Details

Time bar (total: 1.1m)

sample706.0ms

Algorithm
intervals
Results
397.0ms150×body1280valid
134.0ms69×body640valid
19.0ms21×body320valid
5.0ms8×body160valid
2.0ms8×body80valid

simplify74.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
73.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize60.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (- lambda1 lambda2))
0.9b
(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)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
44.0ms
(cos (- lambda1 lambda2))
35.0ms
(* 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))))

simplify2.2s

Counts
34 → 77
Calls
34 calls:
Slowest
490.0ms
(* (* (* 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))))))
147.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
145.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
92.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
84.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.6b

localize74.0ms

Local error

Found 4 expressions with local error:

0.9b
(acos (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
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite23.0ms

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
15.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* 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)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
63.0ms
(* (sin lambda1) (sin lambda2))
43.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
19.0ms
(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
438.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
409.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
396.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
378.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
376.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.9b
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
0.2b
(* R (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.2b
(fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
0.2b
(* (sin phi1) (sin phi2))

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
Counts
4 → 65
Calls
4 calls:
Slowest
22.0ms
(* (sin phi1) (sin phi2))
11.0ms
(* R (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
0.0ms
(fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
453.0ms
(fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
88.0ms
(* (sin phi1) (sin phi2))
50.0ms
(* R (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
19.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify6.2s

Counts
33 → 77
Calls
33 calls:
Slowest
753.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
408.0ms
(* R (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
385.0ms
(* (* (* R R) R) (* (* (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))) (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
383.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
381.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.9b
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
0.6b
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
0.3b
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.2b
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 76
Calls
4 calls:
Slowest
10.0ms
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
3.0ms
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
2.0ms
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series113.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
55.0ms
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
32.0ms
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
15.0ms
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
10.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify12.6s

Counts
45 → 88
Calls
45 calls:
Slowest
446.0ms
(* (* (* R R) R) (* (* (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))) (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))))
406.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
391.0ms
(* (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
388.0ms
(+ (log R) (log (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))))
385.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune2.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 2.4b

regimes1.9s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch8.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
17.7s4794×body1280valid
4.5s2090×body640valid
1.2s663×body320valid
283.0ms299×body160valid
63.0ms146×body80valid
56.0ms9×body2560valid