Details

Time bar (total: 49.2s)

sample772.0ms

Algorithm
intervals
Results
381.0ms93×body1280valid
250.0ms69×body640valid
69.0ms20×body320valid
30.0ms63×body80valid
17.0ms11×body160valid

simplify102.0ms

Counts
1 → 1
Iterations
IterNodes
done64
364
259
136
022

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin delta) (* (cos phi1) (sin theta)))
0.3b
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b
(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)))))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
36×*-un-lft-identity prod-diff
32×add-cube-cbrt
27×associate-*r*
19×associate-*l*
11×pow1 add-cbrt-cube add-exp-log
9×unswap-sqr
6×*-commutative add-log-exp
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×fma-neg
2×distribute-lft-out-- difference-of-squares
1×asin-acos sub-neg flip3-- diff-log flip-- sin-mult
Counts
4 → 125
Calls
4 calls:
64.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
25.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
24.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series600.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
228.0ms
(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
11.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
262.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify2.2s

Counts
137 → 137
Iterations
IterNodes
done5000
21685
1637
0265

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize158.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.4b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
56.7b
(fma (- (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))))) (sin phi1)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×asin-acos fma-udef
Counts
4 → 44
Calls
4 calls:
2.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
1.0ms
(fma (- (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))))) (sin phi1)))

series774.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
10.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
326.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
427.0ms
(fma (- (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))))) (sin phi1)))

simplify3.5s

Counts
56 → 56
Iterations
IterNodes
done5002
43373
31053
2359
1151
084

prune962.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.4b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
56.6b
(fma (- (sin (log1p (expm1 (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))))) (sin phi1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×asin-acos fma-udef
Counts
4 → 44
Calls
4 calls:
7.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
0.0ms
(fma (- (sin (log1p (expm1 (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))))) (sin phi1)))

series687.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
272.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
402.0ms
(fma (- (sin (log1p (expm1 (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))))) (sin phi1)))

simplify3.2s

Counts
56 → 56
Iterations
IterNodes
done5001
43484
31112
2368
1154
085

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize180.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
4.1b
(- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
49.2b
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1) (* (sin (- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
47×*-un-lft-identity
45×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
2×fma-udef difference-of-squares
1×acos-asin asin-acos sub-neg flip3-- diff-log flip-- distribute-lft-out-- associate--r-
Counts
4 → 104
Calls
4 calls:
1.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
1.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
46.0ms
(- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
1.0ms
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1) (* (sin (- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))

series968.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
338.0ms
(fma 1 (cos delta) (- (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1))))
65.0ms
(- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
554.0ms
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1) (* (sin (- (/ PI 2) (acos (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)))

simplify2.3s

Counts
116 → 116
Iterations
IterNodes
done5000
32591
2941
1435
0208

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes924.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify26.0ms

Iterations
IterNodes
done48
248
146
033

end0.0ms

sample26.4s

Algorithm
intervals
Results
16.0s3105×body1280valid
6.8s1828×body640valid
1.4s709×body320valid
1.3s2024×body80valid
407.0ms334×body160valid