Details

sample347.0ms

Algorithm

intervals

Results

248.0ms	156×	body	1280	valid
48.0ms	56×	body	640	valid
20.0ms	31×	body	320	valid
9.0ms	11×	body	160	valid
0.0ms	2×	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: 16.4b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(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:

8.0ms	(* (* (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))

series177.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(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

prune355.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	14	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Merged error: 3.9b

Counts

87 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite23.0ms

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*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
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)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
69.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	518	1639
1	2192	1404
2	5002	1402

prune515.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	12	99
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Merged error: 3.8b

Counts

113 → 14

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.9b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
2.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (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)))))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
47.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (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)))))))))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify141.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	202	1798
1	445	1587
2	1162	1535
3	2063	1535
4	4957	1531
5	5001	1531

prune454.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	74	18	92

Merged error: 3.8b

Counts

92 → 18

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin (- lambda2)))) (cbrt (* (sin lambda1) (sin (- lambda2))))) (cbrt (* (sin lambda1) (sin (- lambda2)))))))))
8.9b	(cbrt (* (sin lambda1) (sin (- lambda2))))
8.9b	(cbrt (* (sin lambda1) (sin (- lambda2))))
8.9b	(cbrt (* (sin lambda1) (sin (- lambda2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Counts

4 → 46

Calls

4 calls:

1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin (- lambda2)))) (cbrt (* (sin lambda1) (sin (- lambda2))))) (cbrt (* (sin lambda1) (sin (- lambda2)))))))))
4.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
4.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
4.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin (- lambda2)))) (cbrt (* (sin lambda1) (sin (- lambda2))))) (cbrt (* (sin lambda1) (sin (- lambda2)))))))))
105.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
105.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
113.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	183	841
1	440	744
2	1463	714
3	5001	702

prune373.0ms

Filtered

58 candidates to 53 candidates (91.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	58	18	76

Merged error: 3.8b

Counts

76 → 18

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	22
1	37	22

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.0s	4797×	body	1280	valid
1.4s	2084×	body	640	valid
326.0ms	709×	body	320	valid
81.0ms	273×	body	160	valid
41.0ms	13×	body	2560	valid
26.0ms	127×	body	80	valid