Details

Time bar (total: 13.3s)

sample277.0ms

Algorithm
intervals
Results
172.0ms103×body1280valid
61.0ms68×body640valid
12.0ms20×body320valid
9.0ms57×body80valid
3.0ms8×body160valid

simplify14.0ms

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: 0.2b

localize33.0ms

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))))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite9.0ms

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:
1.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series656.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
161.0ms
(* (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))))
182.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify79.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0233990
1682875
22786873
35001873

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×sin-mult add-log-exp
5×cos-mult
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×asin-acos frac-sub
2×associate-*r/ associate-*l/ sub-div
1×frac-times sub-neg sqr-cos flip3-- diff-log associate--l+ flip-- difference-of-squares
Counts
4 → 43
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
483.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03261426
113981256
250021223

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(pow (sin phi1) 4)
0.5b
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt add-cube-cbrt
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow add-log-exp
5×add-cbrt-cube
3×cube-prod
2×pow-to-exp distribute-rgt-out-- pow-pow pow-exp sqr-pow
1×cube-mult sub-neg asin-acos flip3-- diff-log unpow3 flip-- rem-cube-cbrt
Counts
4 → 62
Calls
4 calls:
1.0ms
(pow (sin phi1) 3)
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(pow (sin phi1) 4)
7.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

series162.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin phi1) 3)
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
34.0ms
(pow (sin phi1) 4)
91.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

simplify42.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0291484
11129424
25001402

prune643.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.5b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×*-un-lft-identity sin-mult
5×cos-mult
4×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×frac-sub difference-of-squares
2×acos-asin sub-neg flip3-- diff-log associate-*r/ associate-*l/ flip-- sub-div
1×frac-times asin-acos sqr-cos times-frac associate--l+ distribute-lft-out-- associate--r-
Counts
4 → 51
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
497.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
7.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
39.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04061603
116041450
250011417

prune471.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes527.0ms

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 (1.0ms)

IterNodesCost
04356
14356

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.2s3113×body1280valid
1.8s1894×body640valid
459.0ms723×body320valid
330.0ms1978×body80valid
113.0ms292×body160valid