Details

analyze273.0ms

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

sample60.0ms

Algorithm

intervals

Results

19.0ms	97×	body	2560	nan
15.0ms	94×	body	1280	nan
10.0ms	256×	body	80	valid
3.0ms	26×	body	640	nan
2.0ms	22×	body	320	nan
0.0ms	10×	body	80	nan
0.0ms	4×	body	160	nan

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

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: 32.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
30.6b	(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))

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (36.0ms)

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b	(sqrt (- x (sqrt 1.0)))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms	(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))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms	(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))))

simplify32.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5008	1491

prune198.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	97	2	99

Merged error: 0.0b

Counts

99 → 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)))))
1.2b	(/ 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:

17.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
4.0ms	(/ 0.09375 (pow x 4))
23.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
4.0ms	(/ 0.25 (* x x))

series23.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
3.0ms	(/ 0.09375 (pow x 4))
10.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
3.0ms	(/ 0.25 (* x x))

simplify66.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4931	1630
1	4931	1630

prune177.0ms

Filtered

85 candidates to 130 candidates (-52.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0b

Counts

132 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (log 2) (* 2 (log (cbrt x)))) (- (log (cbrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
0.5b	(cbrt x)
0.5b	(cbrt x)
1.2b	(/ 0.25 (* x x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-log-exp`
11×	`sum-log`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
7×	`associate-+r+` `distribute-lft-out`
6×	`pow1` `log-prod` `associate--l+`
4×	`diff-log` `frac-add` `distribute-lft-out--`
3×	`flip3-+` `times-frac` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `pow1/3` `div-exp` `log-pow` `flip--`
1×	`+-commutative` `associate-+r-` `sub-neg` `associate-+l+` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

23.0ms	(+ (+ (log 2) (* 2 (log (cbrt x)))) (- (log (cbrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(/ 0.25 (* x x))

series67.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ (log 2) (* 2 (log (cbrt x)))) (- (log (cbrt x)) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
21.0ms	(cbrt x)
22.0ms	(cbrt x)
3.0ms	(/ 0.25 (* x x))

simplify30.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5212	1403

prune143.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	89	2	91

Merged error: 0b

Counts

91 → 2

regimes27.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

594.0ms	2995×	body	2560	nan
421.0ms	2607×	body	1280	nan
327.0ms	8000×	body	80	valid
159.0ms	1234×	body	640	nan
61.0ms	606×	body	320	nan
21.0ms	306×	body	160	nan
12.0ms	300×	body	80	nan

Details

analyze273.0ms

sample60.0ms

simplify65.0ms

prune3.0ms

localize9.0ms

rewrite17.0ms

series17.0ms

simplify42.0ms

prune88.0ms

localize11.0ms

rewrite24.0ms

series37.0ms

simplify32.0ms

prune198.0ms

localize13.0ms

rewrite52.0ms

series23.0ms

simplify66.0ms

prune177.0ms

localize18.0ms

rewrite35.0ms

series67.0ms

simplify30.0ms

prune143.0ms

regimes27.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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