Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	61×	body	1280	valid
4.0ms	252×	body	80	nan
3.0ms	43×	body	640	valid
2.0ms	132×	body	80	valid
1.0ms	13×	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))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite22.0ms

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))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (33.0ms)

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

prune127.0ms

Filtered

95 candidates to 44 candidates (46.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Merged error: 0.1b

Counts

96 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
28×	`distribute-lft-out`
24×	`times-frac` `sqrt-prod`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
3×	`pow1` `flip3-+` `flip-+`
2×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

2 → 71

Calls

2 calls:

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

series175.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(sqrt (+ x 1.0))
145.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	654
1	1550	602
2	5002	560

prune151.0ms

Filtered

77 candidates to 48 candidates (62.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Merged error: 0.0b

Counts

80 → 7

localize11.0ms

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))

rewrite29.0ms

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:

183.0ms	(/ (+ 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))))
92.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (96.0ms)

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

prune362.0ms

Filtered

112 candidates to 95 candidates (84.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	112	7	119

Merged error: 0.0b

Counts

119 → 7

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)))))

rewrite113.0ms

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)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
48.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
170.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (93.0ms)

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

prune475.0ms

Filtered

336 candidates to 155 candidates (46.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	334	2	336
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	334	9	343

Merged error: 0b

Counts

343 → 9

regimes68.0ms

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

sample639.0ms

Algorithm

intervals

Results

153.0ms	1744×	body	1280	valid
125.0ms	7896×	body	80	nan
80.0ms	1250×	body	640	valid
72.0ms	4077×	body	80	valid
30.0ms	627×	body	320	valid
10.0ms	302×	body	160	valid