Details

Time bar (total: 32.9s)

sample497.0ms

Algorithm
intervals
Results
306.0ms113×body1280valid
115.0ms69×body640valid
34.0ms34×body320valid
9.0ms13×body160valid
8.0ms27×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))
3.2b
(sin (- lambda1 lambda2))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cos-diff fma-def
2×associate-+r+ sub-neg
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 73
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
31.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))
19.0ms
(sin (- lambda1 lambda2))

series196.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
120.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
27.0ms
(cos (- lambda1 lambda2))
40.0ms
(sin (- lambda1 lambda2))

simplify2.4s

Counts
85 → 85
Iterations
IterNodes
done5001
31948
2723
1376
0195

prune860.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
3.2b
(sin (- lambda1 lambda2))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×sin-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ sum-log sub-neg flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 73
Calls
4 calls:
14.0ms
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
19.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
11.0ms
(sin (- lambda1 lambda2))

series556.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
69.0ms
(* (sin lambda1) (sin lambda2))
193.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
38.0ms
(sin (- lambda1 lambda2))

simplify2.7s

Counts
85 → 85
Iterations
IterNodes
done5000
33864
2963
1405
0195

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ sum-log flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
18.0ms
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
13.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

series576.0ms

Counts
4 → 12
Calls
4 calls:
290.0ms
(+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
74.0ms
(* (sin lambda1) (sin lambda2))
197.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

simplify2.7s

Counts
73 → 73
Iterations
IterNodes
done5000
33720
2876
1288
0127

prune889.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize116.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)))
0.5b
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
0.5b
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
0.5b
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×fma-udef
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l*
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
13.0ms
(* (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)))
1.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
1.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
1.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

series792.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)) (fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1)))
182.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
207.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))
168.0ms
(fma (* (cos lambda2) (cos lambda1)) (cos phi2) (cos phi1))

simplify2.3s

Counts
75 → 75
Iterations
IterNodes
done5002
31932
2467
1143
065

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes942.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done35
135
027

end0.0ms

sample14.7s

Algorithm
intervals
Results
8.3s3557×body1280valid
3.8s2325×body640valid
1.7s934×body320valid
275.0ms450×body160valid
227.0ms734×body80valid