Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

264×

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

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.8b

Counts

2 → 1

localize9.0ms

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))
28.3b	(/ (+ (* 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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
76.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify152.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune197.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	7	71

Merged error: 19.4b

Counts

71 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
18.9b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite27.0ms

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:

5.0ms	(/ 1 (* (hypot y.re y.im) 1))
1.0ms	(fma x.re y.re (* x.im y.im))
12.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series380.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (* (hypot y.re y.im) 1))
40.0ms	(fma x.re y.re (* x.im y.im))
178.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
109.0ms	(/ (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 (34.0ms)

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

prune244.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	153	11	164

Merged error: 6.5b

Counts

164 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
18.9b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite14.0ms

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`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

1.0ms	(hypot y.re y.im)
7.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
1.0ms	(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))

series319.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
122.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
40.0ms	(fma x.re y.re (* x.im y.im))
110.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify76.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune259.0ms

Filtered

111 candidates to 88 candidates (79.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	108	14	122

Merged error: 6.4b

Counts

122 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
9.5b	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
9.6b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`associate-r`
8×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-/r` `fma-udef`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `associate-r/` `clear-num` `associate-/l/` `associate-/l`

Counts

4 → 104

Calls

4 calls:

1.0ms	(fma x.re y.re (* x.im y.im))
18.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
9.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
8.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma x.re y.re (* x.im y.im))
178.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
257.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
168.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	404	1276
1	2076	1059
2	5001	1017

prune275.0ms

Filtered

116 candidates to 86 candidates (74.1%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	2	8	10
Picked	0	1	1
Done	0	3	3
Total	117	13	130

Merged error: 6.4b

Counts

130 → 13

regimes260.0ms

Accuracy

37.1% (7.1b remaining)

Error of 13.1b against oracle of 6.0b and baseline of 17.3b

bsearch33.0ms

Steps

Iters	Range		Point
6	1.100743072292938e+120	1.0219163733161167e+121	3.3991102699915446e+120
1	-1.4185660712987705e+171	-1.316853296455673e+171	-1.3422814901664475e+171

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

sample593.0ms

Algorithm

intervals

Results

363.0ms

8443×

body

valid