Details

Time bar (total: 56.2s)

sample837.0ms

Algorithm
intervals
Results
500.0ms156×body1280valid
163.0ms63×body640valid
26.0ms25×body320valid
5.0ms7×body160valid
2.0ms5×body80valid

simplify61.0ms

Counts
1 → 1
Iterations
IterNodes
done39
339
238
127
017

prune91.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.3b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.3b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.9b
(cos (- lambda1 lambda2))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
41.0ms
(* (sin phi2) (sin phi1))
1.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
34.0ms
(cos (- lambda1 lambda2))

series444.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (sin phi2) (sin phi1))
292.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
22.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
45.0ms
(cos (- lambda1 lambda2))

simplify4.1s

Counts
74 → 74
Iterations
IterNodes
done5001
42303
31105
2513
1306
0176

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.2b
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))) R)
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.3b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
24.0ms
(* (sin phi2) (sin phi1))
14.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))) R)
1.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
2.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series711.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (sin phi2) (sin phi1))
90.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))) R)
509.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
24.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify4.4s

Counts
73 → 73
Iterations
IterNodes
done5000
31768
2624
1247
0125

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.4b

localize116.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log expm1-log1p-u log-pow add-cbrt-cube log1p-expm1-u
3×acos-asin log-prod
2×exp-diff
1×log-div rem-log-exp fma-udef rem-exp-log
Counts
4 → 52
Calls
4 calls:
1.0ms
(fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))
12.0ms
(log (exp (acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.0ms
(acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))
5.0ms
(exp (acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))

series688.0ms

Counts
4 → 12
Calls
4 calls:
535.0ms
(fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))
29.0ms
(log (exp (acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
27.0ms
(acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))
97.0ms
(exp (acos (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))

simplify5.5s

Counts
64 → 64
Iterations
IterNodes
done5013
42872
3817
2319
1158
096

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

localize147.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (exp (log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
0.3b
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
0.6b
(log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
8×add-exp-log add-cbrt-cube
7×log-prod
6×associate-*r*
4×expm1-log1p-u exp-sum log1p-expm1-u add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×acos-asin rem-log-exp log-pow sin-mult
Counts
4 → 69
Calls
4 calls:
31.0ms
(* (sin phi1) (sin phi2))
40.0ms
(* (exp (log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
1.0ms
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
3.0ms
(log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (sin phi1) (sin phi2))
109.0ms
(* (exp (log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
23.0ms
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
73.0ms
(log (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))

simplify7.0s

Counts
81 → 81
Iterations
IterNodes
done5001
54319
41921
3925
2442
1207
0118

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.4b

regimes1.8s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample24.4s

Algorithm
intervals
Results
17.0s4768×body1280valid
4.6s2067×body640valid
1.1s735×body320valid
856.0ms285×body160valid
59.0ms8×body2560valid
47.0ms138×body80valid