Details

sample72.0ms

Algorithm

intervals

Results

25.0ms	283×	body	80	nan
23.0ms	256×	body	80	valid

simplify3.0ms

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: 29.9b

Counts

2 → 1

localize22.0ms

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))
27.6b	(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:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (43.0ms)

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

prune214.0ms

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: 5.9b

Counts

123 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify147.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	273	768
1	973	677
2	4633	614
3	5001	580

prune186.0ms

Filtered

71 candidates to 127 candidates (-78.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	126	13	139

Merged error: 5.9b

Counts

139 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
27.6b	(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:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
46.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	464	1397
1	1754	1281
2	5002	1234

prune190.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	119	16	135

Merged error: 5.8b

Counts

135 → 16

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))
1.2b	(pow (log base) 6)
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

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:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(cbrt (pow (log base) 6))
2.0ms	(pow (log base) 6)
3.0ms	(sqrt (+ (* re re) (* im im)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(cbrt (pow (log base) 6))
20.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify218.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	295	609
1	980	549
2	4967	500
3	5001	500

prune117.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	90	15	105

Merged error: 5.8b

Counts

105 → 15

regimes471.0ms

Accuracy

58.4% (10.2b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 31.8b

bsearch74.0ms

Steps

Iters	Range		Point
7	2.468053575058286e+65	2.4896662152219984e+67	1.1982811238590513e+67
7	-2.0493115376630188e+107	-6.385363266190322e+105	-1.2383703560580196e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	43
1	47	43

end0.0ms

sample2.0s

Algorithm

intervals

Results

748.0ms	8000×	body	80	valid
697.0ms	7977×	body	80	nan

Details

sample72.0ms

simplify3.0ms

prune5.0ms

localize22.0ms

rewrite26.0ms

series67.0ms

simplify56.0ms

prune214.0ms

localize21.0ms

rewrite21.0ms

series56.0ms

simplify147.0ms

prune186.0ms

localize22.0ms

rewrite25.0ms

series86.0ms

simplify56.0ms

prune190.0ms

localize23.0ms

rewrite15.0ms

series63.0ms

simplify218.0ms

prune117.0ms

regimes471.0ms

bsearch74.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling