Details

Time bar (total: 13.5s)

sample272.0ms

Algorithm
intervals
Results
175.0ms108×body1280valid
50.0ms57×body640valid
11.0ms19×body320valid
10.0ms64×body80valid
3.0ms8×body160valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222
done7222

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (sin delta)) (cos theta))
0.2b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg prod-diff
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 71
Calls
4 calls:
25.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
160.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
196.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify43.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03381246
112941093
250011088
done50011088

prune454.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(log1p (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×expm1-log1p-u
4×log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
1×sub-neg asin-acos log1p-udef flip3-- diff-log log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(log1p (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
15.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
255.0ms
(log1p (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
159.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
184.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify101.0ms

Counts
74 → 74
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
03011344
19151191
237021184
350011179
done50011179

prune478.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
0.3b
(log1p (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
0.3b
(pow (sin phi1) 2)
0.3b
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×pow1 add-exp-log add-cube-cbrt
13×add-cbrt-cube
9×prod-diff add-log-exp
6×pow-prod-down prod-exp cbrt-unprod
5×expm1-log1p-u
4×log1p-expm1-u
3×unpow-prod-down pow-unpow fma-neg associate-*l*
2×diff-log
1×pow-to-exp sub-neg log1p-udef flip3-- pow-pow log1p-expm1 associate-*r* pow-exp sum-log *-commutative flip-- associate--r+ distribute-lft-out-- unpow2 difference-of-squares sqr-pow
Counts
4 → 84
Calls
4 calls:
61.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
1.0ms
(log1p (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
4.0ms
(pow (sin phi1) 2)
29.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
254.0ms
(log1p (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
18.0ms
(pow (sin phi1) 2)
193.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

simplify65.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04491676
117411137
250011116
done50011116

prune479.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3)))))))
0.4b
(pow (* (cos phi1) (* (cos theta) (sin delta))) 3)
19.8b
(cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×cbrt-prod
6×add-log-exp
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×pow-unpow pow-pow fma-neg associate-*r* associate-*l* prod-diff pow-exp rem-cube-cbrt
2×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
1×pow-to-exp sub-neg flip3-- pow1/3 diff-log *-commutative flip-- rem-cbrt-cube sin-mult unswap-sqr
Counts
4 → 87
Calls
4 calls:
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3)))))))
22.0ms
(pow (* (cos phi1) (* (cos theta) (sin delta))) 3)
9.0ms
(cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))

series556.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))))))
191.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3)))))))
124.0ms
(pow (* (cos phi1) (* (cos theta) (sin delta))) 3)
82.0ms
(cbrt (pow (* (cos phi1) (* (cos theta) (sin delta))) 3))

simplify58.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
03771406
115181261
250011253
done50011253

prune525.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes305.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324
done3324

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.2s3216×body1280valid
1.7s1863×body640valid
411.0ms698×body320valid
339.0ms1950×body80valid
101.0ms273×body160valid