Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

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: 25.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.2b	(- (* x.im y.re) (* x.re y.im))
25.0b	(/ (- (* 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)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
83.0ms	(/ (- (* 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 (32.0ms)

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

prune196.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
1.2b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
32×	`prod-exp`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 120

Calls

4 calls:

0.0ms	(hypot y.re y.im)
26.0ms	(* (/ 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))

series377.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
187.0ms	(* (/ 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))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	546	1122
1	2249	931
2	5002	929

prune320.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

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))
1.2b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite26.0ms

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:

3.0ms	(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))

series307.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
118.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify50.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (36.0ms)

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

prune393.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
1.2b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

249×	`add-exp-log`
171×	`times-frac`
120×	`div-exp`
112×	`prod-exp`
109×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
64×	`1-exp`
50×	`associate-r`
47×	`add-cbrt-cube`
43×	`rec-exp`
19×	`cbrt-undiv`
18×	`associate-/r*` `associate-/r/`
12×	`pow1` `cbrt-unprod`
11×	`div-inv`
9×	`flip3--` `flip--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
5×	`pow-flip` `pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 292

Calls

4 calls:

43.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
9.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
114.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
34.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1166	3296
1	4668	2898
2	5003	2690

prune550.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

regimes196.0ms

Accuracy

33.6% (7.9b remaining)

Error of 12.5b against oracle of 4.6b and baseline of 16.5b

bsearch61.0ms

Steps

Iters	Range		Point
6	2.364246562673592e+136	1.4357828132925017e+137	6.04553138193687e+136
7	-2.6793173153427505e+177	-1.4584171055257321e+175	-2.767633192039507e+175

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	41	15
2	48	15
3	48	15

end0.0ms

sample495.0ms

Algorithm

intervals

Results

299.0ms

8495×

body

valid