Details

Time bar (total: 9.8s)

sample166.0ms

Algorithm
intervals
Results
95.0ms111×body1280valid
40.0ms74×body640valid
10.0ms30×body320valid
3.0ms15×body160valid
3.0ms26×body80valid

simplify6.0ms

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: 1.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(sin (- lambda1 lambda2))
4.2b
(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
33×add-sqr-sqrt sin-sum
31×add-cube-cbrt *-un-lft-identity
12×distribute-rgt-in distribute-lft-in
11×cos-sum
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 102
Calls
4 calls:
9.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series195.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify106.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
05051623
114301236
248731161
350011161

prune377.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

localize30.0ms

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)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
4.0b
(sin (- lambda1 lambda2))

rewrite17.0ms

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:
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
5.0ms
(sin (- lambda1 lambda2))

series395.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin lambda1) (sin lambda2))
197.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
128.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms
(sin (- lambda1 lambda2))

simplify42.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0384825
11173692
25002687

prune436.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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:
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series388.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
197.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify150.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0284848
1949757
24930751
35001751

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

rewrite6.0ms

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:
1.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

series558.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
177.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

simplify181.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0170548
1633507
24290499
35001499

prune445.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes523.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04465
14665
24665

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.2s3550×body1280valid
1.2s2343×body640valid
320.0ms982×body320valid
92.0ms409×body160valid
80.0ms716×body80valid