Details

sample26.0ms

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)))

rewrite20.0ms

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:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(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

prune181.0ms

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 (hypot re im)) re)))
0.8b	(+ (* 1 (hypot re im)) re)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

1.0ms	(hypot re im)
5.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
4.0ms	(+ (* 1 (hypot re im)) re)

series289.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(hypot re im)
187.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
59.0ms	(+ (* 1 (hypot re im)) re)

simplify74.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	219	232
1	647	208
2	2702	200
3	5001	199

prune157.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.8b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

18.0ms	(sqrt (* 2.0 (* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))))
12.0ms	(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))
4.0ms	(+ (* 1 (hypot re im)) re)
4.0ms	(+ (* 1 (hypot re im)) re)

series357.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt (* 2.0 (* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))))
59.0ms	(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))
60.0ms	(+ (* 1 (hypot re im)) re)
53.0ms	(+ (* 1 (hypot re im)) re)

simplify48.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	325	952
1	1146	846
2	5001	816

prune329.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (* 1 (hypot re im)) re))
0.8b	(+ (* 1 (hypot re im)) re)
0.8b	(+ (* 1 (hypot re im)) re)
0.8b	(+ (hypot re im) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`fma-def`
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 → 63

Calls

4 calls:

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

series321.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (+ (* 1 (hypot re im)) re))
58.0ms	(+ (* 1 (hypot re im)) re)
53.0ms	(+ (* 1 (hypot re im)) re)
57.0ms	(+ (hypot re im) re)

simplify64.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	249	335
1	601	305
2	2495	302
3	5001	296

prune347.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.7b

regimes143.0ms

Accuracy

38.1% (3.9b remaining)

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

bsearch54.0ms

Steps

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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample668.0ms

Algorithm

intervals

Results

187.0ms	5995×	body	80	valid
130.0ms	673×	body	2560	valid
79.0ms	505×	body	1280	valid
68.0ms	273×	body	5120	valid
39.0ms	302×	body	640	valid
16.0ms	149×	body	320	valid
6.0ms	103×	body	160	valid