Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	84×	body	1280	valid
4.0ms	143×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	6×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `fma-neg`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `hypot-udef` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

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

series841.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
58.0ms	(hypot 1.0 x)
285.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
379.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	496	1013
1	1734	765
2	5001	762

prune232.0ms

Filtered

85 candidates to 70 candidates (82.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

4 → 45

Calls

4 calls:

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

series565.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot 1.0 x)
63.0ms	(hypot 1.0 x)
283.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
155.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	353	405
1	1227	375
2	5001	366

prune242.0ms

Filtered

57 candidates to 55 candidates (96.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (hypot 1.0 x))
0.3b	(cbrt (hypot 1.0 x))
0.3b	(cbrt (hypot 1.0 x))
0.9b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x)))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series935.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt (hypot 1.0 x))
258.0ms	(cbrt (hypot 1.0 x))
259.0ms	(cbrt (hypot 1.0 x))
153.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x)))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	238	486
1	754	435
2	3245	420
3	5002	415

prune290.0ms

Filtered

61 candidates to 57 candidates (93.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
22×	`add-sqr-sqrt`
18×	`associate-*r/`
16×	`cbrt-div` `sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`flip3-+` `pow1/3` `flip-+`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 95

Calls

4 calls:

7.0ms	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

569.0ms	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
567.0ms	(cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
771.0ms	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
158.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	508	1607
1	1969	1496
2	5001	1419

prune415.0ms

Filtered

107 candidates to 85 candidates (79.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	42
1	56	42
2	61	42
3	62	42
4	62	42

end0.0ms

sample811.0ms

Algorithm

intervals

Results

476.0ms	2888×	body	1280	valid
120.0ms	4085×	body	80	valid
77.0ms	604×	body	640	valid
24.0ms	279×	body	320	valid
8.0ms	144×	body	160	valid