Details

sample38.0ms

Algorithm

intervals

Results

20.0ms	97×	body	1280	valid
5.0ms	125×	body	80	valid
4.0ms	22×	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: 14.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
2.1b	(- 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:

1.0ms	(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))))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(hypot 1.0 x)
273.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
99.0ms	(/ 1.0 (hypot 1.0 x))
346.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

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

prune232.0ms

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: 13.7b

Counts

98 → 5

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 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.6b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

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

series689.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
108.0ms	(/ 1.0 (hypot 1.0 x))
103.0ms	(/ 1.0 (hypot 1.0 x))
155.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (38.0ms)

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

prune308.0ms

Filtered

97 candidates to 85 candidates (87.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.3b

Counts

102 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.6b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`log-pow` `fma-udef` `rem-exp-log`

Counts

4 → 85

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(exp (log (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))

series521.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 1.0 (hypot 1.0 x))
103.0ms	(/ 1.0 (hypot 1.0 x))
157.0ms	(exp (log (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))

simplify160.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	273	648
1	913	592
2	4559	571
3	5001	565

prune328.0ms

Filtered

97 candidates to 82 candidates (84.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.3b

Counts

102 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.6b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-up` `unpow-prod-down` `log-prod`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv`
1×	`pow-to-exp` `e-exp-1` `pow-pow` `log-pow` `fma-udef` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(pow E (log (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))

series801.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1.0 (hypot 1.0 x))
103.0ms	(/ 1.0 (hypot 1.0 x))
427.0ms	(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
161.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	359	776
1	1368	725
2	5002	716

prune341.0ms

Filtered

104 candidates to 85 candidates (81.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Merged error: 0.3b

Counts

109 → 5

regimes289.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	38
1	46	38

end0.0ms

sample1.0s

Algorithm

intervals

Results

609.0ms	2883×	body	1280	valid
152.0ms	4029×	body	80	valid
105.0ms	637×	body	640	valid
35.0ms	284×	body	320	valid
15.0ms	167×	body	160	valid