Details

Time bar (total: 1.0m)

sample1.0s

Algorithm
intervals
Results
697.0ms146×body1280valid
180.0ms75×body640valid
27.0ms24×body320valid
4.0ms5×body160valid
2.0ms6×body80valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
287.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune56.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize120.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (- lambda1 lambda2))
0.7b
(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)))

rewrite67.0ms

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
54.0ms
(cos (- lambda1 lambda2))
9.0ms
(* 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)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
262.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
86.0ms
(cos (- lambda1 lambda2))
46.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
20.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.2s

Counts
34 → 77
Calls
34 calls:
Slowest
452.0ms
(* (* (* 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))))))
150.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
144.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
85.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
85.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize78.0ms

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
(* 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))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (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
(* (sin lambda1) (sin lambda2))
11.0ms
(* 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))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
352.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
66.0ms
(* (sin lambda1) (sin lambda2))
35.0ms
(* R (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))))

simplify6.2s

Counts
33 → 77
Calls
33 calls:
Slowest
406.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
404.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
401.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
391.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
380.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize92.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (exp (* (sin lambda1) (sin lambda2))))
0.7b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin exp-prod exp-to-pow rem-log-exp sin-mult
Counts
4 → 71
Calls
4 calls:
Slowest
19.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
5.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

series158.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(* (sin lambda1) (sin lambda2))
48.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
34.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

simplify6.2s

Counts
39 → 83
Calls
39 calls:
Slowest
796.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
427.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
423.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))
418.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
411.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize101.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (exp (* (sin lambda1) (sin lambda2))))
0.7b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
0.6b
(log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
0.3b
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×log-prod
9×*-un-lft-identity add-cube-cbrt
8×pow1
6×add-cbrt-cube associate-*r* add-exp-log
5×add-log-exp
4×expm1-log1p-u exp-sum log-pow insert-posit16 log1p-expm1-u
3×associate-*l*
2×rem-log-exp unswap-sqr
1×acos-asin exp-prod exp-to-pow pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 68
Calls
4 calls:
Slowest
15.0ms
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))))
10.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
2.0ms
(log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
57.0ms
(log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
48.0ms
(* R (exp (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

simplify9.2s

Counts
37 → 80
Calls
37 calls:
Slowest
405.0ms
(* (sqrt R) (exp (log (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))))
397.0ms
(exp (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))
396.0ms
(exp (log (cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))))
393.0ms
(log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
393.0ms
(* (sqrt R) (sqrt (exp (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))))

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.3b

regimes2.1s

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample24.4s

Algorithm
intervals
Results
18.1s4834×body1280valid
4.4s2052×body640valid
953.0ms703×body320valid
260.0ms273×body160valid
122.0ms129×body80valid
75.0ms11×body2560valid