Details

sample288.0ms

Algorithm

intervals

Results

195.0ms	156×	body	1280	valid
52.0ms	67×	body	640	valid
11.0ms	22×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	5×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

prune17.0ms

Filtered

1 candidates to 1 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: 16.8b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
2.8b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
27.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4918	887
1	4918	887

prune150.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	55	12	67
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	57	12	69

Merged error: 3.4b

Counts

69 → 12

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	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin 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-l*`
7×	`associate-r`
6×	`associate-*r/`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`*-commutative`
2×	`sin-mult` `unswap-sqr`
1×	`acos-asin` `flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 70

Calls

4 calls:

10.0ms	(* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
9.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5098	1541

prune211.0ms

Filtered

52 candidates to 82 candidates (-57.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 3.3b

Counts

94 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))) R)
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (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 lambda1) (sin lambda2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
44.0ms	(* (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 lambda1) (sin lambda2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4931	1173
1	4931	1173

prune160.0ms

Filtered

46 candidates to 76 candidates (-65.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 3.3b

Counts

92 → 13

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(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)))))))))
8.3b	(cbrt (* (sin lambda1) (sin lambda2)))
8.3b	(cbrt (* (sin lambda1) (sin lambda2)))
8.3b	(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)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(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)))))))))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
25.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify58.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5015	613

prune59.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	50	13	63

Merged error: 3.3b

Counts

63 → 13

regimes1.1s

Accuracy

0% (0.4b 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	41
1	34	41

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.4s	4811×	body	1280	valid
1.6s	2104×	body	640	valid
344.0ms	667×	body	320	valid
100.0ms	286×	body	160	valid
24.0ms	136×	body	80	valid
6.0ms	2×	body	2560	valid

Details

sample288.0ms

simplify4.0ms

prune17.0ms

localize25.0ms

rewrite14.0ms

series49.0ms

simplify55.0ms

prune150.0ms

localize34.0ms

rewrite21.0ms

series114.0ms

simplify50.0ms

prune211.0ms

localize34.0ms

rewrite15.0ms

series76.0ms

simplify46.0ms

prune160.0ms

localize37.0ms

rewrite13.0ms

series80.0ms

simplify58.0ms

prune59.0ms

regimes1.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.0s

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