Details

analyze423.0ms

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

sample74.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

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: 34.7b

Counts

2 → 1

localize21.0ms

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) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

10.0ms	(/ (+ (* (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))
5.0ms	(sqrt (+ (* re re) (* im im)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5011	2020

prune238.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

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: 10.7b

Counts

123 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
1.0b	(pow (log base) 4)
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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-+` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
18.0ms	(pow (log base) 4)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5046	938

prune205.0ms

Filtered

65 candidates to 109 candidates (-67.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Merged error: 10.7b

Counts

121 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt (pow (log base) 6))
1.3b	(pow (log base) 6)
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

8.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(cbrt (pow (log base) 6))
2.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(cbrt (pow (log base) 6))
21.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5206	835

prune179.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	88	15	103

Merged error: 10.7b

Counts

103 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
32.2b	(sqrt (+ (* re re) (* im im)))
33.5b	(log (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`log-prod` `sqrt-prod`
2×	`log-div` `flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

4 → 51

Calls

4 calls:

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt base)
23.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(log (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4844	455
1	4844	455

prune83.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	63	15	78

Merged error: 10.7b

Counts

78 → 15

regimes516.0ms

Accuracy

55.3% (11.1b remaining)

Error of 18.5b against oracle of 7.4b and baseline of 32.3b

bsearch183.0ms

Steps

Iters	Range		Point
7	6.725622674481079e+16	7.728378964375066e+18	7.175104160147713e+17
7	4.969163316965519e-170	1.0253525826004215e-168	3.4160082491612644e-169
6	1.0067162130032995e-269	4.2852432342172315e-269	1.3644360600461893e-269
7	-5.1529738760177873e+73	-2.365173995128075e+71	-3.2792927917367154e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	97
1	67	97

end0.0ms

sample1.9s

Algorithm

intervals

Results

707.0ms

8000×

body

valid

Details

analyze423.0ms

sample74.0ms

simplify3.0ms

prune4.0ms

localize21.0ms

rewrite29.0ms

series71.0ms

simplify74.0ms

prune238.0ms

localize29.0ms

rewrite21.0ms

series63.0ms

simplify46.0ms

prune205.0ms

localize23.0ms

rewrite19.0ms

series64.0ms

simplify50.0ms

prune179.0ms

localize33.0ms

rewrite12.0ms

series61.0ms

simplify52.0ms

prune83.0ms

regimes516.0ms

bsearch183.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling