Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

278×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im 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`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

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

series135.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
77.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify141.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune194.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.8b	(fma x.re y.re (* x.im y.im))
14.7b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
21.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms	(fma x.re y.re (* x.im y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series376.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (* (hypot y.re y.im) 1))
178.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
38.0ms	(fma x.re y.re (* x.im y.im))
108.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify47.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune257.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.8b	(fma x.re y.re (* x.im y.im))
14.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

6.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series254.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
38.0ms	(fma x.re y.re (* x.im y.im))
107.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify74.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune246.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.0b	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.8b	(fma x.re y.re (* x.im y.im))
14.8b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite21.0ms

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`
5×	`rec-exp`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 119

Calls

4 calls:

2.0ms	(/ 1 (hypot y.re y.im))
7.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
8.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (hypot y.re y.im))
113.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
38.0ms	(fma x.re y.re (* x.im y.im))
113.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	394	872
1	1636	690
2	5001	663

prune227.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

regimes150.0ms

Accuracy

35.1% (7.4b remaining)

Error of 12.9b against oracle of 5.6b and baseline of 16.9b

bsearch65.0ms

Steps

Iters	Range		Point
8	8.135922673663034e+155	3.4604678307837284e+158	9.413424797641783e+156
7	-1.5405955983178716e+163	-7.477626625472375e+161	-1.7577330110288216e+162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14

end0.0ms

sample515.0ms

Algorithm

intervals

Results

301.0ms

8472×

body

valid