Details

Time bar (total: 56.6s)

sample1.2s

Algorithm
intervals
Results
618.0ms150×body1280valid
436.0ms64×body640valid
33.0ms27×body320valid
6.0ms7×body160valid
4.0ms1×body2560valid
3.0ms7×body80valid

simplify76.0ms

Calls
1 calls:
Slowest
75.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.9b

localize42.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (- lambda1 lambda2))
0.5b
(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)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×cos-sum
1×acos-asin cos-diff sub-neg *-commutative fma-udef
Calls
4 calls:
Slowest
4.0ms
(cos (- lambda1 lambda2))
1.0ms
(* 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))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series328.0ms

Calls
4 calls:
Slowest
231.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
46.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
41.0ms
(cos (- lambda1 lambda2))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify894.0ms

Calls
18 calls:
Slowest
118.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
102.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
84.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2)))))
73.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
65.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b
(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
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin phi2) (sin phi1))

rewrite19.0ms

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
14.0ms
(* (sin phi2) (sin phi1))
3.0ms
(* 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)))

series546.0ms

Calls
4 calls:
Slowest
418.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
78.0ms
(* (sin phi2) (sin phi1))
28.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
22.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify4.0s

Calls
24 calls:
Slowest
381.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
381.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
371.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
357.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
348.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.4b
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
0.3b
(exp (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)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×exp-prod
5×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log-pow insert-posit16 log1p-expm1-u
3×acos-asin log-prod
2×exp-diff
1×log-div rem-log-exp fma-udef rem-exp-log
Calls
4 calls:
Slowest
5.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
2.0ms
(exp (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)))

series474.0ms

Calls
4 calls:
Slowest
407.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
46.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
11.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.6s

Calls
25 calls:
Slowest
373.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
373.0ms
(log (* (cbrt (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))) (cbrt (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))))
363.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
360.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
359.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.4b
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
0.3b
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.2b
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×log-pow
7×associate-*r*
6×pow1
5×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in
2×exp-diff
1×log-div rem-log-exp *-commutative rem-exp-log
Calls
4 calls:
Slowest
4.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
2.0ms
(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))))

series114.0ms

Calls
4 calls:
Slowest
42.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
38.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
24.0ms
(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))))

simplify10.2s

Calls
38 calls:
Slowest
638.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)
359.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
358.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
357.0ms
(sqrt (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
341.0ms
(* R (log (sqrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.0b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch5.0ms

end0.0ms

sample23.8s

Algorithm
intervals
Results
16.9s4779×body1280valid
4.3s2132×body640valid
1.5s681×body320valid
555.0ms249×body160valid
127.0ms149×body80valid
59.0ms10×body2560valid