Details

sample9.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

229.0ms	155×	body	1280	valid
43.0ms	55×	body	640	valid
11.0ms	21×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	16×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune6.0ms

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: 13.6b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite25.0ms

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×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune162.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	11	73

Merged error: 6.7b

Counts

73 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative` `sin-cos-mult`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (cos lambda2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	308	486
1	1294	414
2	5002	414

prune145.0ms

Filtered

56 candidates to 81 candidates (-44.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 0.1b

Counts

92 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))

series76.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (cos lambda2))
48.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms	(* (sin lambda1) (sin lambda2))

simplify64.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	474	790
1	2287	685
2	5001	684

prune177.0ms

Filtered

65 candidates to 96 candidates (-47.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 0.1b

Counts

106 → 11

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-exp-log` `add-cbrt-cube`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `associate-/r` `-commutative`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

24.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
20.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
10.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
71.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
13.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify50.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	912	3295
1	5002	2732

prune208.0ms

Filtered

116 candidates to 202 candidates (-74.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	201	12	213

Merged error: 0.1b

Counts

213 → 12

regimes677.0ms

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	41	40
1	41	40

end0.0ms

sample17.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

6.6s	4615×	body	1280	valid
1.6s	1929×	body	640	valid
310.0ms	578×	body	320	valid
102.0ms	651×	body	80	valid
88.0ms	227×	body	160	valid

Details

sample9.1s

simplify8.0ms

prune6.0ms

localize26.0ms

rewrite25.0ms

series42.0ms

simplify110.0ms

prune162.0ms

localize34.0ms

rewrite21.0ms

series48.0ms

simplify38.0ms

prune145.0ms

localize36.0ms

rewrite25.0ms

series76.0ms

simplify64.0ms

prune177.0ms

localize40.0ms

rewrite75.0ms

series254.0ms

simplify50.0ms

prune208.0ms

regimes677.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample17.9s

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