Details

sample184.0ms

Algorithm

intervals

Results

118.0ms	121×	body	1280	valid
32.0ms	60×	body	640	valid
12.0ms	33×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	28×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

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: 1.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`add-sqr-sqrt` `sin-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`cos-sum`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

9.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
5.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
97.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify111.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	505	1623
1	1430	1236
2	4873	1161
3	5001	1161

prune356.0ms

Filtered

114 candidates to 66 candidates (57.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	14	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	14	115

Merged error: 0.9b

Counts

115 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.4b	(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
6.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(cos (- lambda1 lambda2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
133.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
96.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	427	1128
1	1340	942
2	5001	940

prune373.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	90	12	102

Merged error: 0.1b

Counts

102 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sub-neg` `associate-+r+` `associate-*r/` `prod-diff`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos lambda1) (sin lambda2))
134.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
46.0ms	(* (sin lambda1) (sin lambda2))
212.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	426	862
1	1766	763
2	5001	755

prune416.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	99	12	111

Merged error: 0.1b

Counts

111 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3))
0.6b	(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
4.2b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
12×	`cbrt-prod`
11×	`cos-sum` `sin-sum`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sin-diff` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt (pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3))
2.0ms	(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series320.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3))
180.0ms	(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
20.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	357	1143
1	926	930
2	5001	918

prune271.0ms

Filtered

102 candidates to 56 candidates (54.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	103	11	114

Merged error: 0.1b

Counts

114 → 11

regimes365.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	22
1	30	22

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.5s	3565×	body	1280	valid
1.3s	2350×	body	640	valid
347.0ms	909×	body	320	valid
108.0ms	426×	body	160	valid
94.0ms	750×	body	80	valid

Details

sample184.0ms

simplify5.0ms

prune3.0ms

localize21.0ms

rewrite29.0ms

series192.0ms

simplify111.0ms

prune356.0ms

localize30.0ms

rewrite22.0ms

series258.0ms

simplify44.0ms

prune373.0ms

localize31.0ms

rewrite24.0ms

series439.0ms

simplify51.0ms

prune416.0ms

localize27.0ms

rewrite18.0ms

series320.0ms

simplify45.0ms

prune271.0ms

regimes365.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

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