Details

sample56.0ms

Algorithm

intervals

Results

29.0ms	90×	body	1280	valid
10.0ms	123×	body	80	valid
5.0ms	20×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
2.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series448.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(/ 1.0 (hypot 1.0 x))
349.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	422	844
1	1629	601
2	5001	599

prune177.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.2b

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	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`associate-/r/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
101.0ms	(/ 1.0 (hypot 1.0 x))
1.2s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
151.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	764	1571
1	3539	1461
2	5001	1448

prune458.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.7b	(log (exp (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
33×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`log-pow`
18×	`exp-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*` `distribute-lft-out`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 106

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
12.0ms	(log (exp (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

series2.8s

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
1.2s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.4s	(log (exp (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	815	2313
1	3616	2153
2	5001	2130

prune468.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.4b	(/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-l`
13×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-r` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 128

Calls

4 calls:

22.0ms	(* (/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
11.0ms	(/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms	(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))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.5s	(/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 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))
154.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1069	3601
1	5002	3260

prune506.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes298.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

932.0ms	2867×	body	1280	valid
306.0ms	3989×	body	80	valid
176.0ms	662×	body	640	valid
69.0ms	331×	body	320	valid
20.0ms	151×	body	160	valid