Details

sample30.0ms

Algorithm

intervals

Results

16.0ms	96×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	valid

simplify12.0ms

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: 15.7b

Counts

2 → 1

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
3.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

1.0ms	(hypot 1.0 x)
3.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series806.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(hypot 1.0 x)
163.0ms	(/ 1.0 (hypot 1.0 x))
556.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	638	2117
1	2215	1548
2	5002	1520

prune265.0ms

Filtered

117 candidates to 74 candidates (63.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	5	118

Merged error: 15.0b

Counts

118 → 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))
2.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite20.0ms

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:

11.0ms	(+ 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))

series998.0ms

Counts

4 → 12

Calls

4 calls:

460.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
151.0ms	(/ 1.0 (hypot 1.0 x))
150.0ms	(/ 1.0 (hypot 1.0 x))
237.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	426	681
1	1597	625
2	5002	623

prune382.0ms

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	2	2	4
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 0.2b

Counts

102 → 4

localize42.0ms

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)))))))
2.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite35.0ms

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:

11.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(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))

series19.5s

Counts

4 → 12

Calls

4 calls:

1.9s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.6s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.8s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
235.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	414	1369
1	1591	1263
2	5001	1251

prune525.0ms

Filtered

70 candidates to 64 candidates (91.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 0.2b

Counts

74 → 5

localize25.0ms

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	(expm1 (log1p (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
2.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

15.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
24.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(expm1 (log1p (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))

series8.9s

Counts

4 → 12

Calls

4 calls:

1.7s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.2s	(expm1 (log1p (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
224.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify135.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	692	1603
1	3128	1476
2	5001	1465

prune490.0ms

Filtered

66 candidates to 59 candidates (89.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0.2b

Counts

71 → 5

regimes478.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	49	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

664.0ms	2898×	body	1280	valid
147.0ms	3947×	body	80	valid
94.0ms	640×	body	640	valid
51.0ms	329×	body	320	valid
11.0ms	186×	body	160	valid