Details

analyze270.0ms

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

sample63.0ms

Algorithm

intervals

Results

21.0ms	114×	body	2560	nan
14.0ms	93×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	41×	body	640	nan
3.0ms	28×	body	320	nan
1.0ms	10×	body	160	nan
0.0ms	7×	body	80	nan

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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: 33.6b

Counts

2 → 1

localize7.0ms

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))))
31.2b	(sqrt (- (* x x) 1.0))

rewrite17.0ms

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))

series20.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
11.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5188	615

prune87.0ms

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))))
0.2b	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
0.3b	(/ 0.09375 (pow x 4))
1.1b	(/ 0.25 (* x x))

rewrite73.0ms

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:

30.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
25.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
6.0ms	(/ 0.09375 (pow x 4))
4.0ms	(/ 0.25 (* x x))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
18.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
6.0ms	(/ 0.09375 (pow x 4))
5.0ms	(/ 0.25 (* x x))

simplify78.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4931	1630
1	4931	1630

prune177.0ms

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

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 0.09375 (pow x 4))
0.5b	(cbrt x)
0.5b	(cbrt x)
1.1b	(/ 0.25 (* x x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
8×	`associate-/r*`
6×	`cbrt-prod` `associate-/l*`
5×	`div-exp`
4×	`pow1` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv`
2×	`frac-2neg` `pow1/3` `clear-num` `div-inv`
1×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 88

Calls

4 calls:

4.0ms	(/ 0.09375 (pow x 4))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(/ 0.25 (* x x))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.09375 (pow x 4))
22.0ms	(cbrt x)
24.0ms	(cbrt x)
3.0ms	(/ 0.25 (* x x))

simplify75.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4816	667
1	4816	667

prune141.0ms

Filtered

67 candidates to 100 candidates (-49.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Merged error: 0b

Counts

102 → 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))))

rewrite20.0ms

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)))))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (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

prune152.0ms

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

regimes26.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	24
1	61	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

559.0ms	2993×	body	2560	nan
396.0ms	2518×	body	1280	nan
318.0ms	8000×	body	80	valid
165.0ms	1327×	body	640	nan
57.0ms	619×	body	320	nan
19.0ms	304×	body	160	nan
10.0ms	316×	body	80	nan

Details

analyze270.0ms

sample63.0ms

simplify63.0ms

prune3.0ms

localize7.0ms

rewrite17.0ms

series20.0ms

simplify41.0ms

prune87.0ms

localize13.0ms

rewrite73.0ms

series43.0ms

simplify78.0ms

prune177.0ms

localize17.0ms

rewrite13.0ms

series53.0ms

simplify75.0ms

prune141.0ms

localize10.0ms

rewrite20.0ms

series33.0ms

simplify41.0ms

prune152.0ms

regimes26.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

Profiling