Details

Time bar (total: 34.2s)

sample488.0ms

Algorithm
intervals
Results
357.0ms145×body1280valid
84.0ms71×body640valid
9.0ms11×body320valid
5.0ms20×body80valid
4.0ms9×body160valid

simplify65.0ms

Counts
1 → 1
Iterations
IterNodes
done95
495
378
247
128
017

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b
(sin (- lambda1 lambda2))
3.6b
(cos (- lambda1 lambda2))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×prod-diff
11×pow1 cos-sum add-cbrt-cube sin-sum add-exp-log
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×sub-neg *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 86
Calls
4 calls:
45.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
41.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(sin (- lambda1 lambda2))
14.0ms
(cos (- lambda1 lambda2))

series305.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
144.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms
(sin (- lambda1 lambda2))
25.0ms
(cos (- lambda1 lambda2))

simplify1.5s

Counts
98 → 98
Iterations
IterNodes
done5000
21802
1434
0210

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.2b

localize121.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi1) (sin phi2))
0.1b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b
(cos (- lambda1 lambda2))

rewrite474.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×pow1 add-cbrt-cube add-exp-log
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-diff associate-*l/ *-commutative
2×unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- sin-cos-mult flip--
Counts
4 → 86
Calls
4 calls:
357.0ms
(* (cos phi1) (sin phi2))
47.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
50.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))

series355.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (cos phi1) (sin phi2))
154.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
110.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))

simplify1.5s

Counts
98 → 98
Iterations
IterNodes
done5000
22123
1504
0226

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-cbrt-cube add-exp-log
17×pow-prod-down prod-exp cbrt-unprod
9×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
5×associate-*r* associate-*l*
4×expm1-log1p-u prod-diff log1p-expm1-u sin-cos-mult
3×*-commutative sin-mult
2×frac-times diff-log associate-*l/ associate-*r/ cos-mult
1×sum-log sub-neg distribute-rgt-out flip3-- fma-neg flip-- associate--r+ unswap-sqr
Counts
4 → 96
Calls
4 calls:
63.0ms
(- (* (cos phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
14.0ms
(* (sin lambda1) (sin lambda2))
35.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
60.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series812.0ms

Counts
4 → 12
Calls
4 calls:
459.0ms
(- (* (cos phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
72.0ms
(* (sin lambda1) (sin lambda2))
123.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
158.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify2.2s

Counts
108 → 108
Iterations
IterNodes
done5000
22593
1529
0192

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))
0.2b
(expm1 (log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))))
0.3b
(* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))
0.3b
(log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
6×add-log-exp
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
1×log1p-udef expm1-log1p sub-neg flip3-- fma-neg diff-log associate-*l* prod-diff log1p-expm1 *-commutative flip-- expm1-udef
Counts
4 → 58
Calls
4 calls:
10.0ms
(- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))
0.0ms
(expm1 (log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))))
24.0ms
(* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))
1.0ms
(log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))))

series1.5s

Counts
4 → 12
Calls
4 calls:
380.0ms
(- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))
512.0ms
(expm1 (log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1)))))
227.0ms
(* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))
391.0ms
(log1p (- (* (cos phi1) (sin phi2)) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (sin phi1))))

simplify1.7s

Counts
70 → 70
Iterations
IterNodes
done5000
21861
1334
0130

prune723.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes968.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done46
246
138
028

end0.0ms

sample17.4s

Algorithm
intervals
Results
12.6s4598×body1280valid
3.2s1953×body640valid
565.0ms226×body160valid
445.0ms562×body320valid
197.0ms661×body80valid