Details

Time bar (total: 1.1m)

sample718.0ms

Algorithm
intervals
Results
438.0ms136×body1280valid
167.0ms84×body640valid
26.0ms25×body320valid
5.0ms9×body160valid
5.0ms1×body2560valid
0.0ms1×body80valid

simplify82.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
81.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize75.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (- lambda1 lambda2))
0.8b
(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)))

rewrite29.0ms

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
12.0ms
(cos (- lambda1 lambda2))
12.0ms
(* 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)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
47.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
32.0ms
(cos (- lambda1 lambda2))
9.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.2s

Counts
34 → 77
Calls
34 calls:
Slowest
461.0ms
(* (* (* 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))))))
127.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
106.0ms
(* (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))))))
89.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
88.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize75.0ms

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
(* 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))

rewrite44.0ms

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
30.0ms
(* (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)))))
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)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
51.0ms
(* (sin lambda1) (sin lambda2))
32.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
18.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.1s

Counts
33 → 77
Calls
33 calls:
Slowest
731.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
422.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
392.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
361.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
345.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
0.3b
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.1b
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*l* add-cube-cbrt
7×associate-*r*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×unswap-sqr
1×acos-asin associate-*r/ cos-mult sin-mult
Counts
4 → 76
Calls
4 calls:
Slowest
40.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
23.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
2.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
71.0ms
(* (sin lambda1) (sin lambda2))
31.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
18.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

simplify6.5s

Counts
42 → 88
Calls
42 calls:
Slowest
374.0ms
(+ (log R) (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
362.0ms
(* (sqrt R) (sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
360.0ms
(cbrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
347.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
326.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
0.7b
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
0.4b
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
0.3b
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))

rewrite30.0ms

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
20.0ms
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))
5.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
3.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

series122.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))
45.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
16.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
10.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))

simplify12.1s

Counts
45 → 88
Calls
45 calls:
Slowest
394.0ms
(* (log (cbrt (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))) R)
389.0ms
(exp (sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
381.0ms
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))
373.0ms
(* R (log (cbrt (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))))
367.0ms
(log (* (cbrt (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))) (cbrt (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.0b

regimes1.1s

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch5.0ms

end0.0ms

sample24.6s

Algorithm
intervals
Results
18.7s4756×body1280valid
4.4s2129×body640valid
835.0ms689×body320valid
236.0ms271×body160valid
79.0ms12×body2560valid
55.0ms144×body80valid