Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	89×	body	1280	valid
5.0ms	134×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

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: 13.3b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms	(hypot 1.0 x)
3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
56.0ms	(hypot 1.0 x)
103.0ms	(/ 1.0 (hypot 1.0 x))
362.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	533	1074
1	2023	830
2	5002	827

prune231.0ms

Filtered

97 candidates to 79 candidates (81.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 12.6b

Counts

98 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series690.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1.0 (hypot 1.0 x))
110.0ms	(/ 1.0 (hypot 1.0 x))
327.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
150.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	430	681
1	1662	625
2	5001	623

prune315.0ms

Filtered

97 candidates to 85 candidates (87.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	419	1369
1	1647	1263
2	5002	1251

prune357.0ms

Filtered

70 candidates to 64 candidates (91.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	70	5	75

Merged error: 0.2b

Counts

75 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.3b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod`
2×	`flip3-+` `pow1/3` `flip-+` `fma-udef` `distribute-lft-out`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
9.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series3.1s

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
168.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
156.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	455	1151
1	1727	1050
2	5002	1042

prune343.0ms

Filtered

72 candidates to 65 candidates (90.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	72	5	77

Merged error: 0.2b

Counts

77 → 5

regimes325.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	52
1	46	52

end0.0ms

sample1.1s

Algorithm

intervals

Results

639.0ms	2850×	body	1280	valid
170.0ms	4043×	body	80	valid
111.0ms	621×	body	640	valid
43.0ms	329×	body	320	valid
13.0ms	157×	body	160	valid