Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	181×	body	80	valid
8.0ms	23×	body	2560	valid
7.0ms	16×	body	5120	valid
5.0ms	19×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	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: 41.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

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:

2.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* re re) (* im im))
187.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

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

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
0.6b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `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`

Counts

3 → 39

Calls

3 calls:

0.0ms	(hypot re im)
5.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series316.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(hypot re im)
199.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
63.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify71.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	218	274
1	658	245
2	2414	237
3	5001	233

prune163.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.9b	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1`
9×	`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` `pow-prod-down` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `pow2` `hypot-udef` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
16.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
6.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
14.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series553.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
391.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
53.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
62.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	292	589
1	1053	507
2	5001	452

prune260.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)))
0.2b	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
15.0b	(+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
66×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-r` `unswap-sqr`
21×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`add-exp-log`
9×	`associate-l`
7×	`add-cbrt-cube`
6×	`sqrt-pow1` `add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `pow1/2` `prod-exp`
2×	`cube-mult` `pow-to-exp` `flip3-+` `sqrt-div` `unpow3` `associate-*r/` `pow-exp` `flip-+`
1×	`+-commutative` `fma-def` `pow-prod-down` `sum-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 143

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)))
18.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
3.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
22.0ms	(+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

series437.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)))
47.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
133.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
61.0ms	(+ (* (sqrt 1) (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

simplify80.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	443	1643
1	1947	1175
2	5002	993

prune340.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.3b

regimes206.0ms

Accuracy

21.4% (4.4b remaining)

Error of 11.9b against oracle of 7.5b and baseline of 13.2b

bsearch71.0ms

Steps

Iters	Range		Point
8	-1.1625254677380091e+176	-4.1764951624507323e+173	-1.156054729702237e+174

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

sample1.1s

Algorithm

intervals

Results

416.0ms	6051×	body	80	valid
240.0ms	675×	body	2560	valid
134.0ms	466×	body	1280	valid
122.0ms	295×	body	5120	valid
62.0ms	277×	body	640	valid
25.0ms	149×	body	320	valid
10.0ms	87×	body	160	valid