Details

Time bar (total: 9.1s)

sample169.0ms

Algorithm
intervals
Results
94.0ms106×body1280valid
47.0ms90×body640valid
9.0ms26×body320valid
3.0ms16×body160valid
2.0ms18×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: 1.0b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b
(sin (- lambda1 lambda2))
4.0b
(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+ distribute-lft-out
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ associate-*l* sum-log sin-diff flip-+
Counts
4 → 71
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(sin (- lambda1 lambda2))
6.0ms
(cos (- lambda1 lambda2))

series152.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify73.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
03651023
1800797
22597794
35002745

prune305.0ms

Filtered
83 candidates to 56 candidates (67.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New721183
Fresh000
Picked101
Done000
Total731184

Merged error: 0.8b

Counts
84 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-sqr-sqrt
13×add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×cos-diff
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×fma-def associate-*r*
2×distribute-rgt-in associate-+r+ distribute-lft-in distribute-lft-out
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log cos-mult *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
12.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify95.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0368920
1989763
23930760
35001759

prune424.0ms

Filtered
85 candidates to 61 candidates (71.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New79685
Fresh6410
Picked101
Done000
Total861096

Merged error: 0.1b

Counts
96 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-sqr-sqrt
18×associate-*r*
13×associate-*l*
11×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
9×distribute-lft-out add-log-exp
5×unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-def sum-log *-commutative
2×+-commutative associate-+r+ sin-mult
1×flip3-+ associate-*r/ flip-+
Counts
4 → 88
Calls
4 calls:
10.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))
5.0ms
(* (sin lambda1) (sin lambda2))
40.0ms
(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))
48.0ms
(* (sin lambda1) (sin lambda2))
216.0ms
(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03471092
11476952
25001923

prune516.0ms

Filtered
100 candidates to 75 candidates (75.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New955100
Fresh549
Picked101
Done000
Total1019110

Merged error: 0.1b

Counts
110 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)))
0.5b
(fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
0.7b
(log (exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log
6×exp-prod add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log-prod log-pow log1p-expm1-u
3×associate-*r* associate-*l* fma-udef
2×rem-log-exp exp-sum
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 64
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
2.0ms
(exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)))
1.0ms
(fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
2.0ms
(log (exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))))

series637.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (sin lambda2))
233.0ms
(exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)))
180.0ms
(fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
180.0ms
(log (exp (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))))

simplify56.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0206743
1569643
21993637
35002635

prune389.0ms

Filtered
76 candidates to 57 candidates (75.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73376
Fresh268
Picked101
Done000
Total76985

Merged error: 0.1b

Counts
85 → 9

regimes366.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02922
13122
23122

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.1s3488×body1280valid
1.2s2411×body640valid
312.0ms933×body320valid
98.0ms404×body160valid
81.0ms764×body80valid