Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	7
1	15	7
2	15	7

prune3.0ms

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: 30.1b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`hypot-def`
24×	`times-frac`
22×	`log-pow`
20×	`pow1`
15×	`add-cube-cbrt`
12×	`swap-sqr`
10×	`*-commutative` `unswap-sqr`
8×	`sqrt-prod`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`distribute-lft-out`
4×	`add-exp-log` `sqrt-div` `associate-l` `associate-/r*` `add-cbrt-cube`
2×	`expm1-log1p-u` `log-div` `flip3-+` `div-sub` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 98

Calls

2 calls:

23.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
17.0ms	(sqrt (+ (* re re) (* im im)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	235	687
1	625	652
2	1530	650
3	5001	650

prune220.0ms

Filtered

104 candidates to 60 candidates (57.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	10	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.3b

Counts

105 → 10

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.6b	(/ (log (* 1 (hypot re im))) (log 10.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
20×	`times-frac`
16×	`log-pow`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-prod-down` `associate-/l*`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 53

Calls

2 calls:

1.0ms	(hypot re im)
7.0ms	(/ (log (* 1 (hypot re im))) (log 10.0))

series187.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(hypot re im)
143.0ms	(/ (log (* 1 (hypot re im))) (log 10.0))

simplify390.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	133	409
1	325	384
2	837	377
3	3181	377
4	5001	377

prune150.0ms

Filtered

59 candidates to 41 candidates (69.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	47	12	59
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	57	12	69

Merged error: 0.0b

Counts

69 → 12

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
0.5b	(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

217×	`associate-/r*`
195×	`frac-times`
191×	`add-sqr-sqrt`
187×	`sqrt-prod`
152×	`*-un-lft-identity`
145×	`add-cube-cbrt`
139×	`pow1`
126×	`associate-/l*`
113×	`times-frac`
104×	`log-pow`
39×	`associate-r`
32×	`clear-num`
31×	`frac-2neg` `pow-prod-down`
27×	`add-exp-log`
25×	`associate-l`
17×	`add-cbrt-cube`
15×	`associate-*r/` `unswap-sqr`
13×	`associate-*l/`
9×	`div-exp`
8×	`prod-exp`
5×	`cbrt-undiv`
4×	`un-div-inv` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`hypot-udef` `*-commutative`

Counts

3 → 400

Calls

3 calls:

1.0ms	(hypot re im)
37.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
8.0ms	(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

series420.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(hypot re im)
148.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
222.0ms	(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

simplify127.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	976	4724
1	4954	3884
2	5001	3884

prune519.0ms

Filtered

409 candidates to 139 candidates (34.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	403	6	409
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	412	9	421

Merged error: 0.0b

Counts

421 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
0.2b	(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
3.8b	(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
83×	`add-sqr-sqrt`
75×	`pow-unpow`
73×	`*-un-lft-identity`
71×	`add-cube-cbrt` `log-pow`
54×	`sqrt-prod`
32×	`associate-r`
25×	`associate-l`
24×	`pow1`
21×	`log-prod`
16×	`add-exp-log`
13×	`associate-*l/`
12×	`unpow-prod-down`
9×	`add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `hypot-udef` `prod-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
3×	`pow-pow` `rem-log-exp` `sqrt-pow2` `associate-/l*`
2×	`pow-to-exp` `div-exp` `pow-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 206

Calls

4 calls:

1.0ms	(hypot re im)
6.0ms	(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
30.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
5.0ms	(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
323.0ms	(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
372.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
360.0ms	(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	588	2023
1	2680	1636
2	5001	1475

prune529.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	221	6	227

Merged error: 0b

Counts

227 → 6

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	18	21

end0.0ms

sample499.0ms

Algorithm

intervals

Results

361.0ms

8000×

body

valid