Details

sample277.0ms

Algorithm

intervals

Results

200.0ms	163×	body	1280	valid
46.0ms	70×	body	640	valid
6.0ms	14×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

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

prune5.0ms

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: 16.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.2b	(cos (- lambda1 lambda2))

rewrite17.0ms

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` `sin-mult` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series47.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (sin phi1) (sin phi2))
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

simplify102.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	271	542
1	1029	460
2	4722	460
3	5001	460

prune163.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	13	71

Merged error: 2.0b

Counts

71 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.4b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 70

Calls

4 calls:

8.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
9.0ms	(* (sin phi1) (sin phi2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify144.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	341	1247
1	1242	1031
2	4998	1031
3	5001	1031

prune193.0ms

Filtered

50 candidates to 82 candidates (-64.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 1.8b

Counts

95 → 16

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.4b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r`
4×	`exp-sum` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`acos-asin` `rem-log-exp` `log-pow` `sin-mult`

Counts

4 → 61

Calls

4 calls:

5.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
5.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
9.0ms	(* (sin phi1) (sin phi2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
32.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

simplify204.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	235	1526
1	613	1313
2	1305	1294
3	1952	1292
4	4481	1292
5	5001	1292

prune199.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	72	17	89

Merged error: 1.8b

Counts

89 → 17

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.4b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
3.8b	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 59

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
9.0ms	(* (sin phi1) (sin phi2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
28.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	223	1211
1	700	1022
2	2165	1017
3	5001	1010

prune80.0ms

Filtered

52 candidates to 71 candidates (-36.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	69	19	88

Merged error: 1.8b

Counts

88 → 19

regimes1.3s

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.7s	4754×	body	1280	valid
1.5s	2122×	body	640	valid
325.0ms	695×	body	320	valid
90.0ms	289×	body	160	valid
22.0ms	138×	body	80	valid
16.0ms	4×	body	2560	valid

Details

sample277.0ms

simplify5.0ms

prune5.0ms

localize24.0ms

rewrite17.0ms

series47.0ms

simplify102.0ms

prune163.0ms

localize33.0ms

rewrite19.0ms

series93.0ms

simplify144.0ms

prune193.0ms

localize38.0ms

rewrite14.0ms

series97.0ms

simplify204.0ms

prune199.0ms

localize36.0ms

rewrite13.0ms

series94.0ms

simplify64.0ms

prune80.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.2s

Profiling