Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	263×	body	80	nan
6.0ms	48×	body	1280	valid
4.0ms	144×	body	80	valid
3.0ms	38×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	8×	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: 26.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
12.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	299	1161
1	921	822
2	5001	744

prune128.0ms

Filtered

95 candidates to 44 candidates (46.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	4	96

Merged error: 0.1b

Counts

96 → 4

localize7.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	409	789
1	1675	716
2	5001	675

prune192.0ms

Filtered

103 candidates to 68 candidates (66.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Merged error: 0.0b

Counts

107 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`times-frac`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 100

Calls

4 calls:

12.0ms	(/ (+ 1.0 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))

series465.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
99.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
90.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	938	1649
1	4540	1538
2	5001	1534

prune374.0ms

Filtered

112 candidates to 95 candidates (84.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Merged error: 0.0b

Counts

120 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 324

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

347.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
178.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify137.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	723	3905
1	3885	3364
2	5002	3360

prune473.0ms

Filtered

336 candidates to 154 candidates (45.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	336	9	345

Merged error: 0.0b

Counts

345 → 9

regimes38.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample886.0ms

Algorithm

intervals

Results

211.0ms	1730×	body	1280	valid
203.0ms	8059×	body	80	nan
117.0ms	1215×	body	640	valid
108.0ms	4102×	body	80	valid
42.0ms	607×	body	320	valid
16.0ms	346×	body	160	valid