Details

Time bar (total: 40.9s)

sample494.0ms

Algorithm
intervals
Results
307.0ms101×body1280valid
91.0ms54×body640valid
31.0ms71×body80valid
24.0ms22×body320valid
6.0ms8×body160valid

simplify44.0ms

Counts
1 → 1

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos 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)))))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg asin-acos flip3-- diff-log sin-cos-mult flip-- sin-mult
Counts
4 → 58
Calls
4 calls:
30.0ms
(* (sin phi1) (cos delta))
17.0ms
(* (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))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin phi1) (cos delta))
194.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
225.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.6s

Counts
70 → 70

prune637.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
18.2b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×cbrt-prod
8×*-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×add-cube-cbrt add-log-exp
3×pow-unpow difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-exp sin-mult rem-cube-cbrt
1×pow-to-exp sub-neg asin-acos cbrt-div flip3-- pow1/3 diff-log pow-prod-down prod-exp flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out--
Counts
4 → 65
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
11.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series857.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
258.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
353.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
229.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify2.8s

Counts
77 → 77

prune884.0ms

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
(* (sin phi1) (cos delta))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
3.1b
(log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt log-prod
12×*-un-lft-identity
10×add-cube-cbrt
7×add-exp-log associate--r+
6×pow1 unpow-prod-down add-cbrt-cube
5×add-log-exp
3×asin-acos rem-log-exp associate-*r* associate-*l*
2×log-div sin-diff pow-sub sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-prod-down pow-exp prod-exp log-pow *-commutative sin-cos-mult flip-- cbrt-unprod distribute-lft-out-- associate--r- difference-of-squares unswap-sqr
Counts
4 → 68
Calls
4 calls:
13.0ms
(* (sin phi1) (cos delta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
18.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
11.0ms
(log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series767.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin phi1) (cos delta))
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
367.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
315.0ms
(log (pow (exp (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.4s

Counts
80 → 80

prune768.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(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
(- (+ (* (- (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)) (sin phi1)) (cos delta)) (log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2))))
3.4b
(log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate--r+ add-log-exp
6×unpow-prod-down
5×add-exp-log
4×pow1 asin-acos add-cbrt-cube
3×rem-log-exp
2×log-div diff-log div-sub sin-diff pow-sub sqr-pow
1×pow-to-exp sub-neg flip3-- pow-exp associate--l+ sum-log log-pow flip-- distribute-lft-out-- associate--r- difference-of-squares
Counts
4 → 59
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
135.0ms
(- (+ (* (- (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)) (sin phi1)) (cos delta)) (log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2))))
12.0ms
(log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)))

series862.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
533.0ms
(- (+ (* (- (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)) (sin phi1)) (cos delta)) (log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2))))
309.0ms
(log (pow (exp (sin phi1)) (/ (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 2)))

simplify1.9s

Counts
71 → 71

prune818.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes563.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.3s

end0.0ms

sample20.1s

Algorithm
intervals
Results
12.8s3145×body1280valid
4.6s1805×body640valid
851.0ms2060×body80valid
833.0ms680×body320valid
277.0ms310×body160valid