Details

Time bar (total: 47.6s)

sample1.2s

Algorithm
intervals
Results
964.0ms110×body1280valid
147.0ms57×body640valid
31.0ms65×body80valid
31.0ms19×body320valid
5.0ms5×body160valid

simplify76.0ms

Counts
1 → 1
Iterations
IterNodes
done55
355
254
135
022

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (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))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite66.0ms

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))
26.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms
(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)))))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (sin theta) (sin delta))
243.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
261.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.2s

Counts
74 → 74
Iterations
IterNodes
done2000
32000
2734
1317
0148

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
15×log-prod
14×add-sqr-sqrt
12×*-un-lft-identity sin-sum add-cube-cbrt
7×pow1
6×distribute-rgt-in distribute-lft-in add-cbrt-cube add-exp-log associate--r+ add-log-exp
4×log-pow insert-posit16
3×exp-prod associate-*r* associate-*l*
2×asin-acos
1×log-div sub-neg flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 71
Calls
4 calls:
24.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
11.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
12.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
245.0ms
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
7.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.3s

Counts
83 → 83
Iterations
IterNodes
done2001
32001
2802
1363
0172

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize184.0ms

Local error

Found 4 expressions with local error:

2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×log-pow
12×add-sqr-sqrt log-prod exp-prod *-un-lft-identity add-cube-cbrt
8×pow1
4×log-div asin-acos add-cbrt-cube exp-diff rem-log-exp add-exp-log insert-posit16 add-log-exp
Counts
4 → 68
Calls
4 calls:
6.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series36.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
11.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify2.1s

Counts
80 → 80
Iterations
IterNodes
done2000
92000
81729
7554
6261
5152
4108
393
285
180
060

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize159.0ms

Local error

Found 4 expressions with local error:

2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
16×log-pow
12×add-sqr-sqrt log-prod exp-prod *-un-lft-identity add-cube-cbrt
8×pow1
4×log-div asin-acos add-cbrt-cube exp-diff rem-log-exp add-exp-log insert-posit16 add-log-exp
Counts
4 → 68
Calls
4 calls:
11.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
11.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify2.2s

Counts
80 → 80
Iterations
IterNodes
done2000
92000
81729
7554
6261
5152
4108
393
285
180
060

prune3.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes789.0ms

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
done51
151
038

end0.0ms

sample26.7s

Algorithm
intervals
Results
15.5s3124×body1280valid
7.1s1819×body640valid
1.9s717×body320valid
1.4s2045×body80valid
367.0ms295×body160valid