Details

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample34.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

prune3.0ms

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: 30.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series32.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4916	1166
1	4916	1166

prune180.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	67	16	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	16	84

Merged error: 7.8b

Counts

84 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
0.6b	(/ (log (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (log 10.0))
29.5b	(cbrt (+ (* re re) (* im im)))
29.5b	(cbrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
16×	`log-pow`
10×	`cbrt-prod`
9×	`associate-r`
8×	`add-exp-log` `cbrt-div` `sqrt-prod` `add-cbrt-cube`
6×	`pow-prod-down`
5×	`associate-/l*`
4×	`flip3-+` `sqrt-div` `associate-r/` `associate-/r` `flip-+` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`log-div` `pow1/3` `div-sub`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 97

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
9.0ms	(/ (log (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (log 10.0))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
53.0ms	(/ (log (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (log 10.0))
22.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4894	2455
1	4894	2455

prune203.0ms

Filtered

78 candidates to 109 candidates (-39.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	110	15	125

Merged error: 7.8b

Counts

125 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

29.5b	(cbrt (+ (* re re) (* im im)))
29.5b	(cbrt (+ (* re re) (* im im)))
29.5b	(cbrt (+ (* re re) (* im im)))
29.5b	(cbrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5093	736

prune168.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	64	15	79

Merged error: 7.8b

Counts

79 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.6b	(log (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
83×	`add-sqr-sqrt`
54×	`sqrt-prod`
53×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
22.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
5.0ms	(log (+ (* re re) (* im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
23.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	3029
1	4984	3029

prune281.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	10	3	13
Picked	1	0	1
Done	1	0	1
Total	179	12	191

Merged error: 7.7b

Counts

191 → 12

regimes824.0ms

Accuracy

59.4% (9.9b remaining)

Error of 17.4b against oracle of 7.4b and baseline of 31.9b

bsearch75.0ms

Steps

Iters	Range		Point
11	5.607922810617916e+124	7.454484643111101e+160	1.6388614166303054e+125
6	-3.189506522404743e-305	-6.457487184341905e-306	-1.543974234013711e-305
9	-2.3974527152985597e-232	-1.843190602765369e-237	-3.3370596695886217e-236
7	-1.897932765385982e+88	-2.3287823209570183e+86	-1.5678980394422787e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	115
1	64	115

end0.0ms

sample609.0ms

Algorithm

intervals

Results

471.0ms

8000×

body

valid

Details

analyze8.0ms

sample34.0ms

simplify2.0ms

prune3.0ms

localize10.0ms

rewrite17.0ms

series32.0ms

simplify49.0ms

prune180.0ms

localize14.0ms

rewrite27.0ms

series132.0ms

simplify55.0ms

prune203.0ms

localize21.0ms

rewrite18.0ms

series86.0ms

simplify47.0ms

prune168.0ms

localize13.0ms

rewrite46.0ms

series60.0ms

simplify74.0ms

prune281.0ms

regimes824.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample609.0ms

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