Details

Time bar (total: 14.5s)

sample250.0ms

Algorithm
intervals
Results
175.0ms137×body1280valid
48.0ms67×body640valid
6.0ms13×body320valid
4.0ms32×body80valid
2.0ms7×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02815
14815
27915
39415
49415

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×prod-diff
11×pow1 add-exp-log cos-sum sin-sum add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×sub-neg *-commutative
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff sin-cos-mult unswap-sqr
Counts
4 → 85
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
12.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(sin (- lambda1 lambda2))
7.0ms
(cos (- lambda1 lambda2))

series172.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos phi1) (sin phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04431004
11340773
25001771

prune442.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin phi1) (cos phi2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b
(cos (- lambda1 lambda2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow1 add-exp-log add-cbrt-cube
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-diff *-commutative
2×sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/
Counts
4 → 85
Calls
4 calls:
4.0ms
(* (sin phi1) (cos phi2))
4.0ms
(* (cos phi1) (sin phi2))
12.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))

series200.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin phi1) (cos phi2))
48.0ms
(* (cos phi1) (sin phi2))
91.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0425787
11480631
25001628

prune562.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp sin-cos-mult cbrt-unprod
5×sin-mult
4×expm1-log1p-u frac-times associate-*r/ cos-mult *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×sub-neg flip3-- prod-diff frac-sub flip-- sub-div
1×associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 98
Calls
4 calls:
6.0ms
(* (sin phi1) (cos phi2))
4.0ms
(* (cos phi1) (sin phi2))
6.0ms
(* (sin lambda1) (sin (- lambda2)))
26.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin phi1) (cos phi2))
49.0ms
(* (cos phi1) (sin phi2))
54.0ms
(* (sin lambda1) (sin (- lambda2)))
185.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05151025
12339898
25003897

prune707.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.3b
(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.3b
(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
39×distribute-rgt-in distribute-lft-in
31×add-exp-log add-cbrt-cube
28×associate-*r/
17×pow1
15×add-sqr-sqrt
14×prod-exp cbrt-unprod
11×add-cube-cbrt *-un-lft-identity
10×sub-neg prod-diff
9×associate-*l*
8×pow-prod-down sin-mult
7×associate-*r* cos-mult
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u associate-/l/ add-log-exp
3×flip3-- times-frac associate-/r* associate-/r/ *-commutative frac-sub flip-- sub-div
2×unswap-sqr
1×frac-2neg flip3-+ frac-add sin-neg clear-num distribute-rgt-neg-out flip-+ div-inv associate-/l*
Counts
4 → 137
Calls
4 calls:
6.0ms
(* (sin lambda1) (sin (- lambda2)))
70.0ms
(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
74.0ms
(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
20.0ms
(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin lambda1) (sin (- lambda2)))
610.0ms
(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
342.0ms
(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
180.0ms
(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify134.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
07503772
143753155
250013148

prune859.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes529.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04246
14246

end0.0ms

sample8.5s

Algorithm
intervals
Results
6.1s4612×body1280valid
1.7s1953×body640valid
247.0ms552×body320valid
96.0ms680×body80valid
60.0ms203×body160valid