Details

sample288.0ms

Algorithm

intervals

Results

198.0ms	161×	body	1280	valid
50.0ms	65×	body	640	valid
11.0ms	21×	body	320	valid
2.0ms	5×	body	160	valid
1.0ms	4×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 17.7b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.2b	(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))

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
29.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
8.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify54.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4918	887
1	4918	887

prune166.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	53	14	67
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	14	69

Merged error: 4.4b

Counts

69 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
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)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (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:

4.0ms	(* (sin phi1) (sin phi2))
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)))))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4931	1173
1	4931	1173

prune190.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	73	17	90

Merged error: 4.3b

Counts

90 → 17

localize35.0ms

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)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
3.4b	(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series97.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
24.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify32.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5600	1204

prune177.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	75	17	92

Merged error: 4.3b

Counts

92 → 17

localize34.0ms

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))))))))
0.5b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite12.0ms

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)))))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
27.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
13.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5046	1928

prune66.0ms

Filtered

42 candidates to 70 candidates (-66.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	5	10	15
Picked	1	0	1
Done	1	0	1
Total	71	16	87

Merged error: 4.3b

Counts

87 → 16

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	30
1	34	30

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.0s	4716×	body	1280	valid
1.8s	2192×	body	640	valid
314.0ms	661×	body	320	valid
83.0ms	264×	body	160	valid
43.0ms	13×	body	2560	valid
26.0ms	155×	body	80	valid

Details

sample288.0ms

simplify3.0ms

prune17.0ms

localize23.0ms

rewrite14.0ms

series51.0ms

simplify54.0ms

prune166.0ms

localize30.0ms

rewrite15.0ms

series76.0ms

simplify42.0ms

prune190.0ms

localize35.0ms

rewrite14.0ms

series97.0ms

simplify32.0ms

prune177.0ms

localize34.0ms

rewrite12.0ms

series100.0ms

simplify68.0ms

prune66.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.8s

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