Details

Time bar (total: 9.7s)

sample166.0ms

Algorithm
intervals
Results
94.0ms110×body1280valid
44.0ms78×body640valid
8.0ms25×body320valid
3.0ms32×body80valid
2.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b
(sin (- lambda1 lambda2))
3.9b
(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(sin (- lambda1 lambda2))
7.0ms
(cos (- lambda1 lambda2))

series156.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
24.0ms
(cos (- lambda1 lambda2))

simplify70.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune348.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.6b
(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×sin-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative sub-neg associate-+l+ flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 69
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
7.0ms
(sin (- lambda1 lambda2))

series412.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin lambda1) (sin lambda2))
203.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
134.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
22.0ms
(sin (- lambda1 lambda2))

simplify46.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0382824
11298690
25001683

prune473.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series405.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
52.0ms
(* (sin lambda1) (sin lambda2))
204.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
133.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify40.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0259832
11045742
25001736

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.6b
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod fma-udef
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

series574.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
128.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
136.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
184.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

simplify176.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0170550
1633507
24294499
35001499

prune457.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes479.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04059
14059

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3515×body1280valid
1.2s2351×body640valid
347.0ms962×body320valid
98.0ms425×body160valid
78.0ms747×body80valid