Details

Time bar (total: 57.9s)

sample840.0ms

Algorithm
intervals
Results
535.0ms103×body1280valid
177.0ms63×body640valid
67.0ms67×body80valid
25.0ms14×body320valid
10.0ms9×body160valid

simplify58.0ms

Counts
1 → 1
Iterations
IterNodes
455
355
254
135
022

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 62
Calls
4 calls:
22.0ms
(* (sin theta) (sin delta))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
22.0ms
(* (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)))))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
204.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
310.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts
74 → 74
Iterations
IterNodes
32021
2728
1315
0148

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize138.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* (* (- (cos delta) (* (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)))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times
26×cbrt-div
14×associate-*l/
10×add-log-exp
8×associate-*r/
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×sub-neg diff-log
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 76
Calls
4 calls:
80.0ms
(cbrt (* (* (- (cos delta) (* (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)))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
13.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
14.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
14.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
275.0ms
(cbrt (* (* (- (cos delta) (* (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)))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
287.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
255.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
274.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify5.6s

Counts
88 → 88
Iterations
IterNodes
38246
21226
1344
0155

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize116.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* (* (- (cos delta) (* (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)))))))) (log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.9b
(log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
13×log-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×associate-*l/
9×times-frac
8×cbrt-div flip3-- flip-- add-log-exp
5×pow1 add-exp-log
4×frac-times add-cbrt-cube insert-posit16
2×sub-neg diff-log rem-log-exp associate-*r/
1×cbrt-prod log-div pow1/3 div-exp log-pow div-inv
Counts
4 → 69
Calls
4 calls:
61.0ms
(cbrt (* (* (- (cos delta) (* (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)))))))) (log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
13.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
18.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
12.0ms
(log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
1.1s
(cbrt (* (* (- (cos delta) (* (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)))))))) (log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
249.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
245.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
766.0ms
(log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify2.8s

Counts
81 → 81
Iterations
IterNodes
34547
21126
1419
0185

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize196.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (log (/ (exp (cos delta)) (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.7b
(log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
66×log-prod
54×times-frac
47×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
27×sqrt-prod
22×associate-+l+ associate-+r+
11×pow1 log-pow
9×add-exp-log add-log-exp
5×pow-flip
4×add-cbrt-cube rem-log-exp insert-posit16 distribute-lft-out
3×log-div sqrt-pow1 div-inv
2×sub-neg flip3-- diff-log div-exp flip--
1×+-commutative rec-exp exp-prod associate-+r- sum-log flip3-+ exp-to-pow pow1/2 1-exp log-rec associate-+l- flip-+ inv-pow
Counts
4 → 131
Calls
4 calls:
28.0ms
(+ (log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (log (/ (exp (cos delta)) (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
13.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
12.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
21.0ms
(log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
850.0ms
(+ (log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))) (log (/ (exp (cos delta)) (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
256.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
276.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
492.0ms
(log (/ 1 (sqrt (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

simplify3.0s

Counts
143 → 143
Iterations
IterNodes
33754
21258
1550
0249

prune4.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify22.0ms

Iterations
IterNodes
253
153
042

end0.0ms

sample26.2s

Algorithm
intervals
Results
16.3s3127×body1280valid
6.0s1849×body640valid
1.9s678×body320valid
1.3s2044×body80valid
352.0ms302×body160valid