Details

Time bar (total: 58.4s)

sample859.0ms

Algorithm
intervals
Results
454.0ms91×body1280valid
214.0ms55×body640valid
91.0ms25×body320valid
41.0ms68×body80valid
22.0ms17×body160valid

simplify65.0ms

Counts
1 → 1
Iterations
IterNodes
464
364
259
136
022

prune85.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×fma-neg prod-diff
2×*-commutative
1×asin-acos sub-neg flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 75
Calls
4 calls:
32.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
21.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series627.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
240.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
9.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
258.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.3s

Counts
87 → 87
Iterations
IterNodes
33245
2996
1376
0170

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize152.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
17×pow-prod-down
16×add-cbrt-cube add-exp-log
10×sin-mult
8×prod-exp cbrt-unprod
6×add-log-exp
5×cos-mult
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity pow-sqr pow-prod-up add-cube-cbrt insert-posit16 log1p-expm1-u
3×associate-*l/ associate-*r/ frac-sub
2×frac-times asin-acos pow-plus sub-div
1×pow2 sqr-cos sub-neg flip3-- fma-neg diff-log swap-sqr associate-*r* associate-*l* prod-diff associate--l+ *-commutative flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
61.0ms
(* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
53.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

series829.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
254.0ms
(* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
560.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

simplify6.5s

Counts
98 → 98
Iterations
IterNodes
38873
21747
1470
0182

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize168.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube associate-*l/ add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u
3×asin-acos
2×cos-mult sin-mult
1×sqr-cos sub-neg flip3-- fma-neg diff-log prod-diff associate--l+ frac-sub flip-- sub-div
Counts
4 → 53
Calls
4 calls:
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
85.0ms
(- (* (cos delta) (cos delta)) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
9.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
603.0ms
(- (* (cos delta) (cos delta)) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify4.2s

Counts
65 → 65
Iterations
IterNodes
35569
21227
1324
0127

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b
(fma (cos delta) (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))))
41.3b
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×asin-acos fma-udef
Counts
4 → 44
Calls
4 calls:
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.0ms
(fma (cos delta) (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))))
0.0ms
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1))))

series1.6s

Counts
4 → 12
Calls
4 calls:
9.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
640.0ms
(fma (cos delta) (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))))
938.0ms
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1))))

simplify2.7s

Counts
56 → 56
Iterations
IterNodes
35009
21076
1281
0119

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes997.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations
IterNodes
235
135
026

end0.0ms

sample28.3s

Algorithm
intervals
Results
16.9s3114×body1280valid
8.0s1892×body640valid
1.4s688×body320valid
1.2s2005×body80valid
409.0ms301×body160valid