Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

25.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune7.0ms

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: 32.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
27.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune229.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 6.1b

Counts

123 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 174

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
17.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	687	3341
1	3728	2983
2	5001	2817

prune316.0ms

Filtered

102 candidates to 186 candidates (-82.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	183	18	201

Merged error: 6.1b

Counts

201 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
38.0ms	(cbrt base)
28.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	384	1340
1	1264	1221
2	5001	1183

prune219.0ms

Filtered

66 candidates to 80 candidates (-21.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	79	19	98

Merged error: 6.1b

Counts

98 → 19

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.8b	(pow (* (log base) (log base)) 3)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow1`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `pow-pow` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow2` `pow-unpow` `pow-plus` `pow-prod-down` `prod-exp` `sqrt-prod` `pow-sqr` `pow-prod-up` `cbrt-unprod`
2×	`sqrt-div` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

4.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(pow (* (log base) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
20.0ms	(pow (* (log base) (log base)) 3)
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	249	514
1	930	459
2	5001	398

prune164.0ms

Filtered

68 candidates to 125 candidates (-83.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	16	17
Picked	0	1	1
Done	0	1	1
Total	124	20	144

Merged error: 6.1b

Counts

144 → 20

regimes1.0s

Accuracy

50.8% (12.1b remaining)

Error of 19.5b against oracle of 7.3b and baseline of 32.0b

bsearch273.0ms

Steps

Iters	Range		Point
10	7.354296383416162e+87	2.116359035133955e+98	2.1261068827005115e+97
8	-3.5376163828374087e-184	-1.3546466070330404e-186	-1.3769099797788296e-184
9	-2.6773150536326673e-63	-4.498034212222691e-72	-4.596965218680041e-72
7	-1.8692281912225725e+106	-3.6445205126679645e+104	-3.604420746346338e+105

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	108
1	90	108
2	90	108

end0.0ms

sample3.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

911.0ms	8000×	body	80	valid
44.0ms	480×	body	80	nan

Details

sample2.5s

simplify4.0ms

prune7.0ms

localize20.0ms

rewrite27.0ms

series68.0ms

simplify59.0ms

prune229.0ms

localize24.0ms

rewrite46.0ms

series69.0ms

simplify99.0ms

prune316.0ms

localize25.0ms

rewrite19.0ms

series150.0ms

simplify54.0ms

prune219.0ms

localize28.0ms

rewrite20.0ms

series56.0ms

simplify38.0ms

prune164.0ms

regimes1.0s

bsearch273.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling