Details

sample243.0ms

Algorithm

intervals

Results

176.0ms	156×	body	1280	valid
34.0ms	56×	body	640	valid
13.0ms	31×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	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

localize28.0ms

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))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
41.0ms	(* (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)))))
17.0ms	(cos (- lambda1 lambda2))

simplify102.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	264	773
1	1022	656
2	4705	656
3	5002	656

prune293.0ms

Filtered

69 candidates to 49 candidates (71.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	14	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	14	70

Merged error: 3.9b

Counts

70 → 14

localize32.0ms

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)))))))

rewrite22.0ms

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×	`frac-times` `associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 77

Calls

4 calls:

10.0ms	(* (* (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)))))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
54.0ms	(* (sin lambda1) (sin (- lambda2)))
67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	481	1482
1	2051	1253
2	5002	1248

prune466.0ms

Filtered

89 candidates to 64 candidates (71.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	88	15	103

Merged error: 3.8b

Counts

103 → 15

localize36.0ms

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)))))))

rewrite13.0ms

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`
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 → 58

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))))))))
2.0ms	(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)))))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
45.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
16.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (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)))))))

simplify133.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	191	1646
1	418	1435
2	1067	1383
3	1785	1383
4	4492	1379
5	5002	1379

prune412.0ms

Filtered

70 candidates to 47 candidates (67.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	66	19	85

Merged error: 3.8b

Counts

85 → 19

localize41.0ms

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))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 38

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))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(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)))))))))
102.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
102.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))
104.0ms	(cbrt (* (sin lambda1) (sin (- lambda2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	175	743
1	407	649
2	1322	643
3	5002	610

prune318.0ms

Filtered

50 candidates to 45 candidates (90.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	50	19	69

Merged error: 3.8b

Counts

69 → 19

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

sample7.9s

Algorithm

intervals

Results

5.8s	4797×	body	1280	valid
1.4s	2084×	body	640	valid
314.0ms	709×	body	320	valid
81.0ms	273×	body	160	valid
41.0ms	13×	body	2560	valid
19.0ms	127×	body	80	valid