Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	198×	body	80	valid
9.0ms	24×	body	2560	valid
4.0ms	13×	body	1280	valid
4.0ms	9×	body	5120	valid
2.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `fma-def` `sqrt-prod`
5×	`add-cube-cbrt`
4×	`add-log-exp`
3×	`pow1`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out`

Counts

2 → 38

Calls

2 calls:

15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series13.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (83.0ms)

Iter	Nodes	Cost
0	155	205
1	421	183
2	1067	180
3	3190	179
4	5001	178

prune361.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.5b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

2 → 24

Calls

2 calls:

0.0ms	(hypot re im)
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series15.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(hypot re im)
8.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify95.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 4 (93.0ms)

Iter	Nodes	Cost
0	111	124
1	285	109
2	788	106
3	3168	104
4	5001	103

prune274.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ (* (sqrt 1) (hypot re im)) re))
0.5b	(+ (* (sqrt 1) (hypot re im)) re)
0.5b	(+ (* (sqrt 1) (hypot re im)) re)
0.5b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`+-commutative` `cbrt-prod` `fma-def` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (+ (* (sqrt 1) (hypot re im)) re))
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series52.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (+ (* (sqrt 1) (hypot re im)) re))
9.0ms	(+ (* (sqrt 1) (hypot re im)) re)
9.0ms	(+ (* (sqrt 1) (hypot re im)) re)
9.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify59.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	199	465
1	554	415
2	2019	405
3	5002	389

prune889.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.4b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 95

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
8.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
15.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (hypot re im))
11.0ms	(sqrt (hypot re im))
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify38.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	239	514
1	929	420
2	5001	367

prune666.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.8b

regimes285.0ms

Accuracy

24.6% (4.5b remaining)

Error of 11.9b against oracle of 7.4b and baseline of 13.4b

bsearch34.0ms

Steps

Iters	Range		Point
6	-2.0199682458946676e+123	-4.2189696159604594e+122	-5.904936880911102e+122

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

368.0ms	6005×	body	80	valid
273.0ms	735×	body	2560	valid
144.0ms	460×	body	1280	valid
129.0ms	296×	body	5120	valid
71.0ms	283×	body	640	valid
26.0ms	144×	body	320	valid
9.0ms	77×	body	160	valid