Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	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: 40.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series269.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune151.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
6.1b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.0b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

17.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
21.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
41.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	291	581
1	814	525
2	2384	502
3	5002	493

prune213.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
6.4b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
14.0b	(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
34.0b	(log (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`pow1`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`log-div` `pow-unpow` `pow-pow` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `pow1/2` `rem-log-exp` `pow-prod-down` `pow-exp` `sum-log` `sqrt-prod` `distribute-lft-out` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

15.0ms	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
4.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
20.0ms	(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
3.0ms	(log (+ (* re re) (* im im)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (* 2.0 (+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)))
98.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
88.0ms	(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
54.0ms	(log (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	361	702
1	1098	651
2	3795	637
3	5001	637

prune258.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.5b

localize29.0ms

Local error

Found 4 expressions with local error:

14.0b	(+ (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
34.0b	(log (+ (* re re) (* im im)))
34.0b	(log (+ (* re re) (* im im)))
34.0b	(log (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

53.0ms	(+ (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
2.0ms	(log (+ (* re re) (* im im)))
2.0ms	(log (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
52.0ms	(log (+ (* re re) (* im im)))
58.0ms	(log (+ (* re re) (* im im)))
55.0ms	(log (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	192	815
1	475	626
2	1297	616
3	5001	616

prune278.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.5b

regimes610.0ms

Accuracy

58.9% (8.9b remaining)

Error of 26.6b against oracle of 17.7b and baseline of 39.4b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	36
1	36	36

end0.0ms

sample681.0ms

Algorithm

intervals

Results

189.0ms	5930×	body	80	valid
140.0ms	686×	body	2560	valid
85.0ms	543×	body	1280	valid
79.0ms	318×	body	5120	valid
36.0ms	272×	body	640	valid
14.0ms	151×	body	320	valid
6.0ms	100×	body	160	valid