Details

Time bar (total: 31.0s)

sample543.0ms

Algorithm
intervals
Results
328.0ms109×body1280valid
131.0ms81×body640valid
43.0ms31×body320valid
8.0ms26×body80valid
6.0ms9×body160valid

simplify47.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
120
014

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize45.0ms

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))))
5.1b
(cos (- lambda1 lambda2))
5.2b
(sin (- lambda1 lambda2))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cos-diff fma-def
2×associate-+r+ sub-neg
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 73
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
12.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms
(cos (- lambda1 lambda2))
13.0ms
(sin (- lambda1 lambda2))

series212.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
136.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms
(cos (- lambda1 lambda2))
30.0ms
(sin (- lambda1 lambda2))

simplify4.0s

Counts
85 → 85
Iterations
IterNodes
45761
31784
2699
1365
0195

prune604.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.2b
(sin (- lambda1 lambda2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×sin-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 73
Calls
4 calls:
23.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
20.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
21.0ms
(sin (- lambda1 lambda2))

series467.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
345.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
45.0ms
(sin (- lambda1 lambda2))

simplify1.4s

Counts
85 → 85
Iterations
IterNodes
33790
2905
1397
0200

prune871.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos lambda1) (sin lambda2))
0.3b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+ sin-mult
Counts
4 → 72
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
22.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin lambda1) (sin lambda2))
54.0ms
(* (cos lambda1) (sin lambda2))
29.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
314.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.5s

Counts
84 → 84
Iterations
IterNodes
33928
2994
1348
0145

prune845.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.4b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.5b
(* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
0.6b
(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l*
1×cbrt-prod pow2 distribute-rgt-in distribute-lft-in pow-plus pow1/3 pow3 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up rem-cbrt-cube cbrt-unprod unswap-sqr
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
6.0ms
(* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
12.0ms
(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
254.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
247.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
312.0ms
(* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
222.0ms
(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

simplify1.6s

Counts
77 → 77
Iterations
IterNodes
32908
2552
1166
086

prune706.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes719.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
228
128
022

end0.0ms

sample15.5s

Algorithm
intervals
Results
8.5s3428×body1280valid
4.8s2431×body640valid
1.4s956×body320valid
250.0ms454×body160valid
188.0ms731×body80valid