Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
4.0ms	23×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	2×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
30.5b	(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:

16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (81.0ms)

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

prune128.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.9b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite4.0ms

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)

series106.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(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

prune98.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `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×	`hypot-udef`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
15.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series194.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot re im)
48.0ms	(hypot re im)
43.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
59.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify176.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	186	390
1	680	325
2	4049	286
3	5001	282

prune247.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
7.0b	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
6.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
81.0ms	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

series394.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
117.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
58.0ms	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

simplify41.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	243	737
1	987	659
2	5001	606

prune354.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

regimes119.0ms

Accuracy

27.4% (4.3b remaining)

Error of 11.6b against oracle of 7.2b and baseline of 13.2b

bsearch51.0ms

Steps

Iters	Range		Point
10	-6.858272939628203e-63	-1.3986633063200357e-74	-6.766096896247467e-63

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample671.0ms

Algorithm

intervals

Results

193.0ms	6020×	body	80	valid
143.0ms	694×	body	2560	valid
75.0ms	489×	body	1280	valid
74.0ms	294×	body	5120	valid
34.0ms	283×	body	640	valid
14.0ms	149×	body	320	valid
4.0ms	71×	body	160	valid