Details

Time bar (total: 31.7s)

sample664.0ms

Algorithm
intervals
Results
446.0ms151×body1280valid
88.0ms56×body640valid
75.0ms23×body320valid
6.0ms21×body80valid
3.0ms5×body160valid

simplify87.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.2b
(cos (- lambda1 lambda2))
4.3b
(sin (- lambda1 lambda2))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
54.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
63.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms
(cos (- lambda1 lambda2))
12.0ms
(sin (- lambda1 lambda2))

series303.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
138.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))
43.0ms
(sin (- lambda1 lambda2))

simplify1.7s

Counts
72 → 72

prune406.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.2b
(cos (- lambda1 lambda2))

rewrite165.0ms

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*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff associate-*l/ *-commutative
2×cos-sum unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sin-neg distribute-rgt-neg-out sin-cos-mult flip-+
Counts
4 → 70
Calls
4 calls:
29.0ms
(* (cos lambda1) (sin (- lambda2)))
63.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
57.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms
(cos (- lambda1 lambda2))

series482.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (cos lambda1) (sin (- lambda2)))
225.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
172.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))

simplify803.0ms

Counts
82 → 82

prune718.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×associate-*l/ *-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ cos-mult unswap-sqr
1×flip3-+ flip-+
Counts
4 → 89
Calls
4 calls:
61.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms
(* (sin lambda1) (sin lambda2))
71.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
92.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
70.0ms
(* (sin lambda1) (sin lambda2))
183.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
157.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify1.1s

Counts
101 → 101

prune712.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-div
22×cos-mult sin-cos-mult
20×frac-times
14×associate-*r/ associate-*l/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 82
Calls
4 calls:
134.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
33.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
33.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
31.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
283.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
293.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
292.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

simplify1.7s

Counts
94 → 94

prune901.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes586.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify456.0ms

end0.0ms

sample18.1s

Algorithm
intervals
Results
13.1s4657×body1280valid
3.3s1923×body640valid
805.0ms529×body320valid
227.0ms686×body80valid
143.0ms205×body160valid