Details

sample176.0ms

Algorithm

intervals

Results

111.0ms	120×	body	1280	valid
39.0ms	73×	body	640	valid
6.0ms	18×	body	320	valid
3.0ms	32×	body	80	valid
3.0ms	13×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`add-sqr-sqrt` `sin-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`cos-sum`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

16.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
6.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(sin (- lambda1 lambda2))
8.0ms	(cos (- lambda1 lambda2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify106.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	505	1623
1	1430	1236
2	4873	1161
3	5001	1161

prune360.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b	(cos (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `prod-diff`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`cos-diff` `sub-neg` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
17.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
142.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
100.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	427	1128
1	1340	942
2	5001	940

prune439.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.4b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite33.0ms

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

Counts

4 → 80

Calls

4 calls:

17.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series392.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
48.0ms	(* (sin lambda1) (sin lambda2))
76.0ms	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
129.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify50.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	328	761
1	1490	659
2	5001	658

prune465.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.4b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`expm1-log1p-u` `log-prod` `associate-l` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod`
2×	`*-commutative` `fma-udef` `sin-mult`
1×	`rem-log-exp` `exp-sum` `associate-*l/` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (sin lambda2))
83.0ms	(* (* (sin lambda1) (sin lambda2)) (cos phi2))
129.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
131.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	233	573
1	883	489
2	4240	487
3	5001	487

prune424.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes380.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	36
1	33	36

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s	3554×	body	1280	valid
1.2s	2311×	body	640	valid
316.0ms	948×	body	320	valid
108.0ms	440×	body	160	valid
76.0ms	746×	body	80	valid
2.0ms	1×	body	2560	valid