Details

Time bar (total: 13.9s)

sample262.0ms

Algorithm
intervals
Results
165.0ms101×body1280valid
54.0ms59×body640valid
11.0ms72×body80valid
8.0ms14×body320valid
4.0ms10×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
4.0ms
(* (sin theta) (sin delta))
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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin theta) (sin delta))
155.0ms
(* (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))))
179.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify96.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune396.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.5b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.5b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.4b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×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
3×pow-unpow
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 → 64
Calls
4 calls:
1.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
2.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
4.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series228.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
182.0ms
(- (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))

simplify159.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02261298
17421202
241271196
350021196

prune391.0ms

Filtered
76 candidates to 43 candidates (56.6%)
Pruning

11 alts after pruning (11 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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
0.5b
(pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
7.4b
(cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log cbrt-prod
7×pow1 add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×pow-unpow pow-exp
2×cube-mult unpow-prod-down pow-pow unpow3 cube-prod prod-exp rem-cube-cbrt sqr-pow
1×pow-to-exp sub-neg asin-acos flip3-- pow1/3 diff-log 1-exp pow-prod-down flip-- rem-cbrt-cube cbrt-unprod
Counts
4 → 60
Calls
4 calls:
1.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
3.0ms
(pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
1.0ms
(cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))

series227.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
181.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)))))
31.0ms
(pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3)
7.0ms
(cbrt (pow (* 1 (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))) 3))

simplify107.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
02311139
17391058
233761058
350011054

prune421.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
18×add-exp-log add-cbrt-cube
17×pow-prod-down
16×sin-mult
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
10×cos-mult
8×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*r/ associate-*l/ difference-of-squares
4×pow-sqr pow-prod-up associate-/l* sub-div
3×frac-times associate-/r*
2×flip3-- pow-plus associate-/r/ flip--
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg flip3-+ diff-log div-sub swap-sqr div-exp associate-*r* associate-*l* associate--l+ clear-num *-commutative flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms
(* (* (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)))))))
18.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (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))))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
178.0ms
(* (* (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)))))))
812.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
499.0ms
(- (* (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))))))))

simplify111.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06354487
131143982
250013958

prune703.0ms

Filtered
117 candidates to 84 candidates (71.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes492.0ms

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
03968
13968

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s3132×body1280valid
1.8s1837×body640valid
420.0ms720×body320valid
335.0ms2008×body80valid
139.0ms303×body160valid