Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

268×

body

valid

simplify13.0ms

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: 24.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
24.5b	(/ (- (* 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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* 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))
36.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

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

prune195.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	8	74

Merged error: 13.1b

Counts

74 → 8

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)))
0.7b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite26.0ms

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)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series367.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
176.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
37.0ms	(- (* x.im y.re) (* x.re y.im))
109.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

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

prune312.0ms

Filtered

132 candidates to 91 candidates (68.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	130	10	140

Merged error: 5.3b

Counts

140 → 10

localize13.0ms

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))
0.7b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite21.0ms

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`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 109

Calls

4 calls:

1.0ms	(hypot y.re y.im)
8.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series301.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
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))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	432	989
1	1706	876
2	5002	875

prune318.0ms

Filtered

121 candidates to 96 candidates (79.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	4	3	7
Picked	0	1	1
Done	1	1	2
Total	121	10	131

Merged error: 5.2b

Counts

131 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (hypot y.re y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
7.4b	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
7.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 192

Calls

4 calls:

4.0ms	(/ 1 (sqrt (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1 (sqrt (hypot y.re y.im)))
38.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
198.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	674	2149
1	3214	1899
2	5002	1781

prune454.0ms

Filtered

204 candidates to 119 candidates (58.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	202	12	214

Merged error: 5.0b

Counts

214 → 12

regimes222.0ms

Accuracy

26.5% (8.9b remaining)

Error of 13.5b against oracle of 4.5b and baseline of 16.7b

bsearch65.0ms

Steps

Iters	Range		Point
5	2.88489180373733e+91	8.703037392267446e+91	7.268592019881047e+91
8	-2.3279684182047428e+238	-3.9326462293102055e+235	-3.978558295461232e+235

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	32	15
2	32	15

end0.0ms

sample513.0ms

Algorithm

intervals

Results

299.0ms

8500×

body

valid