Details

sample253.0ms

Algorithm

intervals

Results

184.0ms	158×	body	1280	valid
42.0ms	66×	body	640	valid
8.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	5×	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: 15.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (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)))))
2.9b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

12.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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)))))
5.0ms	(cos (- lambda1 lambda2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms	(* (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)))))
19.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune369.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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

Counts

4 → 86

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (* (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)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
209.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	525	1615
1	2180	1377
2	5002	1374

prune533.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.8b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 66

Calls

4 calls:

6.0ms	(* (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))))))))
3.0ms	(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)))))))

series150.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
44.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify133.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	202	1798
1	445	1587
2	1162	1535
3	2063	1535
4	4957	1531
5	5001	1531

prune479.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))))))) R)
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)))))
0.6b	(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)))))))

rewrite38.0ms

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

Counts

4 → 94

Calls

4 calls:

3.0ms	(* (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))))))) R)
21.0ms	(/ (* (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)))))
9.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms	(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)))))))

series867.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (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))))))) R)
462.0ms	(/ (* (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)))))
184.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
48.0ms	(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)))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	666	3715
1	3484	3119
2	5001	3105

prune622.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.7b

regimes651.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	37
1	38	37

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4771×	body	1280	valid
1.4s	2120×	body	640	valid
286.0ms	690×	body	320	valid
84.0ms	280×	body	160	valid
24.0ms	7×	body	2560	valid
19.0ms	132×	body	80	valid