Details

sample252.0ms

Algorithm

intervals

Results

178.0ms	153×	body	1280	valid
43.0ms	68×	body	640	valid
9.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

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)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite39.0ms

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:

12.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

series107.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sin phi1) (sin phi2))
44.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
15.0ms	(cos (- lambda1 lambda2))

simplify62.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

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

prune345.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize31.0ms

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))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite79.0ms

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`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

54.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
14.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
39.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	494	1387
1	2248	1185
2	5002	1184

prune499.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (sin lambda2))
0.3b	(/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*r/`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`sin-mult`
6×	`associate-r` `associate-l` `cos-mult`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `times-frac` `associate-/r*` `frac-sub` `flip--` `sub-div`
2×	`sub-neg` `prod-diff` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`acos-asin` `frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
200.0ms	(/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
54.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (sin lambda2))
181.0ms	(/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
152.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	557	2413
1	2979	2015
2	5002	2014

prune649.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log-pow` `log1p-expm1-u`
3×	`distribute-rgt-in` `acos-asin` `log-prod` `distribute-lft-in` `associate-r` `associate-l`
2×	`sub-neg` `exp-diff` `prod-diff` `cos-mult` `sin-mult`
1×	`log-div` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `rem-exp-log` `sub-div` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

53.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
34.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
14.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (cos phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	294	2447
1	1177	2162
2	5001	2162

prune486.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.3b

regimes599.0ms

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	19
1	34	19

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.8s	4749×	body	1280	valid
1.4s	2109×	body	640	valid
308.0ms	695×	body	320	valid
93.0ms	313×	body	160	valid
20.0ms	5×	body	2560	valid
19.0ms	129×	body	80	valid