Details

Time bar (total: 35.8s)

sample546.0ms

Algorithm
intervals
Results
358.0ms103×body1280valid
90.0ms60×body640valid
39.0ms25×body320valid
15.0ms58×body80valid
6.0ms10×body160valid

simplify43.0ms

Counts
1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
1×sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 46
Calls
4 calls:
1.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
29.0ms
(* (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))))
19.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
214.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
18.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
320.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.2s

Counts
58 → 58

prune575.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.5b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.6b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite34.0ms

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:
5.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
15.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
9.0ms
(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))

series419.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
303.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
69.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
33.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify2.6s

Counts
76 → 76

prune559.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize137.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×cube-mult unpow3 add-log-exp sqr-pow
3×pow-unpow pow1/3 rem-cbrt-cube
1×pow-to-exp pow-pow pow-exp rem-cube-cbrt
Counts
4 → 86
Calls
4 calls:
5.0ms
(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))
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
3.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series104.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
24.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
16.0ms
(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))

simplify2.5s

Counts
98 → 98

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
4.2b
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
6.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
2×cube-mult unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 62
Calls
4 calls:
2.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
7.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
5.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
5.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series245.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
129.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
17.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
16.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify1.8s

Counts
74 → 74

prune722.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes704.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.5s

end0.0ms

sample20.0s

Algorithm
intervals
Results
12.6s3115×body1280valid
3.9s1798×body640valid
1.6s744×body320valid
809.0ms2041×body80valid
403.0ms302×body160valid