Details

Time bar (total: 39.7s)

sample811.0ms

Algorithm
intervals
Results
487.0ms139×body1280valid
136.0ms75×body640valid
89.0ms28×body320valid
8.0ms11×body160valid
1.0ms3×body80valid

simplify76.0ms

Counts
1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize56.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (- lambda1 lambda2))
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite53.0ms

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
31.0ms
(cos (- lambda1 lambda2))
11.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (sin phi1) (sin phi2))
67.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
32.0ms
(cos (- lambda1 lambda2))
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify731.0ms

Counts
101 → 88

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 76
Calls
4 calls:
Slowest
23.0ms
(* (sin phi1) (sin phi2))
22.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
82.0ms
(* (sin phi1) (sin phi2))
79.0ms
(* (sin lambda1) (sin lambda2))
35.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify372.0ms

Counts
89 → 88

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.7b
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.3b
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))) R)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 70
Calls
4 calls:
Slowest
17.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))) R)
4.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
3.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
475.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))) R)
30.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
18.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
16.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify684.0ms

Counts
86 → 82

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize77.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.5b
(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.3b
(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))) R)
0.2b
(* (sin phi2) (sin phi1))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
53×*-un-lft-identity
49×add-cube-cbrt
39×prod-diff
38×times-frac
13×fma-neg
9×associate-*l*
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv difference-of-squares
2×asin-acos flip3-- pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- unswap-sqr
1×sub-neg diff-log sin-mult associate--r-
Counts
4 → 130
Calls
4 calls:
Slowest
40.0ms
(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))) R)
13.0ms
(* (sin phi2) (sin phi1))
12.0ms
(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))) R)
54.0ms
(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
54.0ms
(* (sin phi2) (sin phi1))
13.0ms
(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify609.0ms

Counts
186 → 142

prune3.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.5b

regimes2.1s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch10.0ms

end0.0ms

sample23.1s

Algorithm
intervals
Results
16.9s4782×body1280valid
4.5s2151×body640valid
840.0ms660×body320valid
195.0ms270×body160valid
99.0ms135×body80valid
56.0ms9×body2560valid