Details

Time bar (total: 28.0s)

sample197.0ms

Algorithm
intervals
Results
85.0ms271×body80valid
38.0ms32×body1280valid
28.0ms33×body640valid
15.0ms21×body320valid
4.0ms11×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5000
51878
4761
3231
272
134
017

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize43.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.7b
(cos (/ (+ phi2 phi1) 2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 56
Calls
3 calls:
9.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
22.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
14.0ms
(cos (/ (+ phi2 phi1) 2))

series815.0ms

Counts
3 → 9
Calls
3 calls:
645.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
127.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
43.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Counts
65 → 65
Iterations
IterNodes
done5008
33527
2896
1307
0128

prune608.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize41.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
2.7b
(cos (* 1/2 (+ phi1 phi2)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×cos-sum pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 58
Calls
3 calls:
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
56.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
9.0ms
(cos (* 1/2 (+ phi1 phi2)))

series891.0ms

Counts
3 → 9
Calls
3 calls:
741.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
118.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
32.0ms
(cos (* 1/2 (+ phi1 phi2)))

simplify2.6s

Counts
67 → 67
Iterations
IterNodes
done5264
33640
2900
1321
0141

prune421.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
0.1b
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
0.2b
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.2b
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity
11×associate-*l*
10×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
9×flip3-- associate-*r* cos-mult flip-- sin-mult
8×frac-times
6×add-log-exp
4×expm1-log1p-u associate-*r/ frac-sub insert-posit16 log1p-expm1-u sub-div
3×distribute-rgt-in sub-neg distribute-lft-in prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*l/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
98.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
24.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
316.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
26.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
65.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
330.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
72.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify2.4s

Counts
118 → 118
Iterations
IterNodes
done5003
22032
1541
0216

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
0.2b
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
2.2b
(* lambda2 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))
3.4b
(* lambda1 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
14×add-sqr-sqrt
12×associate-*l*
10×*-un-lft-identity add-cube-cbrt
8×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u sin-mult add-log-exp
2×associate-*r/ unswap-sqr
Counts
4 → 88
Calls
4 calls:
46.0ms
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
26.0ms
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
101.0ms
(* lambda2 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))
80.0ms
(* lambda1 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
105.0ms
(* (sin (* phi1 1/2)) (sin (* 1/2 phi2)))
117.0ms
(* lambda2 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))
93.0ms
(* lambda1 (* (sin (* phi1 1/2)) (sin (* 1/2 phi2))))

simplify2.9s

Counts
100 → 100
Iterations
IterNodes
done5002
32875
2689
1226
0104

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes741.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.6s8378×body80valid
1.6s844×body1280valid
1.4s1236×body640valid
566.0ms722×body320valid
144.0ms356×body160valid