Details

sample59.0ms

Algorithm

intervals

Results

31.0ms	86×	body	1280	valid
10.0ms	127×	body	80	valid
8.0ms	29×	body	640	valid
2.0ms	11×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

0.0ms	(hypot 1.0 x)
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series678.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(hypot 1.0 x)
270.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
354.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	428	906
1	1480	669
2	5001	655

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.5b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `hypot-udef` `frac-2neg` `pow1/2` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 70

Calls

4 calls:

0.0ms	(hypot 1.0 x)
6.0ms	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot 1.0 x)
1.4s	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
265.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
150.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	826	1456
1	3704	1348
2	5001	1334

prune315.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
0.5b	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.5b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`sqrt-prod`
10×	`times-frac`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-r`
6×	`associate-l`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-/r` `flip-+` `associate-/l`
2×	`associate-*r/` `associate-/r/` `hypot-def` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

4.0ms	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
26.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
176.0ms	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
269.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
143.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	902	1737
1	4472	1607
2	5001	1605

prune405.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.5b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.5b	(log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow`
18×	`exp-prod`
13×	`pow1`
8×	`distribute-lft-out`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `associate-/r/` `flip-+` `fma-udef`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/ (log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms	(log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
266.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
150.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
145.0ms	(log (exp (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	841	2149
1	3681	1968
2	5001	1957

prune382.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes187.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch170.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.002698990951630782
10	-1.7081313977704333	-1.7977825652338532e-10	-0.0018031452709831514

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	59
1	61	59
2	65	59
3	66	59
4	66	59

end0.0ms

sample1.6s

Algorithm

intervals

Results

932.0ms	2896×	body	1280	valid
298.0ms	4055×	body	80	valid
165.0ms	615×	body	640	valid
55.0ms	286×	body	320	valid
21.0ms	148×	body	160	valid