Details

sample142.0ms

Algorithm

intervals

Results

36.0ms	115×	body	2560	nan
28.0ms	519×	body	80	nan
24.0ms	90×	body	1280	nan
16.0ms	256×	body	80	valid
8.0ms	37×	body	640	nan
3.0ms	17×	body	320	nan
1.0ms	10×	body	160	nan

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.9b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `prod-diff`
2×	`log-div` `flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (* x x) 1.0)
10.0ms	(+ x (sqrt (- (* x x) 1.0)))
10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
8.0ms	(sqrt (- (* x x) 1.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* x x) 1.0)
68.0ms	(+ x (sqrt (- (* x x) 1.0)))
191.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
49.0ms	(sqrt (- (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	384	531
1	1360	471
2	5002	457

prune172.0ms

Filtered

83 candidates to 67 candidates (80.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 0b

Counts

84 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (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

28×	`add-sqr-sqrt`
20×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`sqrt-div`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-r/` `associate-l/` `hypot-def` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

4.0ms	(sqrt (+ x (sqrt 1.0)))
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))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ x (sqrt 1.0)))
320.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
275.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
200.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	524	1160
1	1847	1044
2	5001	1027

prune252.0ms

Filtered

108 candidates to 86 candidates (79.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Merged error: 0b

Counts

111 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (/ (/ 0.25 x) x))
0.1b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b	(/ 0.09375 (pow x 4))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

870×	`times-frac`
804×	`add-sqr-sqrt`
668×	`*-un-lft-identity`
570×	`add-cube-cbrt`
544×	`prod-diff`
379×	`associate-+r+`
183×	`associate--l+`
124×	`pow1`
120×	`log-pow`
84×	`unpow-prod-down`
78×	`difference-of-squares`
62×	`distribute-lft-out--`
46×	`div-inv`
28×	`sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/r*` `add-log-exp`
9×	`log-prod`
8×	`distribute-lft-out`
6×	`div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `fma-def` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate-+l+` `sum-log`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `flip--` `flip-+` `associate-/l/`

Counts

4 → 727

Calls

4 calls:

24.0ms	(- (log x) (/ (/ 0.25 x) x))
6.0ms	(/ (/ 0.25 x) x)
70.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))

series456.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(- (log x) (/ (/ 0.25 x) x))
23.0ms	(/ (/ 0.25 x) x)
99.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
34.0ms	(/ 0.09375 (pow x 4))

simplify191.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2647	14534
1	5002	11801

prune1.7s

Filtered

739 candidates to 412 candidates (55.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	739	0	739
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	739	3	742

Merged error: 0b

Counts

742 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
0.2b	(log1p (expm1 (log (+ x (sqrt (- (* x x) 1.0))))))
5.6b	(expm1 (log (+ x (sqrt (- (* x x) 1.0)))))
30.6b	(sqrt (- (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `log-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
2×	`log-div` `sqrt-div`
1×	`rem-sqrt-square` `log1p-udef` `expm1-log1p` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `log1p-expm1` `rem-log-exp` `log-pow` `flip--` `flip-+` `distribute-lft-out` `expm1-udef` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
1.0ms	(log1p (expm1 (log (+ x (sqrt (- (* x x) 1.0))))))
1.0ms	(expm1 (log (+ x (sqrt (- (* x x) 1.0)))))
9.0ms	(sqrt (- (* x x) 1.0))

series827.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
354.0ms	(log1p (expm1 (log (+ x (sqrt (- (* x x) 1.0))))))
235.0ms	(expm1 (log (+ x (sqrt (- (* x x) 1.0)))))
49.0ms	(sqrt (- (* x x) 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	387	591
1	1317	540
2	5001	507

prune172.0ms

Filtered

69 candidates to 59 candidates (85.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	69	3	72

Merged error: 0b

Counts

72 → 3

regimes57.0ms

Accuracy

0% (0.1b 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 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

602.0ms	3062×	body	2560	nan
564.0ms	16376×	body	80	nan
412.0ms	2500×	body	1280	nan
324.0ms	8000×	body	80	valid
162.0ms	1265×	body	640	nan
59.0ms	612×	body	320	nan
21.0ms	313×	body	160	nan

Details

sample142.0ms

simplify8.0ms

prune3.0ms

localize13.0ms

rewrite34.0ms

series345.0ms

simplify42.0ms

prune172.0ms

localize10.0ms

rewrite24.0ms

series856.0ms

simplify52.0ms

prune252.0ms

localize13.0ms

rewrite170.0ms

series456.0ms

simplify191.0ms

prune1.7s

localize11.0ms

rewrite17.0ms

series827.0ms

simplify38.0ms

prune172.0ms

regimes57.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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