Details

Time bar (total: 12.6s)

sample261.0ms

Algorithm
intervals
Results
192.0ms147×body1280valid
39.0ms57×body640valid
8.0ms18×body320valid
4.0ms27×body80valid
2.0ms7×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02815
14815
27915
39415
49415

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b
(sin (- lambda1 lambda2))
4.4b
(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))

series176.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos phi1) (sin phi2))
91.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04431004
11340773
25001771

prune416.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b
(cos (- lambda1 lambda2))

rewrite38.0ms

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 associate-*l/ *-commutative
2×unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sin-cos-mult flip-+
Counts
4 → 86
Calls
4 calls:
14.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms
(* (cos phi1) (sin phi2))
11.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))

series278.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
42.0ms
(* (cos phi1) (sin phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0512984
11910801
25001797

prune559.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×expm1-log1p-u *-commutative sin-cos-mult log1p-expm1-u add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 95
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
13.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
4.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos phi1) (sin phi2))
110.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
47.0ms
(* (sin lambda1) (sin lambda2))
98.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify58.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0429825
11850647
25001647

prune577.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
13×add-sqr-sqrt
10×associate-*l*
9×add-cube-cbrt *-un-lft-identity
8×associate-*r*
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×associate-*r/ sin-mult
2×sin-cos-mult unswap-sqr
1×frac-times associate-*l/ cos-mult
Counts
4 → 92
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
19.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos phi1) (sin phi2))
45.0ms
(* (sin lambda1) (sin lambda2))
98.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
111.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify57.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0444783
11893620
25002620

prune525.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes417.0ms

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
04232
14232

end0.0ms

sample8.2s

Algorithm
intervals
Results
6.0s4569×body1280valid
1.5s2015×body640valid
262.0ms549×body320valid
96.0ms669×body80valid
56.0ms198×body160valid