Details

Time bar (total: 46.5s)

sample731.0ms

Algorithm
intervals
Results
448.0ms145×body1280valid
161.0ms70×body640valid
23.0ms21×body320valid
8.0ms13×body160valid
4.0ms7×body80valid

simplify114.0ms

Calls
1 calls:
Slowest
113.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.6b
(cos (- lambda1 lambda2))
0.8b
(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
(* (sin phi2) (sin phi1))

rewrite11.0ms

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

series274.0ms

Calls
4 calls:
Slowest
171.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
59.0ms
(* (sin phi2) (sin phi1))
26.0ms
(cos (- lambda1 lambda2))
18.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify628.0ms

Calls
24 calls:
Slowest
119.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
101.0ms
(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
95.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
57.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))
46.0ms
(+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

localize64.0ms

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt 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 sin-mult
1×acos-asin fma-udef
Calls
4 calls:
Slowest
9.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (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)))

series425.0ms

Calls
4 calls:
Slowest
290.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
70.0ms
(* (sin lambda1) (sin lambda2))
50.0ms
(* (sin phi2) (sin phi1))
15.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.1s

Calls
30 calls:
Slowest
411.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
340.0ms
(+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))
329.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
314.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
283.0ms
(+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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
9.0ms
(* (sin phi2) (sin phi1))
3.0ms
(* 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)))

series380.0ms

Calls
4 calls:
Slowest
288.0ms
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))
49.0ms
(* (sin phi2) (sin phi1))
25.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
18.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify3.5s

Calls
24 calls:
Slowest
310.0ms
(+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))
290.0ms
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
286.0ms
(- 1 (+ (* 1/2 (pow lambda2 2)) (* 1/2 (pow phi2 2))))
286.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)
285.0ms
(* (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))) R)

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.6b
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin phi2) (sin phi1))

rewrite20.0ms

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))
6.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
4.0ms
(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))))

series130.0ms

Calls
4 calls:
Slowest
53.0ms
(* (sin phi2) (sin phi1))
39.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
19.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
19.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))

simplify5.7s

Calls
34 calls:
Slowest
586.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
360.0ms
(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))))))))
329.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
311.0ms
(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)))))))
301.0ms
(log (sqrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.5b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch10.0ms

end0.0ms

sample24.0s

Algorithm
intervals
Results
17.8s4711×body1280valid
4.5s2164×body640valid
939.0ms658×body320valid
244.0ms312×body160valid
79.0ms12×body2560valid
61.0ms146×body80valid