Details

Time bar (total: 41.6s)

sample615.0ms

Algorithm
intervals
Results
416.0ms99×body1280valid
104.0ms62×body640valid
30.0ms27×body320valid
19.0ms61×body80valid
4.0ms7×body160valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite66.0ms

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))
27.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (sin theta) (sin delta))
250.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
293.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.6s

Counts
84 → 84
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01581747
13221677
27621492
319151479
done50001418

prune816.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
0.9b
(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
8×log-prod
7×pow1
6×add-exp-log prod-diff add-cbrt-cube add-log-exp
5×exp-sum
4×expm1-log1p-u log-pow log1p-expm1-u
3×exp-prod fma-neg associate-*r* associate-*l*
2×sub-neg
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
26.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
13.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series890.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
14.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
297.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
313.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify2.8s

Counts
86 → 86
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01562434
12932305
26502020
317871880
done50001872

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
9×prod-diff
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
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip-- distribute-lft-out-- expm1-udef associate--r- difference-of-squares
Counts
4 → 81
Calls
4 calls:
18.0ms
(* (sin theta) (sin delta))
21.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin theta) (sin delta))
230.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
347.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify3.2s

Counts
93 → 93
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01812957
13612183
28641840
326181635
done50001625

prune823.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
0.5b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
1.3b
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
1.3b
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
22×log-prod
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-prod
12×prod-diff log-pow
10×exp-sum
8×pow1 sqrt-pow1 add-log-exp
6×add-exp-log exp-prod fma-neg
4×expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u
2×log-div flip3-- pow1/2 exp-diff sqrt-div diff-log rem-log-exp flip--
Counts
4 → 96
Calls
4 calls:
8.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
9.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
16.0ms
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
22.0ms
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
282.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
268.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
667.0ms
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))
588.0ms
(log (sqrt (exp (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))))

simplify2.3s

Counts
108 → 108
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01353760
12533626
25433188
315383000
done50012858

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes641.0ms

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
02334
12934
done2934

end0.0ms

sample21.0s

Algorithm
intervals
Results
12.8s3179×body1280valid
5.1s1812×body640valid
992.0ms2010×body80valid
988.0ms682×body320valid
313.0ms317×body160valid