Details

Time bar (total: 1.0m)

sample1.3s

Algorithm
intervals
Results
547.0ms140×body1280valid
175.0ms78×body640valid
89.0ms27×body320valid
41.0ms4×body80valid
6.0ms8×body160valid

simplify125.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
124.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize84.0ms

Local error

Found 4 expressions with local error:

4.5b
(cos (- lambda1 lambda2))
0.6b
(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
(* (sin phi2) (sin phi1))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
8×pow1 add-cbrt-cube add-exp-log
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 cos-diff sub-neg sin-mult
Counts
4 → 76
Calls
4 calls:
Slowest
23.0ms
(cos (- lambda1 lambda2))
22.0ms
(* (sin phi2) (sin phi1))
11.0ms
(* 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))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(* (sin phi2) (sin phi1))
55.0ms
(cos (- lambda1 lambda2))
45.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
17.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.5s

Counts
45 → 88
Calls
45 calls:
Slowest
443.0ms
(* (* (* 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))))))
400.0ms
(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
148.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
100.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
99.0ms
(* (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))))))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b
(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 phi2) (sin phi1))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

rewrite27.0ms

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 phi2) (sin phi1))
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)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
429.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
60.0ms
(* (sin phi2) (sin phi1))
52.0ms
(* 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
399.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
397.0ms
(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
394.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
390.0ms
(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
373.0ms
(+ (log R) (log (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: 5.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.6b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.3b
(* R (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
(fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))

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 phi2) (sin phi1))
6.0ms
(* 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 (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))
87.0ms
(* (sin phi2) (sin phi1))
48.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
10.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify5.6s

Counts
33 → 77
Calls
33 calls:
Slowest
730.0ms
(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
413.0ms
(* (* (* R R) R) (* (* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))) (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))) (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
386.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)
359.0ms
(+ (log R) (log (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
352.0ms
(sqrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.0b

localize71.0ms

Local error

Found 4 expressions with local error:

24.4b
(cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))
0.6b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))))
0.3b
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
0.3b
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1)))))))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
16×sin-mult
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×cbrt-div
6×frac-times *-un-lft-identity associate-*l/ add-cube-cbrt
4×expm1-log1p-u associate-*r* associate-*l* associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 swap-sqr pow3 rem-cbrt-cube unswap-sqr
Counts
4 → 92
Calls
4 calls:
Slowest
210.0ms
(cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))
85.0ms
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
6.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1)))))))
1.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1)))
60.0ms
(cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))
50.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1)))))))
20.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))))

simplify9.9s

Counts
68 → 104
Calls
68 calls:
Slowest
882.0ms
(* (* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1))) (* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1))))
609.0ms
(* (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))) (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))
435.0ms
(cbrt (* (* (- (cos (- phi2 phi1)) (cos (+ phi2 phi1))) (- (cos (- phi2 phi1)) (cos (+ phi2 phi1)))) (- (cos (- phi2 phi1)) (cos (+ phi2 phi1)))))
404.0ms
(cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1)))))))
394.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))))))

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.0b

regimes968.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch7.0ms

end0.0ms

sample24.7s

Algorithm
intervals
Results
18.1s4699×body1280valid
5.0s2179×body640valid
978.0ms671×body320valid
230.0ms301×body160valid
101.0ms13×body2560valid
53.0ms140×body80valid