Details

Time bar (total: 59.1s)

sample1.0s

Algorithm
intervals
Results
600.0ms156×body1280valid
305.0ms65×body640valid
29.0ms21×body320valid
10.0ms11×body160valid
1.0ms3×body80valid

simplify104.0ms

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize66.0ms

Local error

Found 4 expressions with local error:

3.2b
(cos (- lambda1 lambda2))
0.8b
(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)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

rewrite21.0ms

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
Calls
4 calls:
Slowest
12.0ms
(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)))

series315.0ms

Calls
4 calls:
Slowest
215.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
41.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
40.0ms
(cos (- lambda1 lambda2))
18.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.3s

Calls
34 calls:
Slowest
481.0ms
(* (* (* 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))))))
173.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
98.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
97.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
86.0ms
(* (cos (fma (* (cbrt lambda1) (cbrt lambda1)) (cbrt lambda1) (- (* (cbrt lambda2) (* (cbrt lambda2) (cbrt lambda2)))))) (cos (fma (- (cbrt lambda2)) (* (cbrt lambda2) (cbrt lambda2)) (* (cbrt lambda2) (* (cbrt lambda2) (cbrt lambda2))))))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.8b
(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)))
0.2b
(* 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))

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 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
Calls
4 calls:
Slowest
15.0ms
(* (sin phi2) (sin phi1))
9.0ms
(* 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)))

series498.0ms

Calls
4 calls:
Slowest
394.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
61.0ms
(* (sin phi2) (sin phi1))
30.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
13.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify5.9s

Calls
33 calls:
Slowest
375.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
372.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
369.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
364.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
361.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1))))))
0.3b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))))
0.2b
(* (sin phi2) (sin phi1))

rewrite36.0ms

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
Calls
4 calls:
Slowest
17.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))))
16.0ms
(* (sin phi2) (sin phi1))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1))))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))

series537.0ms

Calls
4 calls:
Slowest
436.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))
48.0ms
(* (sin phi2) (sin phi1))
43.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1))))))

simplify5.9s

Calls
33 calls:
Slowest
435.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1)))))))
371.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (sin phi1) (sin phi2))))))
366.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (sin phi1) (sin phi2))))))
363.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1))))))))
360.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (expm1 (log1p (* (sin phi2) (sin phi1))))))))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×associate-*l*
15×add-exp-log
14×*-un-lft-identity
13×pow1 add-cbrt-cube
12×associate-*r* add-cube-cbrt
9×unswap-sqr
7×prod-exp
5×pow-prod-down cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×sin-mult
1×acos-asin 1-exp
Calls
4 calls:
Slowest
24.0ms
(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
22.0ms
(* (sin lambda1) (sin lambda2))
19.0ms
(* (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))))

series173.0ms

Calls
4 calls:
Slowest
72.0ms
(* (sin phi1) (sin phi2))
63.0ms
(* (sin lambda1) (sin lambda2))
27.0ms
(* (* 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))))

simplify7.9s

Calls
59 calls:
Slowest
412.0ms
(* (sqrt (* R 1)) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
410.0ms
(* (* (sqrt R) (sqrt 1)) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
379.0ms
(+ (+ (log R) (log 1)) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
376.0ms
(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
373.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch5.0ms

end0.0ms

sample24.4s

Algorithm
intervals
Results
18.1s4800×body1280valid
4.6s2075×body640valid
928.0ms694×body320valid
210.0ms282×body160valid
173.0ms15×body2560valid
51.0ms136×body80valid