.0ms	97×	body	2560	nan
11.0ms	71×	body	1280	nan
10.0ms	256×	body	80	valid
4.0ms	33×	body	640	nan
2.0ms	17×	body	320	nan
1.0ms	8×	body	160	nan
0.0ms	13×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5257	9

prune3.0ms

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: 31.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.5b	(log (+ x (sqrt (- (* x x) 1.0))))
29.0b	(sqrt (- (* x x) 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

6.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

series18.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (sqrt (- (* x x) 1.0)))
10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5188	615

prune88.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0.0b

Counts

53 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
0.1b	(/ 0.09375 (pow x 4))
0.2b	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
1.0b	(/ 0.25 (* x x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`times-frac`
16×	`distribute-lft-out`
15×	`pow1`
14×	`add-exp-log`
12×	`unpow-prod-down` `distribute-lft-out--`
11×	`log-pow` `add-cbrt-cube` `add-log-exp`
9×	`log-prod`
8×	`associate-/r*`
6×	`associate--l+` `associate-/l*`
5×	`div-exp` `sum-log`
4×	`associate-+r+` `diff-log` `sqr-pow`
3×	`cbrt-undiv` `associate-+l+`
2×	`sub-neg` `frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `associate--r+` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

18.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
4.0ms	(/ 0.09375 (pow x 4))
21.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
4.0ms	(/ 0.25 (* x x))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
4.0ms	(/ 0.09375 (pow x 4))
12.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
3.0ms	(/ 0.25 (* x x))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4931	1630
1	4931	1630

prune178.0ms

Filtered

85 candidates to 130 candidates (-52.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	130	2	132

Merged error: 0b

Counts

132 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.09375 (pow x 4))
0.1b	(+ (log 2) (log (sqrt x)))
0.2b	(+ (+ (log 2) (log (sqrt x))) (- (log (sqrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
1.0b	(/ 0.25 (* x x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
59×	`distribute-lft-out`
38×	`pow1`
34×	`log-pow`
27×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
20×	`distribute-lft-out--`
15×	`log-prod` `add-log-exp`
14×	`add-exp-log`
13×	`associate-+r+`
12×	`unpow-prod-down` `sum-log`
11×	`add-cbrt-cube`
8×	`associate-/r*`
6×	`associate--l+` `sqrt-prod` `associate-/l*`
5×	`div-exp`
4×	`associate-+l+` `flip3-+` `diff-log` `frac-add` `flip-+` `sqr-pow`
3×	`cbrt-undiv`
2×	`+-commutative` `flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`
1×	`pow-to-exp` `associate-+r-` `sub-neg` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

4.0ms	(/ 0.09375 (pow x 4))
6.0ms	(+ (log 2) (log (sqrt x)))
29.0ms	(+ (+ (log 2) (log (sqrt x))) (- (log (sqrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
5.0ms	(/ 0.25 (* x x))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.09375 (pow x 4))
6.0ms	(+ (log 2) (log (sqrt x)))
9.0ms	(+ (+ (log 2) (log (sqrt x))) (- (log (sqrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
3.0ms	(/ 0.25 (* x x))

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4959	2198
1	4959	2198

prune206.0ms

Filtered

93 candidates to 156 candidates (-67.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	156	2	158

Merged error: 0b

Counts

158 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
15.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series33.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
11.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4963	1255
1	4963	1255

prune154.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	76	2	78

Merged error: 0b

Counts

78 → 2

regimes27.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	22
1	59	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

578.0ms	2947×	body	2560	nan
400.0ms	2444×	body	1280	nan
323.0ms	8000×	body	80	valid
157.0ms	1204×	body	640	nan
65.0ms	626×	body	320	nan
23.0ms	336×	body	160	nan
10.0ms	315×	body	80	nan

Details

analyze267.0ms

sample56.0ms

simplify57.0ms

prune3.0ms

localize9.0ms

rewrite18.0ms

series18.0ms

simplify40.0ms

prune88.0ms

localize13.0ms

rewrite52.0ms

series25.0ms

simplify58.0ms

prune178.0ms

localize16.0ms

rewrite50.0ms

series21.0ms

simplify52.0ms

prune206.0ms

localize10.0ms

rewrite22.0ms

series33.0ms

simplify41.0ms

prune154.0ms

regimes27.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

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