Details

Time bar (total: 12.8s)

sample255.0ms

Algorithm
intervals
Results
153.0ms94×body1280valid
60.0ms68×body640valid
11.0ms68×body80valid
7.0ms13×body320valid
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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
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))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 72
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
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))))
5.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin theta) (sin delta))
144.0ms
(* (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))))
176.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune500.0ms

Filtered
84 candidates to 66 candidates (78.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.6b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg prod-diff
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg asin-acos flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube rem-cube-cbrt
Counts
4 → 78
Calls
4 calls:
2.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
3.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series217.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
172.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
32.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify169.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (157.0ms)

IterNodesCost
02581606
18631462
247091451
350011450

prune484.0ms

Filtered
90 candidates to 56 candidates (62.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
0.3b
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))

rewrite13.0ms

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
5×log1p-expm1-u
4×expm1-log1p-u
3×fma-neg associate-*r* associate-*l* prod-diff
1×sub-neg asin-acos expm1-log1p flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult expm1-udef unswap-sqr
Counts
4 → 62
Calls
4 calls:
1.0ms
(expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
5.0ms
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
2.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
149.0ms
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
6.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
173.0ms
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
02811398
19121241
240061235
350011229

prune483.0ms

Filtered
74 candidates to 57 candidates (77.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
0.9b
(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
8×log-prod
7×pow1
6×add-exp-log prod-diff add-cbrt-cube add-log-exp
5×exp-sum
4×expm1-log1p-u log-pow log1p-expm1-u
3×exp-prod fma-neg associate-*r* associate-*l*
2×sub-neg
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
5.0ms
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
2.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
4.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))
6.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
172.0ms
(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
167.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))))

simplify117.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
03101858
19771621
240391499
350011496

prune526.0ms

Filtered
86 candidates to 65 candidates (75.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes353.0ms

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
03426
13426

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.1s3118×body1280valid
1.7s1853×body640valid
426.0ms714×body320valid
345.0ms1975×body80valid
133.0ms340×body160valid