Details

Time bar (total: 42.3s)

sample723.0ms

Algorithm
intervals
Results
471.0ms159×body1280valid
84.0ms61×body640valid
24.0ms23×body320valid
4.0ms8×body160valid
2.0ms5×body80valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
01719
12718
23818
34318
done4318

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.5b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b
(cos (- lambda1 lambda2))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×*-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
73.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
22.0ms
(cos (- lambda1 lambda2))

series356.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
92.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
17.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
40.0ms
(cos (- lambda1 lambda2))

simplify8.8s

Counts
86 → 86
Iterations

Useful iterations: done (8.8s)

IterNodesCost
01961763
13771589
29621325
323201281
438081190
done50011144

prune619.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.5b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r* cos-mult
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative
2×sub-neg flip3-- prod-diff frac-sub flip-- sub-div unswap-sqr
1×acos-asin associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 87
Calls
4 calls:
18.0ms
(* (sin lambda1) (sin (- lambda2)))
8.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
157.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sin lambda1) (sin (- lambda2)))
130.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
376.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
31.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.6s

Counts
99 → 99
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02052400
14822347
217151925
done50011885

prune980.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))
0.3b
(pow (* (sin (- lambda2)) (sin lambda1)) 3)
0.5b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
28.4b
(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
22×prod-diff
13×distribute-rgt-in distribute-lft-in
12×pow1 add-exp-log add-cbrt-cube
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cos-mult
4×cube-div expm1-log1p-u cube-mult unpow-prod-down unpow3 cube-prod pow-prod-down prod-exp cbrt-unprod log1p-expm1-u sin-mult add-log-exp sqr-pow
3×frac-times pow-unpow cbrt-div associate-*r/ associate-*r*
2×sub-neg flip3-- pow-pow pow-exp frac-sub flip-- rem-cube-cbrt
1×distribute-lft-neg-out acos-asin pow-to-exp pow1/3 associate-*l* cube-neg associate-*l/ sin-neg *-commutative rem-cbrt-cube
Counts
4 → 109
Calls
4 calls:
148.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))
12.0ms
(pow (* (sin (- lambda2)) (sin lambda1)) 3)
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
6.0ms
(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

series535.0ms

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))
86.0ms
(pow (* (sin (- lambda2)) (sin lambda1)) 3)
18.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
76.0ms
(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

simplify2.3s

Counts
121 → 121
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02903816
16823049
222082468
done50002379

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))
0.3b
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))
0.4b
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))
0.5b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×add-log-exp
4×expm1-log1p-u log-pow log1p-expm1-u
3×acos-asin log-prod associate-*r* pow-prod-down prod-exp cbrt-unprod
2×exp-diff fma-udef
1×distribute-rgt-in log-div distribute-lft-in rem-log-exp associate-*l* associate-*l/ cos-mult *-commutative rem-exp-log
Counts
4 → 65
Calls
4 calls:
45.0ms
(* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))
7.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))
5.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
299.0ms
(* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))
19.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))
50.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))
22.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))

simplify3.0s

Counts
77 → 77
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01292022
12501969
27551716
329891715
done50011715

prune685.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.2b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02428
12828
done2828

end0.0ms

sample18.7s

Algorithm
intervals
Results
11.9s4750×body1280valid
5.0s2123×body640valid
739.0ms679×body320valid
144.0ms289×body160valid
71.0ms14×body2560valid
48.0ms146×body80valid