Details

Time bar (total: 30.2s)

sample213.0ms

Algorithm
intervals
Results
70.0ms309×body80valid
42.0ms23×body320valid
35.0ms37×body640valid
29.0ms24×body1280valid
4.0ms9×body160valid

simplify3.9s

Counts
1 → 1
Iterations
IterNodes
65440
51878
4761
3231
272
134
017

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.4b
(cos (/ (+ phi2 phi1) 2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×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×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 67
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms
(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
561.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
725.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
95.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Counts
79 → 79
Iterations
IterNodes
33897
21082
1359
0144

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
2.4b
(cos (* 1/2 (+ phi1 phi2)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×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 hypot-udef distribute-lft-in flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 69
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
44.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
16.0ms
(cos (* 1/2 (+ phi1 phi2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
528.0ms
(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
641.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
146.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
24.0ms
(cos (* 1/2 (+ phi1 phi2)))

simplify1.6s

Counts
81 → 81
Iterations
IterNodes
34081
21093
1376
0158

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

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)))

rewrite582.0ms

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:
81.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
43.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
408.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
47.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
70.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
364.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
76.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify832.0ms

Counts
118 → 118
Iterations
IterNodes
22036
1539
0216

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-cbrt-cube add-exp-log
12×associate-*l*
11×*-un-lft-identity add-cube-cbrt
10×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
Counts
4 → 84
Calls
4 calls:
32.0ms
(* (sin (* phi1 1/2)) lambda1)
31.0ms
(* (sin (* 1/2 phi2)) lambda2)
31.0ms
(* lambda2 (cos (* 1/2 phi2)))
67.0ms
(* (sin (* phi1 1/2)) (* (sin (* 1/2 phi2)) lambda2))

series304.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin (* phi1 1/2)) lambda1)
62.0ms
(* (sin (* 1/2 phi2)) lambda2)
76.0ms
(* lambda2 (cos (* 1/2 phi2)))
120.0ms
(* (sin (* phi1 1/2)) (* (sin (* 1/2 phi2)) lambda2))

simplify3.3s

Counts
96 → 96
Iterations
IterNodes
43526
31592
2670
1258
0125

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes775.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
233
133
024

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.9s8520×body80valid
1.8s1269×body640valid
1.0s763×body1280valid
582.0ms756×body320valid
157.0ms370×body160valid