Details

Time bar (total: 18.0s)

sample282.0ms

Algorithm
intervals
Results
173.0ms107×body1280valid
61.0ms56×body640valid
12.0ms21×body320valid
11.0ms68×body80valid
1.0ms4×body160valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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))
0.3b
(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)))

rewrite35.0ms

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:
12.0ms
(* (sin theta) (sin delta))
12.0ms
(* (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))))
8.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin theta) (sin delta))
168.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
7.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
194.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.7s

Counts
84 → 84
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01581747
13221677
27621492
319151479
done50001418

prune476.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×cube-div expm1-log1p-u log1p-expm1-u
3×pow-unpow flip3-- fma-neg prod-diff flip--
2×cube-mult cbrt-div unpow3 sqr-pow
1×pow-to-exp sub-neg asin-acos pow-pow pow1/3 diff-log pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 82
Calls
4 calls:
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(cbrt (pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3))
8.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
8.0ms
(pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3)

series652.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
191.0ms
(cbrt (pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3))
191.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
263.0ms
(pow (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) 3)

simplify585.0ms

Counts
94 → 94
Iterations

Useful iterations: done (582.0ms)

IterNodesCost
01413240
13192919
28592599
done50002550

prune548.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×swap-sqr associate-*r* associate-*l* sin-mult
2×asin-acos associate-*l/ cos-mult
1×pow2 sub-neg sqr-cos flip3-- pow-plus fma-neg diff-log prod-diff pow-prod-down prod-exp associate--l+ pow-sqr *-commutative pow-prod-up frac-sub flip-- cbrt-unprod sqr-sin sub-div unswap-sqr
Counts
4 → 68
Calls
4 calls:
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
30.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
13.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
393.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
166.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify767.0ms

Counts
80 → 80
Iterations

Useful iterations: done (764.0ms)

IterNodesCost
01583029
13862680
212152280
done50001843

prune613.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (* (cos delta) (cos delta)) (* (cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)) (pow (sin phi1) 2)))
0.9b
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
7.8b
(cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×unpow-prod-down add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-unpow
2×sqr-pow
1×pow-to-exp sub-neg asin-acos sqr-cos flip3-- pow-pow fma-neg pow1/3 diff-log prod-diff pow-exp associate--l+ flip--
Counts
4 → 63
Calls
4 calls:
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
21.0ms
(- (* (cos delta) (cos delta)) (* (cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)) (pow (sin phi1) 2)))
4.0ms
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
3.0ms
(cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6))

series967.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
403.0ms
(- (* (cos delta) (cos delta)) (* (cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)) (pow (sin phi1) 2)))
390.0ms
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
166.0ms
(cbrt (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6))

simplify724.0ms

Counts
75 → 75
Iterations

Useful iterations: done (721.0ms)

IterNodesCost
01692198
14022100
211451965
done50001856

prune555.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes445.0ms

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
02435
13035
done3035

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.3s3137×body1280valid
1.7s1861×body640valid
388.0ms674×body320valid
318.0ms1999×body80valid
135.0ms329×body160valid