Details

Time bar (total: 1.0m)

sample1.2s

Algorithm
intervals
Results
624.0ms72×body640valid
449.0ms146×body1280valid
26.0ms20×body320valid
10.0ms1×body2560valid
9.0ms10×body160valid
2.0ms7×body80valid

simplify105.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
104.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.4b

localize82.0ms

Local error

Found 4 expressions with local error:

4.3b
(cos (- lambda1 lambda2))
0.7b
(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
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite22.0ms

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
13.0ms
(cos (- lambda1 lambda2))
6.0ms
(* 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)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
48.0ms
(cos (- lambda1 lambda2))
43.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
18.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.1s

Counts
34 → 77
Calls
34 calls:
Slowest
506.0ms
(* (* (* R R) R) (* (* (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
114.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
103.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
85.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
78.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize95.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.3b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (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 phi2) (sin phi1))

rewrite26.0ms

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
13.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
11.0ms
(* (sin phi2) (sin phi1))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series485.0ms

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)))
55.0ms
(* (sin phi2) (sin phi1))
37.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.1s

Counts
33 → 77
Calls
33 calls:
Slowest
386.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
383.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
376.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
372.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
367.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
0.3b
(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
13×add-sqr-sqrt pow1 add-cbrt-cube
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l* prod-exp
5×pow-prod-down cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×sin-mult unswap-sqr
1×acos-asin 1-exp
Counts
4 → 77
Calls
4 calls:
Slowest
22.0ms
(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
16.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (sin phi1) (sin phi2))
1.0ms
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(* (sin phi1) (sin phi2))
65.0ms
(* (sin lambda1) (sin lambda2))
48.0ms
(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
10.0ms
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify6.1s

Counts
44 → 89
Calls
44 calls:
Slowest
412.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
403.0ms
(+ (+ (log R) 0) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
400.0ms
(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
377.0ms
(+ (log (* R 1)) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
363.0ms
(sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))

prune2.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

localize102.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
0.6b
(log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.3b
(* (* R 1) (exp (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
0.2b
(* (sin phi1) (sin phi2))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
11×add-sqr-sqrt add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
6×log-prod prod-exp
4×expm1-log1p-u associate-*l* pow-prod-down cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum
2×*-commutative
1×acos-asin 1-exp rem-log-exp log-pow sin-mult unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
41.0ms
(* (* R 1) (exp (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
22.0ms
(* (sin phi1) (sin phi2))
2.0ms
(log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series164.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(* (sin phi1) (sin phi2))
41.0ms
(log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
30.0ms
(* (* R 1) (exp (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
18.0ms
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify8.6s

Counts
40 → 85
Calls
40 calls:
Slowest
710.0ms
(sqrt (exp (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
382.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
380.0ms
(cbrt (exp (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
376.0ms
(+ (+ (log R) 0) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
367.0ms
(exp (log (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

regimes2.0s

Accuracy

0% (0.4b remaining)

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

bsearch10.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
17.4s4744×body1280valid
5.1s2087×body640valid
993.0ms743×body320valid
326.0ms280×body160valid
61.0ms11×body2560valid
56.0ms144×body80valid