Details

analyze413.0ms

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

25.0ms	256×	body	80	valid
3.0ms	36×	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: 28.7b

Counts

2 → 1

localize19.0ms

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))
26.6b	(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:

5.0ms	(* (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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5435	2029

prune268.0ms

Filtered

85 candidates to 122 candidates (-43.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	17	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 6.9b

Counts

123 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(pow (log base) 2)
5.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
42.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
14.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5527	1945

prune239.0ms

Filtered

78 candidates to 105 candidates (-34.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	102	20	122

Merged error: 6.9b

Counts

122 → 20

localize24.0ms

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)))
0.6b	(cbrt base)
0.6b	(cbrt base)
26.6b	(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:

12.0ms	(/ (+ (* (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)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (+ (* (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)))
21.0ms	(cbrt base)
23.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4941	1523
1	4941	1523

prune202.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	2	16	18
Picked	1	0	1
Done	0	1	1
Total	79	21	100

Merged error: 6.9b

Counts

100 → 21

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify30.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5393	810

prune166.0ms

Filtered

62 candidates to 79 candidates (-27.4%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	18	19
Picked	0	1	1
Done	0	1	1
Total	78	22	100

Merged error: 6.8b

Counts

100 → 22

regimes838.0ms

Accuracy

56.8% (10.9b remaining)

Error of 17.8b against oracle of 6.9b and baseline of 32.1b

bsearch272.0ms

Steps

Iters	Range		Point
8	3.876663909787781e+29	4.4016837821388e+33	3.5391957870912594e+32
2	-1.3596588596739808e+66	-1.1835879469196704e+66	-1.337649995579692e+66

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	76
1	53	76

end0.0ms

analyze411.0ms

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

sample1.0s

Algorithm

intervals

Results

736.0ms	8000×	body	80	valid
90.0ms	1018×	body	80	nan

Details

analyze413.0ms

sample40.0ms

simplify3.0ms

prune4.0ms

localize19.0ms

rewrite26.0ms

series67.0ms

simplify53.0ms

prune268.0ms

localize20.0ms

rewrite25.0ms

series84.0ms

simplify41.0ms

prune239.0ms

localize24.0ms

rewrite20.0ms

series96.0ms

simplify39.0ms

prune202.0ms

localize30.0ms

rewrite19.0ms

series67.0ms

simplify30.0ms

prune166.0ms

regimes838.0ms

bsearch272.0ms

simplify1.0ms

end0.0ms

analyze411.0ms

sample1.0s

Profiling