Details

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 77.464384%

Results

24.0ms	256×	body	80	valid
2.0ms	16×	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

prune5.0ms

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: 31.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune212.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Merged error: 6.9b

Counts

123 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 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))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

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:

31.0ms	(* (/ 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)))))
14.0ms	(* (log base) (log base))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (74.0ms)

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

prune311.0ms

Filtered

102 candidates to 186 candidates (-82.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	183	15	198

Merged error: 6.8b

Counts

198 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
23.0ms	(cbrt base)
22.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	244	528
1	664	483
2	1904	432
3	5001	430

prune153.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	76	16	92

Merged error: 6.8b

Counts

92 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:

8.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
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	464	1397
1	1754	1281
2	5002	1229

prune134.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	1	12	13
Picked	0	1	1
Done	0	2	2
Total	120	18	138

Merged error: 6.8b

Counts

138 → 18

regimes879.0ms

Accuracy

57.7% (10.4b remaining)

Error of 17.4b against oracle of 7.0b and baseline of 31.7b

bsearch210.0ms

Steps

Iters	Range		Point
9	2.0916318048051712e+68	1.0991532058227116e+75	1.3628109024115157e+73
9	4.875191614027247e-287	3.3874372187462426e-278	1.203153225056966e-283
8	-7.192730793894932e-272	-1.6892791310434517e-274	-3.8728173524078927e-274
8	-3.806895017848867e+156	-1.670641706114265e+153	-1.7016927021197277e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	95
1	90	95
2	90	95

end0.0ms

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 77.464384%

Results

980.0ms	8000×	body	80	valid
44.0ms	493×	body	80	nan

Details

sample1.7s

simplify4.0ms

prune5.0ms

localize19.0ms

rewrite26.0ms

series68.0ms

simplify57.0ms

prune212.0ms

localize24.0ms

rewrite45.0ms

series69.0ms

simplify98.0ms

prune311.0ms

localize26.0ms

rewrite13.0ms

series72.0ms

simplify55.0ms

prune153.0ms

localize20.0ms

rewrite25.0ms

series84.0ms

simplify59.0ms

prune134.0ms

regimes879.0ms

bsearch210.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling