Details

Time bar (total: 20.9s)

sample356.0ms

Algorithm
intervals
Results
174.0ms91×body1280valid
107.0ms61×body640valid
19.0ms11×body160valid
16.0ms22×body320valid
15.0ms71×body80valid

simplify3.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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 sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
22.0ms
(* (sin theta) (sin delta))
15.0ms
(* (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))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (sin theta) (sin delta))
168.0ms
(* (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))))
205.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify85.0ms

Counts
70 → 70

prune406.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.5b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
0.6b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
7.1b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg asin-acos flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube rem-cube-cbrt
Counts
4 → 64
Calls
4 calls:
3.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
5.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series263.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
40.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
206.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
9.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify151.0ms

Counts
76 → 76

prune385.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))
0.5b
(pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
0.6b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
4.1b
(- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
20×*-un-lft-identity
18×cbrt-prod
12×unpow-prod-down cube-prod
10×add-cube-cbrt difference-of-squares
8×add-log-exp
5×pow1 add-exp-log times-frac add-cbrt-cube distribute-lft-out--
4×cube-div flip3-- flip--
3×pow-unpow
2×cube-mult sub-neg cbrt-div diff-log unpow3 sqr-pow
1×acos-asin pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube associate--r- rem-cube-cbrt
Counts
4 → 88
Calls
4 calls:
22.0ms
(cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))
25.0ms
(pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
18.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
21.0ms
(- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))
111.0ms
(pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
472.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
43.0ms
(- (/ PI 2) (acos (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))

simplify49.0ms

Counts
100 → 100

prune529.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
6.2b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.2b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.2b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cbrt-prod cbrt-div pow1/3 sin-mult
1×sub-neg flip3-- diff-log flip--
Counts
4 → 42
Calls
4 calls:
7.0ms
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
14.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
209.0ms
(- (cos delta) (* (* (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
347.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
347.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
350.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify58.0ms

Counts
54 → 54

prune374.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes402.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

end0.0ms

sample15.1s

Algorithm
intervals
Results
9.4s3203×body1280valid
3.7s1829×body640valid
759.0ms689×body320valid
525.0ms1972×body80valid
159.0ms307×body160valid