Details

analyze437.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample40.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
2.0ms	26×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

prune4.0ms

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: 30.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
28.4b	(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:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5011	2020

prune247.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

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: 6.0b

Counts

123 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod`
11×	`log-pow`
10×	`associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
17.0ms	(pow (log base) 2)
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4953	926
1	4953	926

prune203.0ms

Filtered

65 candidates to 110 candidates (-69.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	110	15	125

Merged error: 6.0b

Counts

125 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b	(cbrt base)
0.5b	(cbrt base)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
24.0ms	(cbrt base)
23.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4901	1514
1	4901	1514

prune169.0ms

Filtered

63 candidates to 80 candidates (-27.0%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	78	17	95

Merged error: 5.9b

Counts

95 → 17

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
28.4b	(sqrt (+ (* re re) (* im im)))
28.4b	(sqrt (+ (* re re) (* im im)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4925	1286
1	4925	1286

prune131.0ms

Filtered

63 candidates to 103 candidates (-63.5%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	102	18	120

Merged error: 5.9b

Counts

120 → 18

regimes720.0ms

Accuracy

55.8% (11.0b remaining)

Error of 18.5b against oracle of 7.4b and baseline of 32.4b

bsearch148.0ms

Steps

Iters	Range		Point
10	2.5777292564165565e+92	5.494933334504507e+105	2.370492566939671e+98
6	-2.8466650008363097e-270	-6.440731892514881e-271	-8.579711569628729e-271
8	-8.913424646055849e-159	-8.401198946461104e-162	-9.484903639874046e-162
7	-6.298464475747201e+36	-4.264255717116227e+34	-5.852465244811857e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	117
1	64	117

end0.0ms

sample1.1s

Algorithm

intervals

Results

761.0ms	8000×	body	80	valid
93.0ms	1010×	body	80	nan

Details

analyze437.0ms

sample40.0ms

simplify3.0ms

prune4.0ms

localize20.0ms

rewrite27.0ms

series71.0ms

simplify75.0ms

prune247.0ms

localize26.0ms

rewrite19.0ms

series59.0ms

simplify44.0ms

prune203.0ms

localize26.0ms

rewrite20.0ms

series100.0ms

simplify81.0ms

prune169.0ms

localize29.0ms

rewrite25.0ms

series53.0ms

simplify59.0ms

prune131.0ms

regimes720.0ms

bsearch148.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling