Details

Time bar (total: 32.6s)

sample458.0ms

Algorithm
intervals
Results
318.0ms150×body1280valid
98.0ms61×body640valid
12.0ms18×body320valid
5.0ms24×body80valid
2.0ms3×body160valid

simplify68.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
12824
24724
37824
49924
510024
done10024

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b
(sin (- lambda1 lambda2))
2.6b
(cos (- lambda1 lambda2))

rewrite122.0ms

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:
46.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
42.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms
(sin (- lambda1 lambda2))
14.0ms
(cos (- lambda1 lambda2))

series261.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
118.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
38.0ms
(sin (- lambda1 lambda2))
31.0ms
(cos (- lambda1 lambda2))

simplify926.0ms

Counts
98 → 98
Iterations

Useful iterations: done (923.0ms)

IterNodesCost
02101766
14341442
217701146
done50001095

prune707.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize73.0ms

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)))
2.6b
(cos (- lambda1 lambda2))

rewrite158.0ms

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×unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sin-cos-mult flip-+
Counts
4 → 86
Calls
4 calls:
14.0ms
(* (cos phi1) (sin phi2))
63.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
55.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(cos (- lambda1 lambda2))

series363.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos phi1) (sin phi2))
178.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
111.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms
(cos (- lambda1 lambda2))

simplify1.2s

Counts
98 → 98
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02301609
15301410
222821174
done50001142

prune691.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

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

rewrite187.0ms

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 cbrt-unprod
5×sin-cos-mult 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 → 99
Calls
4 calls:
12.0ms
(* (cos phi1) (sin phi2))
47.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
17.0ms
(* (sin lambda1) (sin (- lambda2)))
108.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (cos phi1) (sin phi2))
147.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
83.0ms
(* (sin lambda1) (sin (- lambda2)))
222.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

simplify2.0s

Counts
111 → 111
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02331892
16281810
235831542
done50001505

prune900.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize423.0ms

Local error

Found 4 expressions with local error:

0.1b
(expm1 (log1p (* (cos phi1) (sin phi2))))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.3b
(log1p (* (cos phi1) (sin phi2)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
5×expm1-log1p-u sin-cos-mult sin-mult
4×frac-times associate-*r/ associate-*l* pow-prod-down prod-exp cos-mult cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg flip3-- prod-diff *-commutative frac-sub flip-- sub-div
1×log1p-udef expm1-log1p log1p-expm1 associate-*l/ sin-neg distribute-rgt-neg-out expm1-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
1.0ms
(expm1 (log1p (* (cos phi1) (sin phi2))))
28.0ms
(* (sin lambda1) (sin (- lambda2)))
120.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms
(log1p (* (cos phi1) (sin phi2)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(expm1 (log1p (* (cos phi1) (sin phi2))))
91.0ms
(* (sin lambda1) (sin (- lambda2)))
287.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
84.0ms
(log1p (* (cos phi1) (sin phi2)))

simplify1.8s

Counts
91 → 91
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01891482
14901405
226921179
done50011143

prune839.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes591.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02942
13742
done3742

end0.0ms

sample19.5s

Algorithm
intervals
Results
14.0s4594×body1280valid
3.9s1959×body640valid
669.0ms545×body320valid
169.0ms678×body80valid
119.0ms224×body160valid