Details

sample78.0ms

Algorithm

intervals

Results

23.0ms	272×	body	80	valid
15.0ms	32×	body	1280	valid
14.0ms	44×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	14×	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: 4.7b

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)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

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))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series900.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
431.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
85.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

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

prune259.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 4.5b

Counts

76 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
12.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series185.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
84.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
25.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	224	596
1	703	507
2	3169	501
3	5002	501

prune295.0ms

Filtered

85 candidates to 66 candidates (77.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Merged error: 4.5b

Counts

97 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))))
0.3b	(expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.4b	(log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

series402.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- lambda1 lambda2) (log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))))
122.0ms	(expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0)))))
124.0ms	(log (expm1 (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	251	767
1	804	586
2	3494	558
3	5001	557

prune298.0ms

Filtered

77 candidates to 59 candidates (76.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	76	14	90

Merged error: 4.5b

Counts

90 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)))
0.3b	(- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)
0.4b	(log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
21×	`log-prod`
16×	`add-cube-cbrt`
9×	`prod-diff` `difference-of-squares`
8×	`pow1`
7×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
6×	`add-cbrt-cube` `add-log-exp`
5×	`associate-l` `distribute-lft-out--`
4×	`expm1-log1p-u` `difference-of-sqr-1` `associate-r` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`log-div` `associate-*l/` `log-pow`
1×	`sub-neg` `expm1-def` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

13.0ms	(* (- lambda1 lambda2) (log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)))
5.0ms	(- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)
5.0ms	(log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series407.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- lambda1 lambda2) (log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)))
127.0ms	(- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1)
123.0ms	(log (- (exp (log1p (exp (cos (/ (+ phi1 phi2) 2.0))))) 1))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	366	1437
1	1277	1195
2	5001	1059

prune336.0ms

Filtered

111 candidates to 73 candidates (65.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	109	16	125

Merged error: 4.5b

Counts

125 → 16

regimes494.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	26	12
2	26	12

end0.0ms

sample2.1s

Algorithm

intervals

Results

654.0ms	8533×	body	80	valid
441.0ms	1318×	body	640	valid
383.0ms	836×	body	1280	valid
173.0ms	718×	body	320	valid
59.0ms	365×	body	160	valid

Details

sample78.0ms

simplify58.0ms

prune8.0ms

localize13.0ms

rewrite17.0ms

series900.0ms

simplify37.0ms

prune259.0ms

localize17.0ms

rewrite30.0ms

series185.0ms

simplify69.0ms

prune295.0ms

localize25.0ms

rewrite15.0ms

series402.0ms

simplify79.0ms

prune298.0ms

localize23.0ms

rewrite30.0ms

series407.0ms

simplify44.0ms

prune336.0ms

regimes494.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

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