Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

277×

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

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: 28.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
27.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
39.0ms	(- (* 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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

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

prune177.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 12.8b

Counts

74 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.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)))
0.3b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

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)
12.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series392.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
203.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
34.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify60.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

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

prune275.0ms

Filtered

132 candidates to 91 candidates (68.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	130	8	138

Merged error: 4.5b

Counts

138 → 8

localize9.0ms

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))
0.3b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite21.0ms

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)
7.0ms	(/ (/ (- (* 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))
5.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series305.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
110.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
39.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* 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

prune297.0ms

Filtered

143 candidates to 112 candidates (78.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	141	10	151

Merged error: 4.5b

Counts

151 → 10

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)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
16.6b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite25.0ms

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

series314.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot y.re y.im)
112.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (45.0ms)

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

prune212.0ms

Filtered

113 candidates to 82 candidates (72.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	113	10	123

Merged error: 4.5b

Counts

123 → 10

regimes180.0ms

Accuracy

30.6% (8.3b remaining)

Error of 13.1b against oracle of 4.8b and baseline of 16.8b

bsearch153.0ms

Steps

Iters	Range		Point
8	8.633873367224804e+204	3.582155701105743e+207	9.058781893372415e+204
10	1.9139836537483146e+77	2.4288808656791134e+92	3.6837815617052844e+85
9	1.7373270540745664e-91	1.0956860242792136e-82	3.772343053981947e-85
6	-4.6778596556519216e+169	-9.141041889454643e+168	-9.278928271868404e+168

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	28
1	38	28
2	38	28

end0.0ms

sample599.0ms

Algorithm

intervals

Results

388.0ms

8502×

body

valid