Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
3.0ms	18×	body	2560	valid
2.0ms	11×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify8.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune153.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.2b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
31.4b	(cbrt (+ (* re re) (* im im)))
31.4b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 66

Calls

4 calls:

12.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
80.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
89.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))

simplify147.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	307	930
1	1159	870
2	4797	842
3	5002	842

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
4.2b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.6b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
23.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
3.0ms	(sqrt (+ (* re re) (* im im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
188.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
65.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune295.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
4.2b	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

44.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
156.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	463	834
1	2015	732
2	5001	726

prune258.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

regimes209.0ms

Accuracy

48.5% (18.3b remaining)

Error of 23.7b against oracle of 5.4b and baseline of 40.9b

bsearch249.0ms

Steps

Iters	Range		Point
7	3.6109288897676345e+140	7.144373856543786e+141	4.940139625520107e+141
7	8.613719199705148e-128	2.2247107605851096e-126	8.697394779672287e-128
6	2.1268824976492846e-253	9.226920354819254e-253	2.694808318755371e-253
7	7.991847353731723e-282	1.110810473879014e-279	1.2766285812733717e-281
8	-6.1566044135874494e-263	-2.025600411185499e-265	-2.576360195020431e-265
9	-1.0928018917701282e+131	-5.157756317616828e+122	-5.577781367361616e+127

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	88
1	108	88
2	109	88
3	109	88

end0.0ms

sample666.0ms

Algorithm

intervals

Results

199.0ms	6006×	body	80	valid
139.0ms	691×	body	2560	valid
74.0ms	314×	body	5120	valid
73.0ms	480×	body	1280	valid
34.0ms	285×	body	640	valid
12.0ms	135×	body	320	valid
5.0ms	89×	body	160	valid