Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

274×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
26.0b	(/ (- (* 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` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(- (* 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)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
81.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune174.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* x.im y.re) (* x.re y.im))
105.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune280.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
17.9b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
18.0b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
6×	`times-frac` `associate-/r*`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
119.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	385	746
1	1875	664
2	5001	660

prune218.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re)) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
2.5b	(/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re))
18.0b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
18.7b	(/ (+ (pow y.re 2) (pow y.im 2)) y.re)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity` `times-frac`
81×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
32×	`unpow-prod-down` `distribute-lft-out`
25×	`associate-/r*`
16×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/r/` `difference-of-squares`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 171

Calls

4 calls:

133.0ms	(- (/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re)) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
19.0ms	(/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re))
6.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
29.0ms	(/ (+ (pow y.re 2) (pow y.im 2)) y.re)

series249.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re)) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(/ x.im (/ (+ (pow y.re 2) (pow y.im 2)) y.re))
46.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(/ (+ (pow y.re 2) (pow y.im 2)) y.re)

simplify80.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	677	1749
1	2946	1656
2	5001	1656

prune478.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

regimes153.0ms

Accuracy

53.7% (1.2b remaining)

Error of 16.2b against oracle of 14.9b and baseline of 17.6b

bsearch78.0ms

Steps

Iters	Range		Point
8	1.5214700919419666e-35	8.479854585245772e-31	8.236248153554255e-31
7	-3.404043874706634e+139	-1.8868057113454914e+138	-4.426353761751041e+138

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample518.0ms

Algorithm

intervals

Results

306.0ms

8457×

body

valid