Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 36.2b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms

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:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(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

prune124.0ms

Filtered

44 candidates to 40 candidates (90.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	3	45

Merged error: 5.7b

Counts

45 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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:

1.0ms	(hypot re im)
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series100.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(hypot re im)
57.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify95.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 4 (92.0ms)

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

prune103.0ms

Filtered

30 candidates to 29 candidates (96.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 5.7b

Counts

33 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0b	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite26.0ms

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))
2.0ms	(sqrt (hypot re im))
6.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
14.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series273.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (hypot re im))
85.0ms	(sqrt (hypot re im))
49.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
54.0ms	(+ (* (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

prune261.0ms

Filtered

107 candidates to 68 candidates (63.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	107	6	113

Merged error: 5.7b

Counts

113 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
0.6b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
10.1b	(+ (* (sqrt 1) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))) re)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-pow1`
81×	`sqrt-prod`
73×	`pow1`
56×	`add-sqr-sqrt`
51×	`pow1/2`
43×	`pow-prod-up`
20×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr`
15×	`associate-r`
13×	`pow-sqr`
12×	`pow-prod-down`
11×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
10×	`associate-l`
7×	`pow-plus`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `sum-log` `rem-square-sqrt` `flip-+`

Counts

4 → 166

Calls

4 calls:

5.0ms	(sqrt (sqrt (hypot re im)))
15.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
10.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
23.0ms	(+ (* (sqrt 1) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))) re)

series299.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (sqrt (hypot re im)))
51.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
85.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
55.0ms	(+ (* (sqrt 1) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))) re)

simplify60.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	431	934
1	1709	732
2	5002	651

prune333.0ms

Filtered

178 candidates to 84 candidates (47.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	179	5	184

Merged error: 5.7b

Counts

184 → 5

regimes105.0ms

Accuracy

30.9% (4.0b remaining)

Error of 11.5b against oracle of 7.5b and baseline of 13.3b

bsearch60.0ms

Steps

Iters	Range		Point
10	-3.402130339251646e+46	-2.7167357396098293e+32	-2.0552943193185366e+44

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample675.0ms

Algorithm

intervals

Results

197.0ms	5977×	body	80	valid
146.0ms	755×	body	2560	valid
72.0ms	461×	body	1280	valid
72.0ms	312×	body	5120	valid
34.0ms	285×	body	640	valid
14.0ms	150×	body	320	valid
4.0ms	60×	body	160	valid