Details

Time bar (total: 1.6m)

sample1.3s

Algorithm
intervals
Results
536.0ms160×body1280valid
119.0ms59×body640valid
77.0ms25×body320valid
9.0ms7×body160valid
2.0ms5×body80valid

simplify90.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
89.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize70.0ms

Local error

Found 4 expressions with local error:

2.6b
(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)))))
0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite20.0ms

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
11.0ms
(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)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
59.0ms
(cos (- lambda1 lambda2))
42.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
16.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify5.8s

Counts
90 → 77
Calls
90 calls:
Slowest
534.0ms
(* (* (* 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))))))
296.0ms
(* (* (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))) (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))) (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
281.0ms
(* (* (* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))) (* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))) (* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
200.0ms
(exp (* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
134.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.8b

localize106.0ms

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))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* R (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)))

rewrite18.0ms

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
11.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(* 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)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(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)))))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify18.9s

Counts
78 → 77
Calls
78 calls:
Slowest
682.0ms
(* (* (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))) (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))) (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
444.0ms
(cbrt (* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
437.0ms
(log1p (* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
434.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
430.0ms
(real->posit16 (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 1.7b

localize88.0ms

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-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 unswap-sqr rem-exp-log
Counts
4 → 67
Calls
4 calls:
Slowest
16.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(log (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
2.0ms
(exp (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))))

series140.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(* (sin lambda1) (sin lambda2))
35.0ms
(exp (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))))
9.0ms
(log (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))

simplify17.3s

Counts
83 → 79
Calls
83 calls:
Slowest
698.0ms
(log (exp (* (cbrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) (cbrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))))
409.0ms
(log (sqrt (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
402.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
370.0ms
(* (cbrt (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))) (cbrt (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
361.0ms
(real->posit16 (log (exp (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))

prune2.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 1.7b

localize98.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))
0.5b
(expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))
0.2b
(* (sin lambda2) (sin lambda1))
0.2b
(* R (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))))

rewrite18.0ms

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*
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin expm1-log1p sin-mult expm1-udef
Counts
4 → 66
Calls
4 calls:
Slowest
11.0ms
(* (sin lambda2) (sin lambda1))
5.0ms
(* R (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))
0.0ms
(expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))

series224.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(* R (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))))
63.0ms
(* (sin lambda2) (sin lambda1))
58.0ms
(expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))
17.0ms
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))

simplify17.3s

Counts
78 → 78
Calls
78 calls:
Slowest
696.0ms
(- (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))) 1)
391.0ms
(log (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))))
383.0ms
(* R (* (cbrt (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))))) (cbrt (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))))))))))))
376.0ms
(sqrt (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))))
376.0ms
(expm1 (expm1 (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1)))))))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 1.6b

regimes1.4s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch6.0ms

end0.0ms

sample24.0s

Algorithm
intervals
Results
17.1s4787×body1280valid
4.6s2059×body640valid
1.4s714×body320valid
362.0ms300×body160valid
52.0ms134×body80valid
41.0ms8×body2560valid