Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	274×	body	80	nan
17.0ms	256×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.1b

Counts

2 → 1

localize19.0ms

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)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.7b	(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:

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)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune430.0ms

Filtered

122 candidates to 84 candidates (68.9%)

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: 6.7b

Counts

123 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.7b	(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)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify153.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	262	720
1	966	639
2	4681	599
3	5001	592

prune529.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	125	17	142

Merged error: 6.6b

Counts

142 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.7b	(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)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
141.0ms	(* (log base) (log base))
141.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify148.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592

prune407.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	125	19	144

Merged error: 6.6b

Counts

144 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (* 2 (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.7b	(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)
4.0ms	(sqrt (+ (* re re) (* im im)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

396.0ms	(* (log base) (* 2 (log (cbrt base))))
183.0ms	(cbrt base)
172.0ms	(cbrt base)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify110.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	344	628
1	950	573
2	3788	534
3	5002	529

prune318.0ms

Filtered

92 candidates to 62 candidates (67.4%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	14	16
Picked	0	1	1
Done	0	2	2
Total	92	19	111

Merged error: 6.6b

Counts

111 → 19

regimes671.0ms

Accuracy

58.8% (10.0b remaining)

Error of 17.3b against oracle of 7.3b and baseline of 31.7b

bsearch220.0ms

Steps

Iters	Range		Point
2	1.7602068828224764e+98	1.9613842008730332e+98	1.9362370361167134e+98
7	7.094327001661075e-293	1.1510876237330226e-291	1.124886252440386e-292
8	-3.255470381464832e-282	-6.552770787433617e-287	-4.8746744212170505e-285
9	-1.202672899220455e+146	-4.752482895507418e+136	-1.8625576543047326e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	94
1	64	94

end0.0ms

sample1.4s

Algorithm

intervals

Results

554.0ms	8000×	body	80	valid
518.0ms	7991×	body	80	nan