Details

sample16.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	273×	body	80	nan

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	11	3
2	13	3
3	13	3

prune2.0ms

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: 0.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`

Counts

1 → 18

Calls

1 calls:

3.0ms

(sqrt (- 1.0 (* x x)))

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(sqrt (- 1.0 (* x x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	165	131
1	568	128
2	2782	126
3	5001	123

prune48.0ms

Filtered

21 candidates to 18 candidates (85.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	2	22

Merged error: 0b

Counts

22 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

6.0ms	(sqrt (- (sqrt 1.0) x))
7.0ms	(sqrt (+ (sqrt 1.0) x))
13.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)))

series270.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(sqrt (- (sqrt 1.0) x))
60.0ms	(sqrt (+ (sqrt 1.0) x))
148.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	336	805
1	1175	768
2	5001	748

prune214.0ms

Filtered

93 candidates to 67 candidates (72.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	93	2	95

Merged error: 0b

Counts

95 → 2

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0b	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
54×	`add-sqr-sqrt`
52×	`associate-r`
32×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
20×	`unpow-prod-down`
12×	`add-exp-log`
9×	`unswap-sqr`
8×	`unpow2` `sqr-pow`
7×	`add-cbrt-cube`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`associate-r/` `div-exp` `associate-l*`
2×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `fma-def` `flip3-+` `pow-prod-down` `frac-add` `pow-exp` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

2 → 97

Calls

2 calls:

15.0ms	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
14.0ms	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

series341.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(* 1/2 (/ (pow x 2) (sqrt 1.0)))
276.0ms	(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	476	745
1	2317	663
2	5001	662

prune239.0ms

Filtered

103 candidates to 60 candidates (58.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	103	2	105

Merged error: 0b

Counts

105 → 2

regimes12.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample397.0ms

Algorithm

intervals

Results

129.0ms	8000×	body	80	valid
108.0ms	7716×	body	80	nan