Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
5.0ms	27×	body	2560	valid
2.0ms	11×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* re re) (* im im))
162.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune387.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.6b

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b	(exp (log (+ (* re re) (* im im))))
16.1b	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
29.7b	(sqrt (exp (log (+ (* re re) (* im im)))))
30.8b	(log (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt` `log-prod`
8×	`pow1` `exp-prod`
7×	`exp-sum`
6×	`log-div` `sqrt-prod` `add-log-exp`
5×	`add-exp-log` `sqrt-pow1`
4×	`flip3-+` `exp-diff` `add-cbrt-cube` `flip-+`
3×	`log-pow`
2×	`rem-sqrt-square` `sqrt-div`
1×	`+-commutative` `pow1/2` `rem-log-exp` `sum-log` `rem-exp-log` `distribute-lft-out`

Counts

4 → 66

Calls

4 calls:

8.0ms	(exp (log (+ (* re re) (* im im))))
41.0ms	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
13.0ms	(sqrt (exp (log (+ (* re re) (* im im)))))
6.0ms	(log (+ (* re re) (* im im)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(exp (log (+ (* re re) (* im im))))
41.0ms	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (exp (log (+ (* re re) (* im im)))))
43.0ms	(log (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	229	555
1	716	490
2	1982	480
3	5002	473

prune213.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.6b

localize19.0ms

Local error

Found 4 expressions with local error:

16.1b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (exp (log (+ (* re re) (* im im)))))
30.8b	(log (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`log-div` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`exp-sum`
2×	`exp-diff` `pow1/3`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 54

Calls

4 calls:

20.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
7.0ms	(cbrt (+ (* re re) (* im im)))
9.0ms	(cbrt (exp (log (+ (* re re) (* im im)))))
6.0ms	(log (+ (* re re) (* im im)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
84.0ms	(cbrt (+ (* re re) (* im im)))
84.0ms	(cbrt (exp (log (+ (* re re) (* im im)))))
43.0ms	(log (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	327	701
1	1062	624
2	3526	595
3	5002	595

prune294.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.6b

localize24.0ms

Local error

Found 4 expressions with local error:

30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (exp (log (+ (* re re) (* im im)))))
30.8b	(log (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `log-prod`
5×	`pow1` `add-exp-log`
4×	`log-div` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `exp-sum`
2×	`exp-diff`
1×	`rem-log-exp` `log-pow`

Counts

4 → 56

Calls

4 calls:

7.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
9.0ms	(cbrt (exp (log (+ (* re re) (* im im)))))
6.0ms	(log (+ (* re re) (* im im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ (* re re) (* im im)))
85.0ms	(cbrt (+ (* re re) (* im im)))
85.0ms	(cbrt (exp (log (+ (* re re) (* im im)))))
43.0ms	(log (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	192	518
1	549	475
2	1799	469
3	5001	469

prune334.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.6b

regimes344.0ms

Accuracy

57.7% (9.0b remaining)

Error of 27.1b against oracle of 18.0b and baseline of 39.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	36
1	38	36

end0.0ms

sample683.0ms

Algorithm

intervals

Results

190.0ms	6027×	body	80	valid
132.0ms	712×	body	2560	valid
68.0ms	306×	body	5120	valid
65.0ms	453×	body	1280	valid
36.0ms	291×	body	640	valid
11.0ms	128×	body	320	valid
5.0ms	83×	body	160	valid