Details

Time bar (total: 34.2s)

sample515.0ms

Algorithm
intervals
Results
322.0ms146×body1280valid
133.0ms64×body640valid
18.0ms20×body320valid
4.0ms8×body160valid
4.0ms18×body80valid

simplify104.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12824
24724
37824
49924
510024
done10024

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))
3.5b
(sin (- lambda1 lambda2))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×prod-diff
11×pow1 add-exp-log cos-sum sin-sum add-cbrt-cube
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:
12.0ms
(* (sin phi1) (cos phi2))
38.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

series259.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (sin phi1) (cos phi2))
131.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))
29.0ms
(sin (- lambda1 lambda2))

simplify1.2s

Counts
98 → 98
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02081720
14271395
216381111
done50001056

prune527.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow1 add-exp-log add-cbrt-cube
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×sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ flip-+
Counts
4 → 87
Calls
4 calls:
13.0ms
(* (sin phi1) (cos phi2))
45.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
48.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))

series471.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin phi1) (cos phi2))
231.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
155.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02131618
14951419
222551185
done50011151

prune922.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp sin-cos-mult cbrt-unprod
5×sin-mult
4×expm1-log1p-u frac-times associate-*r/ cos-mult *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-*l/ unswap-sqr
2×sub-neg flip3-- prod-diff frac-sub flip-- sub-div
1×flip3-+ sin-neg distribute-rgt-neg-out flip-+
Counts
4 → 100
Calls
4 calls:
22.0ms
(* (sin phi1) (cos phi2))
79.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
16.0ms
(* (sin lambda1) (sin (- lambda2)))
126.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (sin phi1) (cos phi2))
164.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
82.0ms
(* (sin lambda1) (sin (- lambda2)))
243.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

simplify2.4s

Counts
112 → 112
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02161901
15851819
234181547
done50001510

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite199.0ms

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 sin-cos-mult cbrt-unprod sin-mult
4×distribute-rgt-in expm1-log1p-u frac-times distribute-lft-in associate-*r/ cos-mult log1p-expm1-u add-log-exp
3×*-commutative
2×sub-neg flip3-- prod-diff frac-sub flip-- fma-udef sub-div unswap-sqr
1×log1p-udef log1p-expm1 associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 90
Calls
4 calls:
18.0ms
(* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))))
34.0ms
(* (sin lambda1) (sin (- lambda2)))
143.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.0ms
(log1p (expm1 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
253.0ms
(* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))))
104.0ms
(* (sin lambda1) (sin (- lambda2)))
333.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
347.0ms
(log1p (expm1 (* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (sin (- lambda2)) (cos lambda1))))))

simplify2.5s

Counts
102 → 102
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02021932
15351853
233501570
done50011538

prune991.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes770.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02952
13752
done3752

end0.0ms

sample18.7s

Algorithm
intervals
Results
13.2s4608×body1280valid
4.0s1915×body640valid
532.0ms575×body320valid
197.0ms691×body80valid
170.0ms211×body160valid