Details

sample264.0ms

Algorithm

intervals

Results

188.0ms	158×	body	1280	valid
44.0ms	66×	body	640	valid
8.0ms	16×	body	320	valid
3.0ms	1×	body	2560	valid
3.0ms	9×	body	160	valid
1.0ms	7×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune4.0ms

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: 19.3b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.1b	(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
48.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune381.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	12	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 4.4b

Counts

87 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
10.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (sin lambda2))
71.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
197.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	494	1387
1	2248	1185
2	5002	1184

prune492.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	80	12	92
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 4.2b

Counts

104 → 14

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod` `cos-mult`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`acos-asin` `frac-times` `log-prod` `associate-r/` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `exp-diff` `frac-add` `flip-+` `sin-mult`
1×	`distribute-rgt-in` `log-div` `distribute-lft-in` `rem-log-exp` `associate-l` `associate-l/` `-commutative` `rem-exp-log`

Counts

4 → 71

Calls

4 calls:

11.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
44.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	438	1581
1	1900	1358
2	5002	1356

prune506.0ms

Filtered

83 candidates to 58 candidates (69.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	81	16	97

Merged error: 4.2b

Counts

97 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`fma-neg`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`frac-times` `associate-r/` `associate-l/`
2×	`asin-acos` `flip3--` `flip3-+` `frac-add` `*-commutative` `flip--` `flip-+` `sin-mult` `distribute-lft-out--`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `associate--r-` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

9.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
11.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
1.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
13.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
202.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
16.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
62.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	686	5914
1	2783	3603
2	5001	3592

prune647.0ms

Filtered

146 candidates to 90 candidates (61.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	135	11	146
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	141	21	162

Merged error: 4.0b

Counts

162 → 21

regimes831.0ms

Accuracy

0% (0.7b remaining)

Error of 4.1b against oracle of 3.4b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	18
1	28	18

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.0s	4746×	body	1280	valid
1.5s	2133×	body	640	valid
324.0ms	698×	body	320	valid
90.0ms	274×	body	160	valid
40.0ms	12×	body	2560	valid
23.0ms	141×	body	80	valid