Details

Time bar (total: 59.3s)

sample909.0ms

Algorithm
intervals
Results
569.0ms111×body1280valid
171.0ms57×body640valid
86.0ms19×body320valid
32.0ms58×body80valid
14.0ms11×body160valid

simplify46.0ms

Counts
1 → 1
Iterations
IterNodes
done70
370
260
136
022

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize89.0ms

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)))))))

rewrite69.0ms

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:
26.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
20.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
17.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
272.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
307.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.3s

Counts
87 → 87
Iterations
IterNodes
done5000
34506
21185
1372
0163

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize197.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

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 (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
23.0ms
(* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
27.0ms
(* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
75.0ms
(* (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))

series1.2s

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
268.0ms
(* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
224.0ms
(* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))
368.0ms
(* (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))

simplify3.0s

Counts
118 → 118
Iterations
IterNodes
done5000
32729
2849
1253
0101

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize177.0ms

Local error

Found 4 expressions with local error:

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

rewrite262.0ms

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 insert-posit16 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 → 130
Calls
4 calls:
24.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
118.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
67.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
51.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
290.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.4s
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
275.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
854.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify3.4s

Counts
142 → 142
Iterations
IterNodes
done5007
23125
1809
0278

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize156.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (log1p (expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (+ (cos delta) (* (sin phi1) (sin (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)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.5b
(expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
18×add-cbrt-cube add-exp-log
17×pow-prod-down
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×sin-mult
9×times-frac
8×prod-exp cbrt-unprod
6×add-log-exp
5×cos-mult log1p-expm1-u
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16
3×associate-/r* associate-*l/ associate-*r/ frac-sub associate-/l*
2×frac-times pow-plus associate-/r/ sub-div
1×pow2 cbrt-undiv sqr-cos expm1-log1p clear-num sub-neg frac-2neg flip3-+ flip3-- fma-neg diff-log swap-sqr div-exp associate-*r* associate-*l* prod-diff associate--l+ *-commutative flip-+ div-inv flip-- expm1-udef difference-of-squares
Counts
4 → 108
Calls
4 calls:
16.0ms
(/ (log1p (expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
98.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
101.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series3.9s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (log1p (expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
285.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
978.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.2s
(expm1 (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify2.6s

Counts
120 → 120
Iterations
IterNodes
done5000
22973
1743
0275

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes688.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done43
143
031

end0.0ms

sample29.5s

Algorithm
intervals
Results
17.4s3194×body1280valid
7.6s1843×body640valid
1.9s1984×body80valid
1.7s694×body320valid
364.0ms285×body160valid