Details

Time bar (total: 46.1s)

sample922.0ms

Algorithm
intervals
Results
522.0ms149×body1280valid
145.0ms75×body640valid
136.0ms22×body320valid
6.0ms7×body160valid
1.0ms3×body80valid

simplify84.0ms

Calls
1 calls:
Slowest
83.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize91.0ms

Local error

Found 4 expressions with local error:

4.1b
(cos (- lambda1 lambda2))
0.4b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.3b
(* (sin phi2) (sin phi1))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×cos-sum *-commutative
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp cbrt-unprod sin-mult
Calls
4 calls:
Slowest
9.0ms
(* (sin phi2) (sin phi1))
7.0ms
(cos (- lambda1 lambda2))
3.0ms
(* R (acos (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))))

series130.0ms

Calls
4 calls:
Slowest
60.0ms
(* (sin phi2) (sin phi1))
34.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
27.0ms
(cos (- lambda1 lambda2))
9.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify871.0ms

Calls
27 calls:
Slowest
150.0ms
(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
130.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
80.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2)))))
57.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))
57.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.3b
(* (sin phi2) (sin phi1))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod sin-mult
1×acos-asin
Calls
4 calls:
Slowest
9.0ms
(* (sin phi2) (sin phi1))
9.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* R (acos (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))))

series171.0ms

Calls
4 calls:
Slowest
57.0ms
(* (sin lambda1) (sin lambda2))
53.0ms
(* (sin phi2) (sin phi1))
41.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
20.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify3.5s

Calls
33 calls:
Slowest
403.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
369.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
361.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
359.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
338.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.3b
(* (sin phi2) (sin phi1))
0.3b
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.1b
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×*-commutative
1×acos-asin pow-prod-down prod-exp cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
4.0ms
(* (sin phi2) (sin phi1))
1.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))

series390.0ms

Calls
4 calls:
Slowest
289.0ms
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))
52.0ms
(* (sin phi2) (sin phi1))
40.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
10.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify3.8s

Calls
24 calls:
Slowest
403.0ms
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
327.0ms
(cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
324.0ms
(sqrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
316.0ms
(+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))
309.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.3b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-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 insert-posit16 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 rem-exp-log
Calls
4 calls:
Slowest
9.0ms
(* (sin phi2) (sin phi1))
4.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
2.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

series142.0ms

Calls
4 calls:
Slowest
75.0ms
(* (sin phi2) (sin phi1))
45.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
12.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
10.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify5.8s

Calls
34 calls:
Slowest
390.0ms
(exp (* (cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))) (cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
386.0ms
(log (* (cbrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))) (cbrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))))
367.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
357.0ms
(log (sqrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
344.0ms
(exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch5.0ms

end0.0ms

sample21.0s

Algorithm
intervals
Results
15.4s4797×body1280valid
3.9s2096×body640valid
850.0ms683×body320valid
544.0ms260×body160valid
77.0ms15×body2560valid
49.0ms154×body80valid