Details

Time bar (total: 45.5s)

sample446.0ms

Algorithm
intervals
Results
213.0ms96×body1280valid
86.0ms59×body640valid
55.0ms22×body320valid
16.0ms68×body80valid
5.0ms11×body160valid

simplify34.0ms

Counts
1 → 1
Iterations
IterNodes
done64
364
259
136
022

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize98.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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 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 → 71
Calls
4 calls:
47.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
18.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
12.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
7.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
239.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
673.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.0s

Counts
83 → 83
Iterations
IterNodes
done5000
33382
21008
1371
0166

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
9×prod-diff
7×add-log-exp
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg
2×diff-log *-commutative
1×asin-acos log1p-udef sub-neg flip3-- flip-- sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 80
Calls
4 calls:
40.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
9.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
6.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
7.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
275.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
384.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

simplify3.4s

Counts
92 → 92
Iterations
IterNodes
done5001
33647
21020
1409
0189

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize138.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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 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 → 71
Calls
4 calls:
23.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
16.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
12.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series652.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
14.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
223.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
307.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify2.8s

Counts
83 → 83
Iterations
IterNodes
done5000
33382
21008
1371
0166

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize204.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
20×add-cbrt-cube add-exp-log
18×pow-prod-down
17×add-sqr-sqrt sin-mult
15×*-un-lft-identity add-cube-cbrt
12×times-frac
10×cos-mult
9×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*l/ associate-*r/ difference-of-squares
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up log1p-expm1-u associate-/l* sub-div
3×frac-times associate-/r*
2×pow-plus flip3-- associate-/r/ *-commutative flip--
1×pow2 cbrt-undiv sqr-cos clear-num sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub swap-sqr div-exp prod-diff associate--l+ flip-+ div-inv unswap-sqr
Counts
4 → 126
Calls
4 calls:
15.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
66.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
50.0ms
(* (* (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)))))))
43.0ms
(- (* (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))))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
307.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0s
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
302.0ms
(* (* (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)))))))
606.0ms
(- (* (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))))))))

simplify2.8s

Counts
138 → 138
Iterations
IterNodes
done5000
22944
1810
0275

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes908.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done43
143
033

end0.0ms

sample20.6s

Algorithm
intervals
Results
12.7s3083×body1280valid
5.0s1902×body640valid
1.1s720×body320valid
792.0ms1984×body80valid
289.0ms311×body160valid