Details

sample31.0ms

Algorithm

intervals

Results

12.0ms

279×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune3.0ms

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: 25.1b

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.re y.re) (* x.im y.im))
24.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

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` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* 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)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify127.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4437	477
3	5002	477

prune102.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 24.4b

Counts

63 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
14.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune129.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	93	12	105

Merged error: 23.4b

Counts

105 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
14.2b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
14.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	385	911
1	1913	826
2	5002	802

prune124.0ms

Filtered

73 candidates to 106 candidates (-45.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	106	12	118

Merged error: 23.4b

Counts

118 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

8.8b	(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-exp-log`
40×	`add-sqr-sqrt`
33×	`times-frac` `associate-r`
32×	`prod-exp`
28×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-cbrt-cube`
23×	`sqrt-prod`
22×	`div-exp`
16×	`cbrt-prod`
12×	`1-exp`
8×	`cbrt-unprod`
7×	`pow1` `cbrt-undiv` `associate-l`
6×	`rec-exp` `cbrt-div`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp` `unswap-sqr`
2×	`pow1/3` `associate-/r/` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 123

Calls

4 calls:

21.0ms	(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	803	2163
1	3759	1868
2	5002	1847

prune141.0ms

Filtered

91 candidates to 135 candidates (-48.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	134	13	147

Merged error: 23.4b

Counts

147 → 13

regimes458.0ms

Accuracy

0% (2.9b remaining)

Error of 25.7b against oracle of 22.7b and baseline of 25.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample728.0ms

Algorithm

intervals

Results

367.0ms

8498×

body

valid

Details

sample31.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite15.0ms

series41.0ms

simplify127.0ms

prune102.0ms

localize13.0ms

rewrite21.0ms

series55.0ms

simplify81.0ms

prune129.0ms

localize13.0ms

rewrite28.0ms

series58.0ms

simplify49.0ms

prune124.0ms

localize19.0ms

rewrite36.0ms

series219.0ms

simplify79.0ms

prune141.0ms

regimes458.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample728.0ms

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