Details

Time bar (total: 14.1s)

sample294.0ms

Algorithm
intervals
Results
203.0ms121×body1280valid
47.0ms52×body640valid
12.0ms57×body80valid
8.0ms15×body320valid
5.0ms11×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (sin delta)) (cos theta))
0.2b
(* (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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
9.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
5.0ms
(* (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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
159.0ms
(* (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))))
181.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0305974
11167862
25002860

prune401.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.8b
(log (exp (* (* (cos phi1) (sin delta)) (cos theta))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
6×add-exp-log add-cbrt-cube
3×log-prod associate-*r* associate-*l* log-pow
1×sub-neg asin-acos exp-prod flip3-- exp-to-pow diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 53
Calls
4 calls:
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.0ms
(log (exp (* (* (cos phi1) (sin delta)) (cos theta))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta))))))
186.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (log (exp (* (* (cos phi1) (sin delta)) (cos theta)))))))))
76.0ms
(log (exp (* (* (cos phi1) (sin delta)) (cos theta))))

simplify98.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
02451076
1789959
23501957
35002956

prune428.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.4b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube difference-of-squares sqr-pow
6×unpow-prod-down pow-unpow cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3
1×difference-cubes cube-div sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 76
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.0ms
(pow (cos delta) 3)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.0s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
753.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms
(pow (cos delta) 3)
240.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify92.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
04871389
124451288
250011284

prune569.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.6b
(pow (cos delta) 6)
0.7b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log pow-unpow
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
6×pow-pow pow-exp
4×pow-to-exp cube-prod add-log-exp sqr-pow
3×rem-cube-cbrt
2×cube-mult unpow3 pow-prod-down prod-exp
1×cube-div cbrt-unprod sin-mult
Counts
4 → 80
Calls
4 calls:
1.0ms
(pow (cos delta) 3)
3.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
1.0ms
(pow (cos delta) 6)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

series730.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (cos delta) 3)
239.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
40.0ms
(pow (cos delta) 6)
421.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

simplify51.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0360847
11504765
25001759

prune597.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes339.0ms

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
03526
13526

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.2s3155×body1280valid
1.9s1815×body640valid
435.0ms706×body320valid
329.0ms2010×body80valid
120.0ms314×body160valid