Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	50×	body	1280	valid
4.0ms	227×	body	80	nan
3.0ms	52×	body	640	valid
2.0ms	123×	body	80	valid
1.0ms	25×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 32.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1.0))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune91.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
83.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5001	533

prune161.0ms

Filtered

80 candidates to 53 candidates (66.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 0.0b

Counts

84 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

10.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
12.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series470.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
101.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
90.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	850	1475
1	3967	1385
2	5002	1364

prune350.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	99	9	108

Merged error: 0.0b

Counts

108 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
32.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
167.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
533.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify136.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	1033	8862
1	4120	7704
2	5001	7681

prune532.0ms

Filtered

457 candidates to 146 candidates (31.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	452	5	457
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	457	9	466

Merged error: 0.0b

Counts

466 → 9

regimes36.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

end0.0ms

sample654.0ms

Algorithm

intervals

Results

142.0ms	1630×	body	1280	valid
134.0ms	8087×	body	80	nan
82.0ms	1262×	body	640	valid
77.0ms	4166×	body	80	valid
31.0ms	634×	body	320	valid
10.0ms	308×	body	160	valid