Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	80×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	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: 17.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 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)))))
2.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
10.0ms	(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))))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1.0 (hypot 1.0 x))
58.0ms	(hypot 1.0 x)
261.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
352.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	533	1074
1	2023	830
2	5001	827

prune253.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 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)))))))
0.0b	(+ 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))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

9.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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)))))))
3.0ms	(+ 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))

series2.0s

Counts

4 → 12

Calls

4 calls:

273.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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)))))))
321.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
148.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	826	1625
1	3588	1518
2	5001	1506

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
2.3b	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
13×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
12×	`pow1`
8×	`associate-*r/`
6×	`div-inv` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `associate-*l/` `frac-sub`
2×	`frac-times` `pow-exp` `sub-div` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-pow` `pow-plus` `fma-neg` `diff-log` `unpow3` `prod-diff` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `fma-udef` `sqr-pow`

Counts

4 → 149

Calls

4 calls:

12.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
4.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
6.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 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))

series727.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
216.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
224.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 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))

simplify39.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	907	1275
1	5001	1090

prune639.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
2.3b	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
13×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
12×	`pow1`
8×	`associate-*r/`
6×	`div-inv` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `associate-*l/` `frac-sub`
2×	`frac-times` `pow-exp` `sub-div` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-pow` `pow-plus` `fma-neg` `diff-log` `unpow3` `prod-diff` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `fma-udef` `sqr-pow`

Counts

4 → 149

Calls

4 calls:

13.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
4.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
6.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 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))

series738.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
220.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
221.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
160.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	907	1275
1	5001	1090

prune689.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes139.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.8b

bsearch217.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	0.0003514920989147014
9	-13600.963204601821	-0.00047371797307045637	-0.002598170786684672

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	96
1	62	96

end0.0ms

sample802.0ms

Algorithm

intervals

Results

464.0ms	2850×	body	1280	valid
116.0ms	4115×	body	80	valid
77.0ms	600×	body	640	valid
24.0ms	273×	body	320	valid
9.0ms	162×	body	160	valid