Details

sample90.0ms

Algorithm

intervals

Results

36.0ms	95×	body	1280	valid
19.0ms	89×	body	640	valid
11.0ms	255×	body	80	valid
7.0ms	43×	body	320	valid
3.0ms	27×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

Iter	Nodes	Cost
0	23	7
1	60	7
2	112	7
3	236	7
4	520	6
5	702	6
6	1514	6
7	2284	6
8	5001	6

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.0b

Counts

2 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp (- im)) (exp im))
0.0b	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-l`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`+-commutative` `fma-def` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`sum-log`

Counts

2 → 57

Calls

2 calls:

5.0ms	(+ (exp (- im)) (exp im))
13.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (exp (- im)) (exp im))
59.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	341	510
1	1570	445
2	5001	441

prune162.0ms

Filtered

63 candidates to 47 candidates (74.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Merged error: 0b

Counts

65 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 0.5 (exp im) (/ 0.5 (exp im)))
0.0b	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
0.0b	(/ 0.5 (exp im))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`div-exp`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

1.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
4.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
4.0ms	(/ 0.5 (exp im))

series131.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
71.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
13.0ms	(/ 0.5 (exp im))

simplify123.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	217	418
1	724	368
2	4403	368
3	5001	366

prune174.0ms

Filtered

69 candidates to 52 candidates (75.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	69	4	73

Merged error: 0b

Counts

73 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
0.0b	(/ 0.5 (exp im))
0.0b	(pow (/ 0.5 (exp im)) 3)
1.0b	(cbrt (pow (/ 0.5 (exp im)) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
48×	`add-cube-cbrt`
45×	`times-frac`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
18×	`cube-div`
13×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`cbrt-div` `associate-/r` `associate-/l`
7×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `pow-unpow` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `pow-exp` `clear-num`
2×	`cbrt-undiv` `cube-mult` `unpow3` `rem-cbrt-cube` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

4.0ms	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
4.0ms	(/ 0.5 (exp im))
7.0ms	(pow (/ 0.5 (exp im)) 3)
10.0ms	(cbrt (pow (/ 0.5 (exp im)) 3))

series135.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
17.0ms	(/ 0.5 (exp im))
38.0ms	(pow (/ 0.5 (exp im)) 3)
13.0ms	(cbrt (pow (/ 0.5 (exp im)) 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	531	1025
1	2582	898
2	5001	884

prune380.0ms

Filtered

172 candidates to 104 candidates (60.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	174	2	176

Merged error: 0b

Counts

176 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 1 (sqrt (exp im))) 3)
0.0b	(pow (/ 0.5 (sqrt (exp im))) 3)
0.0b	(* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3))
1.0b	(cbrt (* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

836×	`add-sqr-sqrt`
648×	`cube-div`
440×	`times-frac`
402×	`*-un-lft-identity`
382×	`sqrt-prod`
332×	`add-cube-cbrt`
324×	`associate-/r*`
288×	`frac-times`
284×	`unpow-prod-down` `cube-prod`
201×	`cbrt-prod`
192×	`unswap-sqr`
168×	`cbrt-div`
162×	`associate-/l*`
100×	`associate-r` `associate-l`
60×	`add-exp-log`
54×	`frac-2neg` `clear-num`
46×	`sqr-pow`
34×	`pow-exp`
24×	`associate-r/` `associate-l/` `prod-exp`
18×	`pow-unpow`
17×	`div-exp`
12×	`pow1` `pow-to-exp` `pow-prod-down` `add-cbrt-cube` `div-inv`
11×	`pow-pow`
6×	`cube-mult` `pow-flip` `unpow3`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `rem-cbrt-cube` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`exp-prod`
2×	`cbrt-undiv` `*-commutative`
1×	`pow1/2` `pow1/3` `cbrt-unprod` `inv-pow`

Counts

4 → 953

Calls

4 calls:

9.0ms	(pow (/ 1 (sqrt (exp im))) 3)
8.0ms	(pow (/ 0.5 (sqrt (exp im))) 3)
65.0ms	(* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3))
74.0ms	(cbrt (* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (/ 1 (sqrt (exp im))) 3)
63.0ms	(pow (/ 0.5 (sqrt (exp im))) 3)
56.0ms	(* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3))
14.0ms	(cbrt (* (pow (/ 1 (sqrt (exp im))) 3) (pow (/ 0.5 (sqrt (exp im))) 3)))

simplify160.0ms

Algorithm

egg-herbie

Counts

965 → 965

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1690	14437
1	5002	13102

prune1.6s

Filtered

965 candidates to 307 candidates (31.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	965	0	965
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	965	2	967

Merged error: 0b

Counts

967 → 2

regimes50.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	14
1	20	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2873×	body	1280	valid
529.0ms	2380×	body	640	valid
392.0ms	8458×	body	80	valid
186.0ms	1188×	body	320	valid
58.0ms	596×	body	160	valid