Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

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: 31.8b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

29.6b

(sqrt (+ (* re re) (* im im)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

3.0ms

(sqrt (+ (* re re) (* im im)))

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(sqrt (+ (* re re) (* im im)))

simplify138.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 5 (132.0ms)

Iter	Nodes	Cost
0	89	100
1	215	97
2	503	97
3	1265	97
4	4227	97
5	5002	96

prune34.0ms

Filtered

18 candidates to 15 candidates (83.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Merged error: 7.1b

Counts

19 → 5

localize9.0ms

Local error

Found 2 expressions with local error:

5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

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

series72.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 5 (139.0ms)

Iter	Nodes	Cost
0	136	253
1	280	247
2	583	238
3	1387	232
4	4698	232
5	5001	228

prune115.0ms

Filtered

43 candidates to 29 candidates (67.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	41	7	48

Merged error: 7.1b

Counts

48 → 7

localize19.0ms

Local error

Found 2 expressions with local error:

6.3b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
30.8b	(log (+ (* re re) (* im im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod`
5×	`pow1`
4×	`log-div` `pow-unpow` `pow-pow`
3×	`unpow-prod-up` `add-exp-log` `unpow-prod-down` `exp-prod`
2×	`flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `pow-sub` `add-log-exp`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

2 → 40

Calls

2 calls:

6.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
3.0ms	(log (+ (* re re) (* im im)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
46.0ms	(log (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	206	369
1	565	346
2	1779	341
3	5001	337

prune105.0ms

Filtered

46 candidates to 33 candidates (71.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	43	10	53

Merged error: 7.1b

Counts

53 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

7.9b	(pow (exp 1/4) (log (+ (* re re) (* im im))))
7.9b	(pow (exp 1/4) (log (+ (* re re) (* im im))))
30.8b	(log (+ (* re re) (* im im)))
30.8b	(log (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`log-prod`
10×	`pow1`
8×	`log-div` `pow-unpow` `pow-pow`
6×	`unpow-prod-up` `add-exp-log` `unpow-prod-down` `exp-prod`
4×	`flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `pow-sub` `add-log-exp`
2×	`pow-to-exp` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

6.0ms	(pow (exp 1/4) (log (+ (* re re) (* im im))))
6.0ms	(pow (exp 1/4) (log (+ (* re re) (* im im))))
3.0ms	(log (+ (* re re) (* im im)))
3.0ms	(log (+ (* re re) (* im im)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(pow (exp 1/4) (log (+ (* re re) (* im im))))
114.0ms	(pow (exp 1/4) (log (+ (* re re) (* im im))))
45.0ms	(log (+ (* re re) (* im im)))
50.0ms	(log (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	243	762
1	727	714
2	2385	704
3	5002	702

prune229.0ms

Filtered

92 candidates to 72 candidates (78.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	92	10	102

Merged error: 7.1b

Counts

102 → 10

regimes321.0ms

Accuracy

56% (10.5b remaining)

Error of 18.5b against oracle of 8.0b and baseline of 31.8b

bsearch94.0ms

Steps

Iters	Range		Point
8	2.1558392991063154e+98	3.0943356273139873e+102	2.032966617252637e+102
9	-1.0921927090926265e-299	-4.707778381284133e-306	-1.026373738544412e-303
6	-6.699760191485107e-158	-1.388315075739649e-158	-1.4047799893311319e-158
9	-5.7624267828213205e+137	-6.4141430665981575e+128	-6.254434311354175e+129

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample362.0ms

Algorithm

intervals

Results

237.0ms

8000×

body

valid