Details

sample250.0ms

Algorithm

intervals

Results

185.0ms	164×	body	1280	valid
37.0ms	59×	body	640	valid
8.0ms	21×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	5×	body	80	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize24.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.5b	(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 72

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)))))
7.0ms	(cos (- lambda1 lambda2))

series123.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	323	995
1	789	819
2	2620	818
3	5002	793

prune354.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

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

series173.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (sin lambda2))
46.0ms	(* (sin phi1) (sin phi2))
67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	274	1015
1	872	860
2	2115	860
3	3356	860
4	5001	860

prune481.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.5b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.5b	(log (exp (* (sin phi1) (sin phi2))))

rewrite11.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 67

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.0ms	(log (exp (* (sin phi1) (sin phi2))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
70.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
48.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	227	1074
1	658	920
2	1490	920
3	2259	920
4	5002	920

prune497.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize35.0ms

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) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.6b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite10.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 67

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 (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
50.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	1094
1	699	935
2	1610	935
3	2413	935
4	5001	935

prune422.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

regimes589.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	34	24

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.8s	4801×	body	1280	valid
1.4s	2094×	body	640	valid
315.0ms	680×	body	320	valid
72.0ms	262×	body	160	valid
24.0ms	159×	body	80	valid
22.0ms	7×	body	2560	valid