Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	16×	body	1280	valid
4.0ms	22×	body	2560	valid
3.0ms	11×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.1b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
9.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
176.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune216.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 8.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2.0 (+ (* (sqrt 1) (hypot re im)) re))
0.1b	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
1.2b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

7.0ms	(* 2.0 (+ (* (sqrt 1) (hypot re im)) re))
6.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series317.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* 2.0 (+ (* (sqrt 1) (hypot re im)) re))
198.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
56.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify39.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	270	417
1	1076	370
2	5002	357

prune188.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
0.4b	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
1.2b	(+ (* (sqrt 1) (hypot re im)) re)
1.2b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-pow1`
64×	`pow1`
27×	`sqrt-prod`
26×	`sqrt-div`
24×	`add-sqr-sqrt`
23×	`pow-prod-down`
19×	`pow1/2`
16×	`associate-*r/`
14×	`pow-prod-up`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `fma-def` `associate-*l/` `sum-log`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

6.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
19.0ms	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series504.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
193.0ms	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
60.0ms	(+ (* (sqrt 1) (hypot re im)) re)
60.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify59.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	321	1124
1	1273	1017
2	5001	960

prune352.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))) 4)
1.2b	(+ (* (sqrt 1) (hypot re im)) re)
1.2b	(+ (* (sqrt 1) (hypot re im)) re)
1.2b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

5.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))) 4)
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)
5.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series628.0ms

Counts

4 → 12

Calls

4 calls:

451.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))) 4)
61.0ms	(+ (* (sqrt 1) (hypot re im)) re)
56.0ms	(+ (* (sqrt 1) (hypot re im)) re)
61.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify127.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	325	715
1	985	654
2	4419	609
3	5001	600

prune390.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.4b

regimes107.0ms

Accuracy

24.3% (4.4b remaining)

Error of 11.9b against oracle of 7.5b and baseline of 13.3b

bsearch51.0ms

Steps

Iters	Range		Point
7	-1.6130657792099538e+163	-4.1161059723711623e+161	-8.475123035003605e+161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	34	15
2	34	15

end0.0ms

sample698.0ms

Algorithm

intervals

Results

206.0ms	6018×	body	80	valid
146.0ms	717×	body	2560	valid
83.0ms	486×	body	1280	valid
73.0ms	277×	body	5120	valid
36.0ms	279×	body	640	valid
15.0ms	151×	body	320	valid
5.0ms	72×	body	160	valid