Details

Time bar (total: 37.8s)

sample605.0ms

Algorithm
intervals
Results
320.0ms99×body1280valid
127.0ms71×body640valid
86.0ms54×body80valid
20.0ms16×body160valid
18.0ms16×body320valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:
17.0ms
(* (sin theta) (sin delta))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
28.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
19.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (sin theta) (sin delta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
228.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
291.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.6s

Counts
84 → 84
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01571824
13211677
27941492
320581479
done50011418

prune729.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg associate-*r* associate-*l*
1×sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef sin-mult distribute-lft-out-- expm1-udef associate--r- difference-of-squares unswap-sqr
Counts
4 → 70
Calls
4 calls:
0.0ms
(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))))
12.0ms
(* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
20.0ms
(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
14.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
249.0ms
(* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
338.0ms
(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))

simplify3.0s

Counts
82 → 82
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01502990
12952217
27481868
326521663
done50011653

prune780.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×fma-udef
1×asin-acos pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
Counts
4 → 51
Calls
4 calls:
25.0ms
(* (sin theta) (sin delta))
1.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
14.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(fma (- (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (sin phi1) (cos delta))

series547.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin theta) (sin delta))
176.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
11.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
292.0ms
(fma (- (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (sin phi1) (cos delta))

simplify2.9s

Counts
63 → 63
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0106958
1191950
2431834
31023829
43061828
done5000828

prune620.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.5b
(fma (- (sin (cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)))) (sin phi1) (cos delta))
0.6b
(pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)
5.6b
(cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp asin-acos pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(fma (- (sin (cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)))) (sin phi1) (cos delta))
6.0ms
(pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)
5.0ms
(cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3))

series376.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
267.0ms
(fma (- (sin (cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)))) (sin phi1) (cos delta))
79.0ms
(pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3)
16.0ms
(cbrt (pow (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))) 3))

simplify2.9s

Counts
80 → 80
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0991971
11911728
24621515
324401502
done50001501

prune635.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes437.0ms

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

sample19.6s

Algorithm
intervals
Results
11.3s3148×body1280valid
5.1s1821×body640valid
1.3s1989×body80valid
896.0ms714×body320valid
367.0ms328×body160valid