Details

sample36.0ms

Algorithm

intervals

Results

17.0ms

272×

body

valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune4.0ms

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: 26.0b

Counts

2 → 1

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
25.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

6.0ms	(- (* x.im y.re) (* x.re y.im))
14.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421

prune151.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 12.1b

Counts

57 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* x.re y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite27.0ms

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:

1.0ms	(hypot y.re y.im)
4.0ms	(- (* x.im y.re) (* x.re y.im))
13.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series366.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
35.0ms	(- (* x.im y.re) (* x.re y.im))
178.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify61.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (47.0ms)

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

prune295.0ms

Filtered

132 candidates to 91 candidates (68.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	130	10	140

Merged error: 4.5b

Counts

140 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* x.re y.im))
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite25.0ms

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:

1.0ms	(hypot y.re y.im)
4.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series304.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
37.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify52.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

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

prune355.0ms

Filtered

143 candidates to 112 candidates (78.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	6	2	8
Picked	0	1	1
Done	0	1	1
Total	144	9	153

Merged error: 4.5b

Counts

153 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* x.re y.im))
0.1b	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
16.0b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `associate-/l/` `add-log-exp`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 101

Calls

4 calls:

1.0ms	(hypot y.re y.im)
4.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
9.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
35.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
113.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	419	840
1	1832	701
2	5001	680

prune263.0ms

Filtered

113 candidates to 81 candidates (71.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	114	8	122

Merged error: 4.5b

Counts

122 → 8

regimes220.0ms

Accuracy

36.6% (8.0b remaining)

Error of 12.5b against oracle of 4.5b and baseline of 17.1b

bsearch130.0ms

Steps

Iters	Range		Point
9	6.8936041022612285e+124	2.2139006002200146e+132	3.708838431511528e+128
8	4.239010840471068e+114	1.6648652189877165e+118	5.729735287031129e+117
4	13523.20185778739	24418.2543350018	15887.488683001407
9	-1.7937751735940947e+171	-3.504983770057452e+165	-3.801771634560153e+166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	34
1	46	34
2	46	34

end0.0ms

sample488.0ms

Algorithm

intervals

Results

292.0ms

8486×

body

valid