Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

274×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
23.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	316	555
1	1343	496
2	5001	481

prune192.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
23.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series386.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (* (hypot y.re y.im) 1))
181.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
39.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify60.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	555	1207
1	2306	1003
2	5003	995

prune327.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.re y.im)
9.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series308.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify54.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	460	1435
1	1669	1331
2	5001	1322

prune415.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
0.3b	(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

1566×	`times-frac`
738×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
564×	`sqrt-prod`
98×	`associate-/l*`
59×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
6×	`div-sub` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 763

Calls

4 calls:

10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
35.0ms	(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series469.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
114.0ms	(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
120.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify163.0ms

Algorithm

egg-herbie

Counts

775 → 775

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1959	16693
1	5001	15325

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.8b

regimes317.0ms

Accuracy

40% (8.8b remaining)

Error of 12.4b against oracle of 3.6b and baseline of 18.3b

bsearch135.0ms

Steps

Iters	Range	Point
8	2.1094038086309138e+184	2.478812726885913e+188	1.959057585947063e+185
7	2.902118318427606e+139	9.077080724431092e+140	3.2259502147858646e+139
9	-1.0625869734742917e+147	-5.243708513897943e+137	-5.242142167300306e+138

Iters

Range

Point

2.1094038086309138e+184

2.478812726885913e+188

1.959057585947063e+185

2.902118318427606e+139

9.077080724431092e+140

3.2259502147858646e+139

-1.0625869734742917e+147

-5.243708513897943e+137

-5.242142167300306e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	44	30
2	44	30

end0.0ms

sample866.0ms

Algorithm

intervals

Results

656.0ms

8450×

body

valid