Details

Time bar (total: 50.2s)

sample735.0ms

Algorithm
intervals
Results
448.0ms109×body1280valid
137.0ms57×body640valid
63.0ms62×body80valid
30.0ms21×body320valid
6.0ms7×body160valid

simplify131.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 72
Calls
4 calls:
25.0ms
(* (sin theta) (sin delta))
28.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series773.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (sin theta) (sin delta))
311.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
358.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.6s

Counts
84 → 84
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01571824
13381678
212651533
done50001485

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
0.4b
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
3.3b
(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
198×prod-diff
192×add-sqr-sqrt
187×*-un-lft-identity
185×add-cube-cbrt
168×sin-sum
145×times-frac
84×distribute-rgt-in distribute-lft-in associate--r+
16×fma-neg div-inv
8×add-log-exp
6×pow1 add-exp-log acos-asin sub-neg add-cbrt-cube
5×associate--r-
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l*
2×flip3-- diff-log flip-- difference-of-squares
1×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 289
Calls
4 calls:
164.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
2.0ms
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
65.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
47.0ms
(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
15.0ms
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
365.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
93.0ms
(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

simplify1.7s

Counts
301 → 301
Iterations

Useful iterations: done (1.7s)

IterNodesCost
062833844
1160420453
done500115737

prune5.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize155.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
14.5b
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
58.2b
(cos (/ PI 2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log acos-asin expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-neg prod-diff
2×associate--r+
1×distribute-rgt-in sub-neg flip3-- cos-PI/2 distribute-lft-in diff-log cos-acos flip--
Counts
4 → 53
Calls
4 calls:
1.0ms
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
17.0ms
(- (cos delta) (* (sin phi1) (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
5.0ms
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
8.0ms
(cos (/ PI 2))

series604.0ms

Counts
4 → 10
Calls
4 calls:
14.0ms
(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
349.0ms
(- (cos delta) (* (sin phi1) (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
240.0ms
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
0.0ms
(cos (/ PI 2))

simplify4.7s

Counts
63 → 63
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01231452
12441362
27971131
346501115
done50001115

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize167.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) 3)
0.6b
(- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
14.5b
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
58.2b
(cos (/ PI 2))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-unpow fma-neg cube-prod prod-diff
2×cube-div flip3-- flip--
1×acos-asin cos-diff cube-mult pow-to-exp sub-neg cos-PI/2 pow-pow diff-log unpow3 pow-exp cos-acos rem-cube-cbrt sqr-pow
Counts
4 → 68
Calls
4 calls:
17.0ms
(pow (- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) 3)
16.0ms
(- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
5.0ms
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
8.0ms
(cos (/ PI 2))

series1.6s

Counts
4 → 10
Calls
4 calls:
480.0ms
(pow (- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) 3)
855.0ms
(- (cos delta) (* (cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
246.0ms
(cos (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))
0.0ms
(cos (/ PI 2))

simplify1.6s

Counts
78 → 78
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01452226
13862014
215521768
done50001760

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02981
13481
done3481

end0.0ms

sample24.4s

Algorithm
intervals
Results
13.5s3131×body1280valid
6.3s1879×body640valid
1.8s703×body320valid
1.4s1987×body80valid
331.0ms300×body160valid