Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

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: 27.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(- (* x.im y.re) (* x.re y.im))
26.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
63.0ms	(- (* x.im y.re) (* x.re y.im))
99.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

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

prune192.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.6b

localize12.0ms

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)))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite42.0ms

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))

series397.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (* (hypot y.re y.im) 1))
186.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (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))

simplify60.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	555	1211
1	2307	1003
2	5001	995

prune310.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

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) 1))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

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) 1))
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))

series326.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(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) 1))
39.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	432	989
1	1705	876
2	5001	875

prune331.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.1b	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.1b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

2.0ms	(/ 1 (hypot y.re y.im))
9.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
3.0ms	(- (* x.im y.re) (* x.re y.im))
14.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (hypot y.re y.im))
114.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
35.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	524	1094
1	2272	875
2	5001	842

prune281.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

regimes192.0ms

Accuracy

33.6% (8.1b remaining)

Error of 12.7b against oracle of 4.6b and baseline of 16.8b

bsearch101.0ms

Steps

Iters	Range	Point
7	1.4093456040126877e+169	8.513757049106065e+170	1.4267271815310314e+169
7	-2.85855713936286e-142	-2.3598379269180502e-144	-1.2987370292207596e-142
7	-9.149408721955617e+132	-1.9322020034710515e+131	-5.392764808821395e+132

Iters

Range

Point

1.4093456040126877e+169

8.513757049106065e+170

1.4267271815310314e+169

-2.85855713936286e-142

-2.3598379269180502e-144

-1.2987370292207596e-142

-9.149408721955617e+132

-1.9322020034710515e+131

-5.392764808821395e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	42	24
2	42	24

end0.0ms

sample517.0ms

Algorithm

intervals

Results

307.0ms

8469×

body

valid