Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	28×	body	2560	valid
3.0ms	12×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	6×	body	640	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
32.9b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
13.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
12.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune228.0ms

Filtered

100 candidates to 72 candidates (72.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.3b	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
1.0b	(- (* 1 (hypot re im)) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

1.0ms	(hypot re im)
6.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
7.0ms	(- (* 1 (hypot re im)) re)

series275.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(hypot re im)
175.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
54.0ms	(- (* 1 (hypot re im)) re)

simplify33.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	235	265
1	803	220
2	5002	213

prune148.0ms

Filtered

53 candidates to 46 candidates (86.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* 1 (hypot re im)) re))
0.0b	(hypot re im)
0.4b	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
1.0b	(- (* 1 (hypot re im)) re)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-r`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `prod-diff` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `hypot-udef` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

5.0ms	(sqrt (- (* 1 (hypot re im)) re))
1.0ms	(hypot re im)
8.0ms	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
4.0ms	(- (* 1 (hypot re im)) re)

series407.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (- (* 1 (hypot re im)) re))
49.0ms	(hypot re im)
181.0ms	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
57.0ms	(- (* 1 (hypot re im)) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	350	567
1	1333	489
2	5001	478

prune262.0ms

Filtered

94 candidates to 78 candidates (83.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
0.2b	(* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
1.0b	(- (hypot re im) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`sqrt-prod`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`associate-l`
16×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
9×	`associate-r` `prod-diff`
6×	`associate-*r/` `add-log-exp` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `sqrt-unprod` `flip--`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `hypot-udef` `diff-log`

Counts

4 → 110

Calls

4 calls:

1.0ms	(hypot re im)
12.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
9.0ms	(* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series542.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
185.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
248.0ms	(* (sqrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
59.0ms	(- (hypot re im) re)

simplify55.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	425	893
1	1781	742
2	5001	722

prune306.0ms

Filtered

122 candidates to 89 candidates (73.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.9b

regimes123.0ms

Accuracy

-5.9% (6.8b remaining)

Error of 14.6b against oracle of 7.8b and baseline of 14.2b

bsearch169.0ms

Steps

Iters	Range		Point
9	-2.2675790174521313e-129	-5.716279481001832e-138	-1.1924184649113615e-129
6	-5.394032098073118e-83	-9.640169736704656e-84	-9.798897039788843e-84
6	-1.8381966296202437e-28	-2.4234279006071815e-29	-1.0006834861368125e-28
8	-3.718406892214352e+108	-3.9002556620280977e+105	-4.785303185749175e+107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	47
1	71	47
2	71	47

end0.0ms

sample685.0ms

Algorithm

intervals

Results

198.0ms	5946×	body	80	valid
150.0ms	753×	body	2560	valid
82.0ms	502×	body	1280	valid
67.0ms	293×	body	5120	valid
34.0ms	281×	body	640	valid
13.0ms	147×	body	320	valid
5.0ms	78×	body	160	valid