Details

Time bar (total: 12.9s)

sample270.0ms

Algorithm
intervals
Results
156.0ms90×body1280valid
67.0ms74×body640valid
11.0ms19×body320valid
9.0ms60×body80valid
5.0ms13×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
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 → 48
Calls
4 calls:
4.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
19.0ms
(* (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)))))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
138.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
163.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0233990
1682875
22786873
35001873

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sin-sum
8×*-un-lft-identity add-log-exp
6×pow1 add-exp-log distribute-rgt-in acos-asin add-cube-cbrt sub-neg distribute-lft-in add-cbrt-cube associate--r+
5×associate--r-
3×associate-*r* associate-*l*
2×flip3-- diff-log flip-- difference-of-squares
1×times-frac pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
60.0ms
(* (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))))
11.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
21.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series356.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
7.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
172.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
34.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
03111574
19101391
236611325
350021306

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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 (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
2.6b
(log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1)))
15.1b
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt unpow-prod-down associate--r+
5×add-exp-log add-log-exp
4×pow1 acos-asin add-cbrt-cube
3×cos-diff rem-log-exp
2×exp-sum sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-exp log-pow cos-acos flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 58
Calls
4 calls:
2.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(- (cos delta) (log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
10.0ms
(log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1)))
4.0ms
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
208.0ms
(- (cos delta) (log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
196.0ms
(log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1)))
113.0ms
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
02701305
15771138
218691115
350021102

prune440.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1))))
2.6b
(log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate--r+
6×unpow-prod-down
5×add-exp-log add-log-exp
4×pow1 add-cbrt-cube
3×rem-log-exp
2×asin-acos sqr-pow
1×pow-to-exp sub-neg flip3-- sin-asin diff-log pow-exp log-pow sin-diff flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
3.0ms
(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))))
14.0ms
(- (cos delta) (log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1))))
11.0ms
(log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
209.0ms
(- (cos delta) (log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1))))
198.0ms
(log (pow (exp (* (sin (/ PI 2)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (sin phi1)))

simplify71.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
02551403
15511233
220641199
350011169

prune439.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes230.0ms

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
04029
14029

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s3111×body1280valid
1.8s1929×body640valid
411.0ms663×body320valid
320.0ms1998×body80valid
131.0ms299×body160valid