Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	182×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	14×	body	5120	valid
3.0ms	19×	body	1280	valid
1.0ms	6×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	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: 39.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

15.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune185.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.1b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.8b	(+ re (hypot re im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

0.0ms	(hypot re im)
10.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
3.0ms	(+ re (hypot re im))

series293.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(hypot re im)
185.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
58.0ms	(+ re (hypot re im))

simplify81.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	208	209
1	808	191
2	3269	185
3	5001	185

prune157.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 2.0 (* 1 (* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im)))))))
0.4b	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))
0.8b	(+ re (hypot re im))
0.8b	(+ re (hypot re im))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity` `sqrt-div`
29×	`pow1`
27×	`sqrt-prod`
26×	`add-sqr-sqrt`
20×	`associate-*r/`
14×	`add-cube-cbrt` `flip3-+` `flip-+`
12×	`sqrt-pow1`
11×	`swap-sqr`
9×	`pow1/2` `pow-prod-down`
8×	`frac-times` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`+-commutative` `sum-log`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

70.0ms	(sqrt (* 2.0 (* 1 (* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im)))))))
20.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))
2.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))

series481.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (* 2.0 (* 1 (* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im)))))))
186.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))
53.0ms	(+ re (hypot re im))
59.0ms	(+ re (hypot re im))

simplify50.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	326	801
1	1371	737
2	5001	722

prune324.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ re (hypot re im)))
0.8b	(+ re (hypot re im))
0.8b	(+ re (hypot re im))
0.8b	(+ re (hypot re im))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

2.0ms	(cbrt (+ re (hypot re im)))
2.0ms	(+ re (hypot re im))
2.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))

series311.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (+ re (hypot re im)))
53.0ms	(+ re (hypot re im))
56.0ms	(+ re (hypot re im))
56.0ms	(+ re (hypot re im))

simplify45.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	180	308
1	443	283
2	1525	280
3	5001	277

prune348.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.7b

regimes137.0ms

Accuracy

38% (4.0b remaining)

Error of 11.2b against oracle of 7.2b and baseline of 13.6b

bsearch55.0ms

Steps

Iters	Range		Point
9	-7.149461396458222e+22	-5224788577222825.0	-3.741043568701442e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	30	13
2	30	13

end0.0ms

sample656.0ms

Algorithm

intervals

Results

193.0ms	5995×	body	80	valid
129.0ms	673×	body	2560	valid
79.0ms	505×	body	1280	valid
68.0ms	273×	body	5120	valid
36.0ms	302×	body	640	valid
14.0ms	149×	body	320	valid
6.0ms	103×	body	160	valid