Details

Time bar (total: 34.1s)

sample563.0ms

Algorithm
intervals
Results
276.0ms90×body1280valid
112.0ms59×body640valid
106.0ms71×body80valid
27.0ms24×body320valid
8.0ms12×body160valid

simplify506.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (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))))
0.4b
(- (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)))))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (sin theta) (sin delta))
257.0ms
(* (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))))
298.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01571824
13381678
212651533
done50001485

prune772.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.4b
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
0.7b
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite84.0ms

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 delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
15.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
37.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series908.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
15.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
319.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
316.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify1.0s

Counts
86 → 86
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01522434
13132305
211812028
done50002006

prune908.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.4b
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
0.7b
(log (exp (/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
14×log-pow
13×exp-prod
12×pow1
9×times-frac
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod swap-sqr associate-*r* associate-*l*
2×asin-acos
1×pow2 log-div pow-plus exp-diff div-sub rem-log-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin div-inv sin-mult unswap-sqr
Counts
4 → 77
Calls
4 calls:
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
31.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
20.0ms
(log (exp (/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
8.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
236.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
1.0s
(log (exp (/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))))

simplify1.6s

Counts
89 → 89
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01963992
14563699
220443269
done50012776

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin delta) 2)
0.3b
(pow (cos theta) 2)
0.3b
(pow (sin phi1) 3)
0.4b
(pow (sin phi1) 4)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down pow-unpow
8×pow1 add-exp-log
5×add-cbrt-cube
4×expm1-log1p-u pow-to-exp pow-pow pow-exp log1p-expm1-u add-log-exp sqr-pow
3×cube-prod
2×unpow2
1×cube-mult unpow3 rem-cube-cbrt
Counts
4 → 84
Calls
4 calls:
4.0ms
(pow (sin delta) 2)
3.0ms
(pow (cos theta) 2)
5.0ms
(pow (sin phi1) 3)
4.0ms
(pow (sin phi1) 4)

series141.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (sin delta) 2)
24.0ms
(pow (cos theta) 2)
48.0ms
(pow (sin phi1) 3)
40.0ms
(pow (sin phi1) 4)

simplify1.1s

Counts
96 → 96
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0148661
1437561
21794515
done5000511

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes729.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
04190
15390
done5390

end0.0ms

sample20.1s

Algorithm
intervals
Results
12.0s3191×body1280valid
4.9s1819×body640valid
1.5s686×body320valid
689.0ms1999×body80valid
352.0ms305×body160valid