Details

sample23.0ms

Algorithm

intervals

Results

15.0ms

333×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	3
1	23	3
2	30	3
3	31	3
4	31	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (* y y))
4.8b	(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-r` `associate-l`
2×	`expm1-log1p-u` `flip3-+` `associate-*r/` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 40

Calls

2 calls:

2.0ms	(+ 1.0 (* y y))
7.0ms	(* x (+ 1.0 (* y y)))

series103.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ 1.0 (* y y))
55.0ms	(* x (+ 1.0 (* y y)))

simplify89.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	176	185
1	831	149
2	3617	145
3	5001	144

prune91.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (sqrt (+ 1.0 (* y y))))
0.1b	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
4.7b	(sqrt (+ 1.0 (* y y)))
4.7b	(sqrt (+ 1.0 (* y y)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`sqrt-div`
13×	`pow1` `sqrt-prod`
12×	`associate-r`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `hypot-def` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* x (sqrt (+ 1.0 (* y y))))
19.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms	(sqrt (+ 1.0 (* y y)))
3.0ms	(sqrt (+ 1.0 (* y y)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* x (sqrt (+ 1.0 (* y y))))
85.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
41.0ms	(sqrt (+ 1.0 (* y y)))
46.0ms	(sqrt (+ 1.0 (* y y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	318	722
1	1367	620
2	5002	595

prune263.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* y y))
0.0b	(* x (* 1 (hypot (sqrt 1.0) y)))
0.1b	(* (* x (* 1 (hypot (sqrt 1.0) y))) (sqrt (+ 1.0 (* y y))))
4.7b	(sqrt (+ 1.0 (* y y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`pow1`
18×	`add-cbrt-cube`
14×	`prod-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `cbrt-unprod`
7×	`associate-r`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-l` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`1-exp` `associate-r/` `-commutative`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def`

Counts

4 → 84

Calls

4 calls:

2.0ms	(+ 1.0 (* y y))
6.0ms	(* x (* 1 (hypot (sqrt 1.0) y)))
22.0ms	(* (* x (* 1 (hypot (sqrt 1.0) y))) (sqrt (+ 1.0 (* y y))))
3.0ms	(sqrt (+ 1.0 (* y y)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ 1.0 (* y y))
155.0ms	(* x (* 1 (hypot (sqrt 1.0) y)))
275.0ms	(* (* x (* 1 (hypot (sqrt 1.0) y))) (sqrt (+ 1.0 (* y y))))
46.0ms	(sqrt (+ 1.0 (* y y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	425	634
1	1894	539
2	5001	497

prune267.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) y)
0.0b	(hypot (sqrt 1.0) y)
0.0b	(* x (* 1 (hypot (sqrt 1.0) y)))
0.1b	(* (* x (* 1 (hypot (sqrt 1.0) y))) (hypot (sqrt 1.0) y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
18×	`pow1` `add-cbrt-cube`
14×	`prod-exp`
9×	`pow-prod-down` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `1-exp` `*-commutative`

Counts

4 → 65

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) y)
0.0ms	(hypot (sqrt 1.0) y)
6.0ms	(* x (* 1 (hypot (sqrt 1.0) y)))
18.0ms	(* (* x (* 1 (hypot (sqrt 1.0) y))) (hypot (sqrt 1.0) y))

series585.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(hypot (sqrt 1.0) y)
103.0ms	(hypot (sqrt 1.0) y)
168.0ms	(* x (* 1 (hypot (sqrt 1.0) y)))
214.0ms	(* (* x (* 1 (hypot (sqrt 1.0) y))) (hypot (sqrt 1.0) y))

simplify138.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	275	506
1	1136	392
2	4856	377
3	5001	375

prune188.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	18	6
2	18	6

end0.0ms

sample650.0ms

Algorithm

intervals

Results

485.0ms

10635×

body

valid