Details

Time bar (total: 39.5s)

sample772.0ms

Algorithm
intervals
Results
488.0ms147×body1280valid
116.0ms79×body640valid
21.0ms20×body320valid
5.0ms7×body160valid
1.0ms4×body80valid

simplify52.0ms

Counts
1 → 1
Iterations
IterNodes
done46
446
344
238
127
017

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b
(* (sin phi2) (sin phi1))
0.7b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.6b
(cos (- lambda1 lambda2))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log
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:
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
19.0ms
(* (sin phi2) (sin phi1))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
25.0ms
(cos (- lambda1 lambda2))

series331.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
80.0ms
(* (sin phi2) (sin phi1))
12.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
39.0ms
(cos (- lambda1 lambda2))

simplify3.1s

Counts
74 → 74
Iterations
IterNodes
done5001
33819
2782
1306
0176

prune928.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* (sin phi2) (sin phi1))
0.8b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
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:
11.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
13.0ms
(* (sin phi2) (sin phi1))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
366.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
79.0ms
(* (sin phi2) (sin phi1))
17.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify3.0s

Counts
73 → 73
Iterations
IterNodes
done5000
34620
2809
1256
0126

prune992.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
0.2b
(* (sin phi2) (sin phi1))
0.8b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
3.4b
(log (exp (* (sin phi2) (sin phi1))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×log-prod associate-*r* associate-*l* log-pow
1×acos-asin exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
1.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
14.0ms
(* (sin phi2) (sin phi1))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
3.0ms
(log (exp (* (sin phi2) (sin phi1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
439.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
491.0ms
(* (sin phi2) (sin phi1))
23.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
92.0ms
(log (exp (* (sin phi2) (sin phi1))))

simplify3.6s

Counts
69 → 69
Iterations
IterNodes
done5000
33630
2661
1219
0119

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.4b
(exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
0.5b
(log (exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
0.8b
(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u log-pow log1p-expm1-u
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr rem-exp-log
Counts
4 → 63
Calls
4 calls:
19.0ms
(* (sin phi1) (sin phi2))
3.0ms
(exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
16.0ms
(log (exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.0ms
(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

series180.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin phi1) (sin phi2))
61.0ms
(exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
25.0ms
(log (exp (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
25.0ms
(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify2.2s

Counts
75 → 75
Iterations
IterNodes
done5000
32250
2477
1173
0107

prune885.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.2b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample18.9s

Algorithm
intervals
Results
13.4s4851×body1280valid
3.7s2089×body640valid
707.0ms678×body320valid
225.0ms246×body160valid
77.0ms133×body80valid
36.0ms7×body2560valid