Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
20.0ms	242×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune8.0ms

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: 29.8b

Counts

2 → 1

localize20.0ms

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))
0.5b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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

series70.0ms

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)))
22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

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

prune240.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

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: 5.9b

Counts

123 → 15

localize25.0ms

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))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify151.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	273	769
1	973	677
2	4633	614
3	5001	580

prune216.0ms

Filtered

71 candidates to 127 candidates (-78.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	127	15	142

Merged error: 5.9b

Counts

142 → 15

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)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

15.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	581	1547
1	2548	1393
2	5001	1339

prune216.0ms

Filtered

84 candidates to 133 candidates (-58.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	131	17	148

Merged error: 5.9b

Counts

148 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (* 2 (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(* (log base) (* 2 (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
5.0ms	(sqrt (+ (* re re) (* im im)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (log base) (* 2 (log (cbrt base))))
22.0ms	(cbrt base)
23.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	352	650
1	916	597
2	3877	557
3	5001	534

prune97.0ms

Filtered

57 candidates to 92 candidates (-61.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	89	20	109

Merged error: 5.8b

Counts

109 → 20

regimes940.0ms

Accuracy

56.4% (10.9b remaining)

Error of 18.1b against oracle of 7.2b and baseline of 32.2b

bsearch77.0ms

Steps

Iters	Range		Point
8	3.6590528007313582e+112	4.748587642570593e+115	9.511615933341011e+114
6	-1.8403519906758512e+62	-2.384484096631437e+61	-1.675300425766197e+62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	41
1	72	41
2	72	41

end0.0ms

sample2.0s

Algorithm

intervals

Results

709.0ms	8000×	body	80	valid
662.0ms	7895×	body	80	nan

Details

sample67.0ms

simplify3.0ms

prune8.0ms

localize20.0ms

rewrite28.0ms

series70.0ms

simplify56.0ms

prune240.0ms

localize25.0ms

rewrite23.0ms

series56.0ms

simplify151.0ms

prune216.0ms

localize21.0ms

rewrite34.0ms

series67.0ms

simplify78.0ms

prune216.0ms

localize27.0ms

rewrite18.0ms

series106.0ms

simplify91.0ms

prune97.0ms

regimes940.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling