Details

sample308.0ms

Algorithm

intervals

Results

201.0ms	149×	body	1280	valid
50.0ms	63×	body	640	valid
10.0ms	20×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	15×	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

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: 10.9b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite22.0ms

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:

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
27.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune177.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	57	15	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 4.6b

Counts

73 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(cos (- lambda1 lambda2))

rewrite25.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos phi1) (sin phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series64.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (cos phi1) (sin phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	357	648
1	1484	552
2	5002	552

prune164.0ms

Filtered

55 candidates to 81 candidates (-47.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.1b

Counts

96 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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` `cbrt-unprod`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 84

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))

series89.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (cos phi1) (sin phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify70.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	526	952
1	2538	823
2	5001	823

prune184.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.0b

Counts

108 → 14

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `log-pow` `*-commutative` `sin-cos-mult`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `rem-log-exp` `associate-*l/` `sin-mult`

Counts

4 → 76

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	421	778
1	1924	649
2	5002	646

prune94.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	88	14	102

Merged error: 0.0b

Counts

102 → 14

regimes710.0ms

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	35	27
1	35	27

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.3s	4564×	body	1280	valid
1.5s	2021×	body	640	valid
271.0ms	536×	body	320	valid
111.0ms	671×	body	80	valid
64.0ms	208×	body	160	valid

Details

sample308.0ms

simplify8.0ms

prune5.0ms

localize26.0ms

rewrite22.0ms

series49.0ms

simplify107.0ms

prune177.0ms

localize34.0ms

rewrite25.0ms

series64.0ms

simplify45.0ms

prune164.0ms

localize35.0ms

rewrite29.0ms

series89.0ms

simplify70.0ms

prune184.0ms

localize39.0ms

rewrite23.0ms

series71.0ms

simplify56.0ms

prune94.0ms

regimes710.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.7s

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