Details

Time bar (total: 49.4s)

sample649.0ms

Algorithm
intervals
Results
446.0ms111×body1280valid
119.0ms57×body640valid
25.0ms19×body320valid
22.0ms58×body80valid
8.0ms11×body160valid

simplify496.0ms

Counts
1 → 1
Iterations
IterNodes
done64
364
259
136
022

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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-*r* add-log-exp
4×expm1-log1p-u associate-*l* 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:
53.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
193.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
252.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.9s

Counts
87 → 87
Iterations
IterNodes
done5000
34278
21107
1372
0163

prune985.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize167.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
22×add-cbrt-cube add-exp-log
20×pow-prod-down
16×add-sqr-sqrt
11×prod-exp cbrt-unprod
10×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
7×sin-mult
4×expm1-log1p-u pow-sqr *-commutative pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×pow-plus
1×pow2 frac-times swap-sqr associate-*l/ associate-*r/
Counts
4 → 106
Calls
4 calls:
23.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
23.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
12.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
41.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))

series898.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
231.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
183.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
240.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))

simplify2.8s

Counts
118 → 118
Iterations
IterNodes
done5004
32228
2750
1238
096

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize171.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-cbrt-cube add-exp-log
12×associate-*r*
11×*-un-lft-identity add-cube-cbrt
10×associate-*l*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u sin-mult add-log-exp
3×unswap-sqr
1×associate-*l/
Counts
4 → 88
Calls
4 calls:
12.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
12.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
11.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
23.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
255.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
224.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
233.0ms
(* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))
505.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))

simplify3.8s

Counts
100 → 100
Iterations
IterNodes
done5000
33662
2865
1246
099

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize208.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))
0.3b
(* (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))) (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))))
11.6b
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
11.6b
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
148×pow1
80×pow-prod-down
66×sqrt-pow1
17×pow-prod-up
14×pow1/2
11×add-sqr-sqrt add-cbrt-cube add-exp-log pow-sqr
9×*-un-lft-identity add-cube-cbrt
8×associate-*l/
7×associate-*r* sin-mult
6×sqrt-div sqrt-prod
5×associate-*l*
4×expm1-log1p-u swap-sqr prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*r/ unswap-sqr
Counts
4 → 126
Calls
4 calls:
30.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))
234.0ms
(* (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))) (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))))
34.0ms
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
39.0ms
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))

series2.9s

Counts
4 → 12
Calls
4 calls:
444.0ms
(* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))
459.0ms
(* (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))) (sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))))))))
961.0ms
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
1.0s
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))

simplify3.6s

Counts
138 → 138
Iterations
IterNodes
done5000
34357
21012
1321
0134

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes674.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations
IterNodes
done41
141
032

end0.0ms

sample22.0s

Algorithm
intervals
Results
14.5s3194×body1280valid
4.4s1843×body640valid
999.0ms694×body320valid
830.0ms1984×body80valid
739.0ms285×body160valid