Details

Time bar (total: 15.1s)

sample263.0ms

Algorithm
intervals
Results
147.0ms90×body1280valid
70.0ms74×body640valid
11.0ms19×body320valid
9.0ms60×body80valid
5.0ms13×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×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-neg associate-*r* associate-*l* prod-diff
2×asin-acos
1×sub-neg flip3-- sin-asin diff-log pow-prod-down prod-exp sin-diff *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
6.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
164.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
189.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
02661272
18101115
234021110
350011103

prune446.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.3b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
4.4b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
198×prod-diff
192×add-sqr-sqrt
187×*-un-lft-identity
185×add-cube-cbrt
168×sin-sum
145×times-frac
84×distribute-rgt-in distribute-lft-in associate--r+
16×fma-neg div-inv
8×add-log-exp
6×pow1 add-exp-log acos-asin sub-neg add-cbrt-cube
5×associate--r-
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l*
2×flip3-- diff-log flip-- difference-of-squares
1×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 289
Calls
4 calls:
82.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
28.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
27.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
8.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
193.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
37.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify178.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0136521106
1359513739
2500113583

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.8b
(log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
15.1b
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt log-prod
12×prod-diff
8×associate--r+
6×unpow-prod-down
5×add-exp-log add-log-exp
4×pow1 expm1-log1p-u log-pow add-cbrt-cube log1p-expm1-u
3×neg-sub0 cos-diff fma-neg rem-log-exp
2×unpow-prod-up sqr-pow
1×cos-neg acos-asin pow-to-exp sub-neg flip3-- diff-log pow-exp flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 81
Calls
4 calls:
2.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
10.0ms
(log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
4.0ms
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
191.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
157.0ms
(log (pow (exp (sin phi1)) (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
82.0ms
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify224.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (208.0ms)

IterNodesCost
03002494
17901739
244181704
350011682

prune577.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (cos delta) (log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
0.4b
(log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.8b
(log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
15.1b
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
14×log-prod
12×prod-diff
7×associate--r+
6×unpow-prod-down
5×add-exp-log expm1-log1p-u add-log-exp
4×pow1 log-pow add-cbrt-cube log1p-expm1-u
3×fma-neg rem-log-exp
2×log-div expm1-udef pow-sub sqr-pow
1×cos-neg neg-sub0 cos-diff pow-to-exp sub-neg log1p-udef flip3-- diff-log log1p-expm1 pow-exp flip-- distribute-lft-out-- associate--r- difference-of-squares
Counts
4 → 82
Calls
4 calls:
12.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
0.0ms
(log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.0ms
(log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
4.0ms
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series637.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
124.0ms
(log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
196.0ms
(log (pow (exp (sin phi1)) (expm1 (log1p (cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
83.0ms
(cos (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify154.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
03022716
17791832
242651779
350011749

prune536.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes317.0ms

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
03427
13427

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3111×body1280valid
1.8s1929×body640valid
381.0ms663×body320valid
325.0ms1998×body80valid
116.0ms299×body160valid