Details

sample41.0ms

Algorithm

intervals

Results

22.0ms	104×	body	1280	valid
5.0ms	116×	body	80	valid
4.0ms	22×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	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: 16.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
269.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
99.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
342.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5001	876

prune249.0ms

Filtered

104 candidates to 84 candidates (80.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Merged error: 16.2b

Counts

105 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.1b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(+ 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))

series677.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
103.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
102.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	412	549
1	1441	494
2	5001	493

prune240.0ms

Filtered

73 candidates to 67 candidates (91.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Merged error: 0.2b

Counts

77 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.1b	(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×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
6×	`fma-def`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 62

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series523.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
104.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
155.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
154.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	263	531
1	822	468
2	3994	468
3	5001	460

prune244.0ms

Filtered

74 candidates to 67 candidates (90.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	74	3	77

Merged error: 0.2b

Counts

77 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.4b	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.4b	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

180×	`sqrt-prod`
126×	`prod-diff`
108×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
88×	`add-cube-cbrt`
44×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`sqrt-pow1`
9×	`associate-r`
8×	`sqrt-div` `difference-of-squares`
6×	`add-exp-log` `fma-neg` `associate-*r/` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`expm1-log1p-u` `frac-times` `flip3--` `pow1/2` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `pow-prod-down`
2×	`rem-sqrt-square` `associate-*l/` `distribute-lft-out`
1×	`diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 234

Calls

4 calls:

18.0ms	(* (+ (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
8.0ms	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
11.0ms	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series3.2s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (+ (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
503.0ms	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
489.0ms	(sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
633.0ms	(- (sqrt 1.0) (sqrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify149.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	997	8787
1	4385	6187
2	5001	6171

prune482.0ms

Filtered

246 candidates to 126 candidates (51.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	246	3	249

Merged error: 0.2b

Counts

249 → 3

regimes198.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.9b

bsearch151.0ms

Steps

Iters	Range		Point
7	1.578317661697433e-06	0.0002141056345597589	0.00013624945209359787
11	-4.816760182774211e+16	-0.0014803844373699059	-0.002831278663826302

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	36
1	50	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

635.0ms	2845×	body	1280	valid
164.0ms	4046×	body	80	valid
110.0ms	625×	body	640	valid
38.0ms	314×	body	320	valid
13.0ms	170×	body	160	valid