Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	259×	body	80	nan
4.0ms	47×	body	1280	valid
3.0ms	41×	body	640	valid
2.0ms	130×	body	80	valid
1.0ms	24×	body	320	valid
0.0ms	14×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

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:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify176.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	295	1161
1	887	822
2	4889	705
3	5001	675

prune115.0ms

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 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite29.0ms

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:

4.0ms	(sqrt (+ x 1.0))
8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
151.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	405	789
1	1641	716
2	5001	675

prune176.0ms

Filtered

103 candidates to 68 candidates (66.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Merged error: 0.0b

Counts

106 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
20×	`times-frac`
19×	`distribute-lft-out`
13×	`cbrt-prod`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`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 → 110

Calls

4 calls:

21.0ms	(/ (+ 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))

series489.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
106.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
94.0ms	(cbrt (+ x 1.0))
95.0ms	(cbrt (+ x 1.0))

simplify130.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	929	1753
1	4478	1628
2	5001	1624

prune365.0ms

Filtered

122 candidates to 95 candidates (77.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	121	8	129

Merged error: 0.0b

Counts

129 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 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))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
20×	`times-frac`
19×	`distribute-lft-out`
13×	`cbrt-prod`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`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 → 110

Calls

4 calls:

27.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
9.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series533.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
113.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
103.0ms	(cbrt (+ x 1.0))
102.0ms	(cbrt (+ x 1.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	929	1753
1	4478	1628
2	5001	1624

prune420.0ms

Filtered

122 candidates to 95 candidates (77.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 0.0b

Counts

130 → 8

regimes42.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample643.0ms

Algorithm

intervals

Results

145.0ms	1688×	body	1280	valid
127.0ms	7818×	body	80	nan
82.0ms	1267×	body	640	valid
77.0ms	4113×	body	80	valid
32.0ms	602×	body	320	valid
11.0ms	330×	body	160	valid