Details

Time bar (total: 43.1s)

sample940.0ms

Algorithm
intervals
Results
552.0ms157×body1280valid
169.0ms62×body640valid
34.0ms25×body320valid
6.0ms9×body160valid
1.0ms3×body80valid

simplify83.0ms

Counts
1 → 1

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize58.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (- lambda1 lambda2))
1.2b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite52.0ms

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 insert-posit16 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 unswap-sqr
Counts
4 → 65
Calls
4 calls:
Slowest
34.0ms
(cos (- lambda1 lambda2))
12.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
2.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
38.0ms
(cos (- lambda1 lambda2))
37.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify1.6s

Counts
77 → 77

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize82.0ms

Local error

Found 4 expressions with local error:

1.2b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
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))

rewrite17.0ms

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 insert-posit16 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 → 65
Calls
4 calls:
Slowest
10.0ms
(* (sin phi2) (sin phi1))
5.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
382.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
85.0ms
(* (sin phi2) (sin phi1))
33.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
16.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.4s

Counts
77 → 77

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

localize126.0ms

Local error

Found 4 expressions with local error:

1.2b
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))
0.9b
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
0.2b
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 76
Calls
4 calls:
Slowest
20.0ms
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))))
5.0ms
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))
4.0ms
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
42.0ms
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))))
20.0ms
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))
20.0ms
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))

simplify2.2s

Counts
88 → 88

prune2.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.7b

localize87.0ms

Local error

Found 4 expressions with local error:

1.2b
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))
0.6b
(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
0.2b
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))))
0.2b
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1 log-prod
6×add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u exp-sum insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×unswap-sqr
1×acos-asin rem-log-exp pow-prod-down prod-exp log-pow *-commutative cbrt-unprod fma-udef
Counts
4 → 62
Calls
4 calls:
Slowest
12.0ms
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))))
1.0ms
(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
366.0ms
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))
37.0ms
(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
28.0ms
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))

simplify1.9s

Counts
74 → 74

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.7b

regimes1.5s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch6.0ms

end0.0ms

sample22.7s

Algorithm
intervals
Results
16.0s4776×body1280valid
5.0s2157×body640valid
882.0ms654×body320valid
247.0ms285×body160valid
54.0ms9×body2560valid
45.0ms122×body80valid