Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	220×	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: 30.4b

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)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.0b	(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:

99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

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

prune457.0ms

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: 7.2b

Counts

123 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
28.0b	(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:

10.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5001	1115

prune569.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	103	17	120

Merged error: 7.1b

Counts

120 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.6b	(* (pow (log base) 2) (pow (log base) 2))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`unpow-prod-down`
34×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`add-exp-log`
17×	`add-cube-cbrt`
16×	`unswap-sqr`
15×	`pow1`
14×	`unpow2` `sqr-pow`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `prod-exp`
8×	`pow-to-exp` `pow-exp` `log-pow`
6×	`pow-unpow` `add-cbrt-cube`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow-pow` `sqrt-div`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+`

Counts

4 → 120

Calls

4 calls:

2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
8.0ms	(* (pow (log base) 2) (pow (log base) 2))
4.0ms	(sqrt (+ (* re re) (* im im)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (log base) 2)
145.0ms	(pow (log base) 2)
159.0ms	(* (pow (log base) 2) (pow (log base) 2))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	263	601
1	982	502
2	5001	477

prune434.0ms

Filtered

132 candidates to 66 candidates (50.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	131	18	149

Merged error: 7.1b

Counts

149 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
175.0ms	(cbrt base)
177.0ms	(cbrt base)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	225	495
1	626	452
2	1627	429
3	5001	422

prune342.0ms

Filtered

77 candidates to 58 candidates (75.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	75	20	95

Merged error: 7.1b

Counts

95 → 20

regimes740.0ms

Accuracy

56.8% (10.9b remaining)

Error of 18.0b against oracle of 7.1b and baseline of 32.4b

bsearch290.0ms

Steps

Iters	Range		Point
4	7.723717393936413e+80	1.182396247124819e+81	8.731285705977964e+80
8	4.6392126302617956e-172	1.250504832357626e-169	5.494148632356097e-172
9	-2.0882995619980032e-306	1.2603146542730875e-305	-3.3378995032617328e-307
8	-3.6754680269419286e+140	-9.938214279124584e+135	-2.711372934131348e+136

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	80
1	89	80
2	92	80
3	92	80

end0.0ms

sample1.4s

Algorithm

intervals

Results

541.0ms	8000×	body	80	valid
519.0ms	8005×	body	80	nan