Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	83×	body	1280	valid
6.0ms	135×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series492.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ 1.0 (hypot 1.0 x))
55.0ms	(hypot 1.0 x)
343.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	467	896
1	1795	649
2	5001	646

prune245.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(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

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

Counts

4 → 78

Calls

4 calls:

0.0ms	(hypot 1.0 x)
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series403.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot 1.0 x)
100.0ms	(/ 1.0 (hypot 1.0 x))
105.0ms	(/ 1.0 (hypot 1.0 x))
145.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	285	518
1	1019	474
2	5002	470

prune430.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))

rewrite18.0ms

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:

8.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series484.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1.0 (hypot 1.0 x))
96.0ms	(/ 1.0 (hypot 1.0 x))
147.0ms	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
143.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify165.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (156.0ms)

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

prune497.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))

rewrite15.0ms

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:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 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))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series761.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1.0 (hypot 1.0 x))
97.0ms	(/ 1.0 (hypot 1.0 x))
416.0ms	(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
150.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (35.0ms)

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

prune531.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

regimes261.0ms

Accuracy

97.2% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 15.8b

bsearch165.0ms

Steps

Iters	Range		Point
7	5.9790464235888496e-05	0.007285382865895221	0.0025926341159730297
10	-569.2304264003914	-7.772245281701499e-10	-1.0792455260796796

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	54
1	64	54

end0.0ms

sample823.0ms

Algorithm

intervals

Results

470.0ms	2867×	body	1280	valid
124.0ms	4056×	body	80	valid
80.0ms	630×	body	640	valid
28.0ms	321×	body	320	valid
7.0ms	126×	body	160	valid