Details

sample38.0ms

Algorithm

intervals

Results

12.0ms	189×	body	80	valid
8.0ms	30×	body	2560	valid
3.0ms	15×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	10×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

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: 35.2b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (sqrt (+ (* re re) (* im im))) re)
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

2 → 30

Calls

2 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	135	228
1	332	216
2	839	212
3	2503	211
4	5002	210

prune102.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	6	37

Merged error: 17.7b

Counts

37 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.4b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune249.0ms

Filtered

138 candidates to 73 candidates (52.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	138	6	144

Merged error: 17.7b

Counts

144 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.4b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
20.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
50.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 4 (97.0ms)

Iter	Nodes	Cost
0	196	624
1	441	565
2	1120	495
3	3440	483
4	5002	468

prune233.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	76	6	82

Merged error: 17.7b

Counts

82 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

16.4b	(- (* (sqrt (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
27.4b	(cbrt (+ (* re re) (* im im)))
27.4b	(cbrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

22.0ms	(- (* (sqrt (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (sqrt (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	243	783
1	826	670
2	2707	656
3	5001	655

prune308.0ms

Filtered

65 candidates to 57 candidates (87.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	65	6	71

Merged error: 17.7b

Counts

71 → 6

regimes184.0ms

Accuracy

54.3% (9.5b remaining)

Error of 27.5b against oracle of 18.0b and baseline of 38.9b

bsearch203.0ms

Steps

Iters	Range		Point
5	1.4228083020126992e+227	3.0462269034550035e+227	1.439181536280825e+227
9	4.0160950957056723e+121	1.2392158031794936e+127	1.0745198052201521e+127
9	-6.526510436812601e-287	-1.6227712220164164e-292	-1.6409955006042464e-292
9	-9.054381491912354e+157	-5.630651790137533e+148	-1.2007831066903334e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	36
1	57	36

end0.0ms

sample872.0ms

Algorithm

intervals

Results

284.0ms	6062×	body	80	valid
175.0ms	669×	body	2560	valid
105.0ms	485×	body	1280	valid
92.0ms	281×	body	5120	valid
52.0ms	295×	body	640	valid
22.0ms	144×	body	320	valid
8.0ms	64×	body	160	valid