Timeout in 10.0m

Use the --timeout flag to change the timeout.

Details

Time bar (total: 1.1m)Debug log

sample237.0ms

Algorithm
intervals

simplify121.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

120.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize40.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
4.1b
(cos (/ (+ phi1 phi2) 2))
4.1b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Counts
4 → 129
Calls

4 calls. Slowest were:

48.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
42.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
4.0ms
(cos (/ (+ phi1 phi2) 2))

series555.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

435.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
88.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
17.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))

simplify30.5s

Counts
118 → 141
Calls

118 calls. Slowest were:

1.1s
(* (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
727.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ lambda1 lambda2) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))
604.0ms
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))

prune3.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.8b

localize33.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
4.1b
(cos (/ (+ phi1 phi2) 2))
4.1b
(cos (/ (+ phi1 phi2) 2))
4.1b
(cos (/ (+ phi1 phi2) 2))

rewrite171.0ms

Algorithm
rewrite-expression-head
Counts
4 → 99
Calls

4 calls. Slowest were:

161.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.0ms
(cos (/ (+ phi1 phi2) 2))
2.0ms
(cos (/ (+ phi1 phi2) 2))

series490.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

438.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
22.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))

simplify25.7s

Counts
82 → 111
Calls

82 calls. Slowest were:

713.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* (+ lambda1 lambda2) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))
650.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ phi1 phi2)) (* (+ lambda1 lambda2) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
585.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (* (+ lambda1 lambda2) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))

prune3.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 25.8b

localize43.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
26.3b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
26.3b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
26.3b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))

rewrite2.1s

Algorithm
rewrite-expression-head
Counts
4 → 5889
Calls

4 calls. Slowest were:

300.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
24.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
23.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

386.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
280.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
278.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
275.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))

Reproduce

herbie shell --seed 2019002 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Equirectangular approximation to distance on a great circle"
  (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))))