Details

sample32.0ms

Algorithm

intervals

Results

17.0ms	102×	body	1280	valid
4.0ms	125×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	7×	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: 16.5b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

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

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:

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

series837.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
262.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
101.0ms	(/ 1.0 (hypot 1.0 x))
366.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (46.0ms)

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

prune238.0ms

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: 15.8b

Counts

105 → 4

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))))))
1.4b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite17.0ms

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))
7.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 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))

series679.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
107.0ms	(/ 1.0 (hypot 1.0 x))
318.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
153.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

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

prune300.0ms

Filtered

97 candidates to 85 candidates (87.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0.3b

Counts

101 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0b	(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.4b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0ms	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0ms	(log1p (+ 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))

series2.5s

Counts

4 → 12

Calls

4 calls:

317.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.1s	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
922.0ms	(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
157.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	583	861
1	2521	783
2	5002	781

prune256.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Merged error: 0.3b

Counts

65 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(log1p (expm1 (/ 1.0 (hypot 1.0 x))))
0.5b	(expm1 (/ 1.0 (hypot 1.0 x)))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (log1p (expm1 (/ 1.0 (hypot 1.0 x))))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(log1p (expm1 (/ 1.0 (hypot 1.0 x))))
1.0ms	(expm1 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (log1p (expm1 (/ 1.0 (hypot 1.0 x))))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
555.0ms	(log1p (expm1 (/ 1.0 (hypot 1.0 x))))
176.0ms	(expm1 (/ 1.0 (hypot 1.0 x)))
543.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (log1p (expm1 (/ 1.0 (hypot 1.0 x))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	512	1181
1	1948	852
2	5002	848

prune240.0ms

Filtered

94 candidates to 75 candidates (79.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	94	4	98

Merged error: 0.3b

Counts

98 → 4

regimes261.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 15.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms

sample880.0ms

Algorithm

intervals

Results

510.0ms	2909×	body	1280	valid
128.0ms	4032×	body	80	valid
84.0ms	611×	body	640	valid
32.0ms	285×	body	320	valid
10.0ms	163×	body	160	valid