Details

Time bar (total: 1.0m)

sample885.0ms

Algorithm
intervals
Results
523.0ms103×body1280valid
205.0ms63×body640valid
39.0ms67×body80valid
26.0ms14×body320valid
13.0ms9×body160valid

simplify69.0ms

Counts
1 → 1
Iterations
IterNodes
464
364
259
136
022

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin delta) (* (cos phi1) (sin theta)))
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))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite67.0ms

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:
43.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
13.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series635.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
11.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
269.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
275.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify1.4s

Counts
87 → 87
Iterations
IterNodes
33202
2998
1376
0170

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
0.6b
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
0.9b
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
8×log-prod
7×pow1
6×add-cbrt-cube prod-diff add-exp-log add-log-exp
5×exp-sum
4×expm1-log1p-u log-pow insert-posit16 log1p-expm1-u
3×exp-prod fma-neg associate-*r* associate-*l*
2×sub-neg
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 78
Calls
4 calls:
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
13.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
8.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
15.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series755.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
264.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
261.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))
225.0ms
(log (exp (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify1.4s

Counts
90 → 90
Iterations
IterNodes
32381
2875
1324
0158

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize140.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
0.6b
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
0.9b
(log (exp (+ (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
54.6b
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log
5×log-pow
4×expm1-log1p-u log-prod exp-prod insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×fma-udef
1×rem-log-exp exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out unswap-sqr
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
0.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
19.0ms
(log (exp (+ (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
1.0ms
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
279.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
567.0ms
(log (exp (+ (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
388.0ms
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

simplify13.2s

Counts
76 → 76
Iterations
IterNodes
46289
31977
2722
1278
0141

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize183.0ms

Local error

Found 4 expressions with local error:

0.6b
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
0.6b
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
0.9b
(log (exp (+ (cbrt (* (* (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
54.6b
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt
5×pow1 log-pow
4×expm1-log1p-u log-prod exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×rem-log-exp exp-sum distribute-lft-out
Counts
4 → 53
Calls
4 calls:
0.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
0.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
18.0ms
(log (exp (+ (cbrt (* (* (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
0.0ms
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
257.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
260.0ms
(fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
560.0ms
(log (exp (+ (cbrt (* (* (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))) (fma 1 (cos delta) (- (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))) (fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))))
416.0ms
(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))

simplify2.3s

Counts
65 → 65
Iterations
IterNodes
44089
31355
2439
1186
0103

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes1.1s

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
344
244
142
031

end1.0ms

sample27.3s

Algorithm
intervals
Results
17.2s3127×body1280valid
6.6s1849×body640valid
1.5s678×body320valid
1.2s2044×body80valid
455.0ms302×body160valid