Details

Time bar (total: 30.9s)

sample433.0ms

Algorithm
intervals
Results
308.0ms138×body1280valid
71.0ms65×body640valid
16.0ms22×body320valid
9.0ms23×body80valid
3.0ms8×body160valid

simplify59.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite152.0ms

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:
37.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
39.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(sin (- lambda1 lambda2))
57.0ms
(cos (- lambda1 lambda2))

series256.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
110.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

simplify1.6s

Counts
72 → 72

prune430.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))

rewrite186.0ms

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 sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ flip-+
Counts
4 → 70
Calls
4 calls:
15.0ms
(* (sin lambda1) (cos lambda2))
86.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
63.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

series404.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (sin lambda1) (cos lambda2))
182.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
140.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms
(cos (- lambda1 lambda2))

simplify722.0ms

Counts
82 → 82

prune681.0ms

Pruning

10 alts after pruning (10 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)) (* (sin lambda1) (sin lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite574.0ms

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:
77.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
351.0ms
(* (sin lambda1) (sin lambda2))
59.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
82.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series604.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
63.0ms
(* (sin lambda1) (sin lambda2))
171.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
161.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.0s

Counts
101 → 101

prune624.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

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))))

rewrite266.0ms

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:
140.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
41.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
40.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
41.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
453.0ms
(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
316.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
363.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
301.0ms
(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

simplify728.0ms

Counts
94 → 94

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes567.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.3s

end0.0ms

sample17.5s

Algorithm
intervals
Results
12.3s4526×body1280valid
3.7s1971×body640valid
537.0ms599×body320valid
189.0ms701×body80valid
153.0ms203×body160valid