Details

sample67.0ms

Algorithm

intervals

Results

15.0ms	240×	body	80	valid
14.0ms	51×	body	640	valid
10.0ms	26×	body	1280	valid
4.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
4.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series925.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
445.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
86.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	328	677
1	1130	579
2	5001	569

prune264.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	62	13	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	13	76

Merged error: 3.1b

Counts

76 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.3b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.4b	(log1p (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`expm1-log1p-u` `associate-l`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

7.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
1.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series443.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
52.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
58.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	191	432
1	547	363
2	2476	363
3	5001	363

prune226.0ms

Filtered

67 candidates to 53 candidates (79.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	66	14	80

Merged error: 3.1b

Counts

80 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
0.4b	(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b	(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1` `add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube`
3×	`fma-def`
2×	`log-div` `expm1-log1p` `log1p-def` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow` `expm1-udef`

Counts

4 → 56

Calls

4 calls:

1.0ms	(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
3.0ms	(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
7.0ms	(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series168.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
56.0ms	(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	172	419
1	539	344
2	1602	339
3	5002	339

prune251.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	68	14	82

Merged error: 3.1b

Counts

82 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify174.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	88	284
1	165	254
2	433	252
3	1255	252
4	4860	243
5	5001	243

prune189.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	52	14	66

Merged error: 3.1b

Counts

66 → 14

regimes406.0ms

Accuracy

0% (0.2b remaining)

Error of 4.1b against oracle of 3.9b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

534.0ms	8275×	body	80	valid
376.0ms	1325×	body	640	valid
319.0ms	786×	body	1280	valid
153.0ms	745×	body	320	valid
46.0ms	335×	body	160	valid