Details

Time bar (total: 9.7s)

sample176.0ms

Algorithm
intervals
Results
110.0ms117×body1280valid
35.0ms67×body640valid
10.0ms28×body320valid
3.0ms14×body160valid
3.0ms30×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.9b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b
(sin (- lambda1 lambda2))
2.1b
(cos (- lambda1 lambda2))

rewrite34.0ms

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:
13.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series193.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))

simplify114.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
05051623
114301236
248731161
350011161

prune374.0ms

Filtered
114 candidates to 66 candidates (57.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10014114
Fresh000
Picked101
Done000
Total10114115

Merged error: 0.7b

Counts
115 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (sin lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.1b
(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×cos-sum prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×cos-diff sub-neg fma-def
2×associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+
Counts
4 → 87
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin lambda2))
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(cos (- lambda1 lambda2))

series300.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos lambda1) (sin lambda2))
135.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0482981
11652820
25001818

prune433.0ms

Filtered
99 candidates to 72 candidates (72.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New97299
Fresh31013
Picked101
Done000
Total10112113

Merged error: 0.1b

Counts
113 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.7b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite17.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- fma-udef sin-mult
Counts
4 → 68
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series322.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
44.0ms
(* (sin lambda1) (sin lambda2))
137.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
121.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify120.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0292936
11106822
24839821
35001821

prune390.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New76480
Fresh2911
Picked101
Done000
Total791392

Merged error: 0.1b

Counts
92 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.7b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.8b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite15.0ms

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 log-prod log-pow log1p-expm1-u
3×distribute-rgt-in distribute-lft-in associate-*r* associate-*l* fma-udef
2×sub-neg associate-*r/ exp-sum prod-diff
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 70
Calls
4 calls:
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
2.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
159.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
120.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
124.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify106.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0270821
1943728
24179724
35001723

prune395.0ms

Filtered
82 candidates to 66 candidates (80.5%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New78482
Fresh21012
Picked101
Done000
Total811495

Merged error: 0.1b

Counts
95 → 14

regimes518.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03125
13125

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.4s3578×body1280valid
1.3s2321×body640valid
351.0ms952×body320valid
96.0ms415×body160valid
80.0ms734×body80valid