Details

sample38.0ms

Algorithm

intervals

Results

21.0ms

484×

body

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	44	6
2	58	6
3	60	6
4	60	6

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 20.0b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
21.2b	(/ (* x x) (* y y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

1.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
7.0ms	(/ (* x x) (* y y))

series117.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
27.0ms	(/ (* x x) (* y y))

simplify85.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	178	240
1	755	177
2	3369	172
3	5003	172

prune85.0ms

Filtered

39 candidates to 26 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	35	6	41

Merged error: 0.2b

Counts

41 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (/ z t) (/ x y))
0.0b	(hypot (/ z t) (/ x y))
0.4b	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`hypot-udef`
5×	`add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

1.0ms	(hypot (/ z t) (/ x y))
1.0ms	(hypot (/ z t) (/ x y))
4.0ms	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

series259.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(hypot (/ z t) (/ x y))
73.0ms	(hypot (/ z t) (/ x y))
115.0ms	(* (hypot (/ z t) (/ x y)) (hypot (/ z t) (/ x y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	104	364
1	351	302
2	1561	276
3	5001	271

prune127.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	6	58
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	54	10	64

Merged error: 0.1b

Counts

64 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
0.5b	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
2.4b	(sqrt (hypot (/ z t) (/ x y)))
2.4b	(sqrt (hypot (/ z t) (/ x y)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

38×	`pow1`
31×	`add-sqr-sqrt`
24×	`sqrt-prod`
16×	`sqrt-pow1` `pow1/2`
15×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-up`
11×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-l`
7×	`associate-r`
6×	`pow-prod-down`
5×	`pow-sqr` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `hypot-udef` `pow-plus` `rem-square-sqrt`

Counts

4 → 110

Calls

4 calls:

8.0ms	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
6.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
1.0ms	(sqrt (hypot (/ z t) (/ x y)))
2.0ms	(sqrt (hypot (/ z t) (/ x y)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (hypot (/ z t) (/ x y)) (* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y)))))
95.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (sqrt (hypot (/ z t) (/ x y))))
81.0ms	(sqrt (hypot (/ z t) (/ x y)))
72.0ms	(sqrt (hypot (/ z t) (/ x y)))

simplify214.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	207	791
1	721	625
2	4379	603
3	5001	603

prune201.0ms

Filtered

122 candidates to 66 candidates (54.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	119	13	132

Merged error: 0.0b

Counts

132 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot (/ z t) (/ x y))) (* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (sqrt (hypot (/ z t) (/ x y))))))
2.4b	(sqrt (hypot (/ z t) (/ x y)))
2.4b	(sqrt (hypot (/ z t) (/ x y)))
2.4b	(sqrt (hypot (/ z t) (/ x y)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 93

Calls

4 calls:

17.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (sqrt (hypot (/ z t) (/ x y))))))
2.0ms	(sqrt (hypot (/ z t) (/ x y)))
1.0ms	(sqrt (hypot (/ z t) (/ x y)))
2.0ms	(sqrt (hypot (/ z t) (/ x y)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sqrt (hypot (/ z t) (/ x y))) (* (sqrt (sqrt (hypot (/ z t) (/ x y)))) (sqrt (sqrt (hypot (/ z t) (/ x y))))))
71.0ms	(sqrt (hypot (/ z t) (/ x y)))
71.0ms	(sqrt (hypot (/ z t) (/ x y)))
68.0ms	(sqrt (hypot (/ z t) (/ x y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	186	544
1	445	441
2	1305	432
3	5002	432

prune190.0ms

Filtered

105 candidates to 63 candidates (60.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	11	11
Picked	1	0	1
Done	1	0	1
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

regimes291.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	27
1	21	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

700.0ms

15484×

body

valid