Details

Time bar (total: 42.1s)

sample542.0ms

Algorithm
intervals
Results
312.0ms91×body1280valid
137.0ms59×body640valid
30.0ms25×body320valid
24.0ms73×body80valid
6.0ms8×body160valid

simplify88.0ms

Counts
1 → 1
Iterations
IterNodes
done64
364
259
136
022

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(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)))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 76
Calls
4 calls:
14.0ms
(* (sin theta) (sin delta))
14.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(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)))))))

series602.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (sin theta) (sin delta))
237.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
297.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.9s

Counts
88 → 88
Iterations
IterNodes
done5000
32591
2896
1355
0166

prune974.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
5×fma-udef
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg prod-diff
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod associate--r+ unswap-sqr
1×sub-neg flip3-- diff-log flip-- sin-mult
Counts
4 → 79
Calls
4 calls:
11.0ms
(* (sin theta) (sin delta))
0.0ms
(fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))
13.0ms
(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
14.0ms
(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (sin theta) (sin delta))
191.0ms
(fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))
241.0ms
(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
246.0ms
(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

simplify3.1s

Counts
91 → 91
Iterations
IterNodes
done5001
32835
2907
1334
0147

prune902.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
0.2b
(* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
0.4b
(log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
0.5b
(- (cos delta) (* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
1×log1p-udef expm1-log1p sub-neg flip3-- diff-log pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- expm1-udef unswap-sqr
Counts
4 → 66
Calls
4 calls:
0.0ms
(expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
15.0ms
(* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
0.0ms
(log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
11.0ms
(- (cos delta) (* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
270.0ms
(expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
331.0ms
(* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
221.0ms
(log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
316.0ms
(- (cos delta) (* (sin phi1) (expm1 (log1p (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

simplify2.9s

Counts
78 → 78
Iterations
IterNodes
done5000
32234
2719
1273
0121

prune936.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))
0.2b
(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
0.3b
(log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
0.5b
(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×expm1-log1p-u
4×fma-udef insert-posit16 log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
2×distribute-rgt-in distribute-lft-in associate--r+
1×log1p-udef expm1-log1p sub-neg flip3-- diff-log pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- expm1-udef unswap-sqr
Counts
4 → 70
Calls
4 calls:
0.0ms
(expm1 (log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))
9.0ms
(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
1.0ms
(log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
13.0ms
(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
417.0ms
(expm1 (log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))
260.0ms
(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
322.0ms
(log1p (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))))
231.0ms
(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

simplify2.7s

Counts
82 → 82
Iterations
IterNodes
done5000
32410
2826
1310
0135

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes581.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample21.2s

Algorithm
intervals
Results
13.2s3045×body1280valid
5.0s1878×body640valid
1.3s2049×body80valid
896.0ms697×body320valid
358.0ms331×body160valid