Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	133×	body	80	valid
4.0ms	51×	body	1280	valid
4.0ms	255×	body	80	nan
3.0ms	42×	body	640	valid
1.0ms	23×	body	320	valid
0.0ms	7×	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: 29.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.9b	(- (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))

series106.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (53.0ms)

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

prune68.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Merged error: 0.1b

Counts

42 → 3

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))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1.0))
69.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

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

prune155.0ms

Filtered

80 candidates to 53 candidates (66.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	73	10	83

Merged error: 0.0b

Counts

83 → 10

localize9.0ms

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))

rewrite26.0ms

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)))
8.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series464.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
98.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
89.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (+ x 1.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (86.0ms)

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

prune312.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 0.0b

Counts

108 → 11

localize8.0ms

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))))

rewrite96.0ms

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))))
31.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
335.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
145.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify141.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (68.0ms)

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

prune480.0ms

Filtered

457 candidates to 147 candidates (32.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	453	4	457
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	460	8	468

Merged error: 0.0b

Counts

468 → 8

regimes31.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms

sample652.0ms

Algorithm

intervals

Results

143.0ms	1670×	body	1280	valid
133.0ms	7950×	body	80	nan
85.0ms	1252×	body	640	valid
79.0ms	4160×	body	80	valid
31.0ms	613×	body	320	valid
13.0ms	305×	body	160	valid