Details

Time bar (total: 16.5s)

sample281.0ms

Algorithm
intervals
Results
158.0ms96×body1280valid
63.0ms67×body640valid
23.0ms25×body320valid
14.0ms59×body80valid
4.0ms9×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03622
16122
27122
37222
47222

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

rewrite14.0ms

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:
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)))))))

series384.0ms

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)))))))

simplify111.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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))))
0.6b
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
1.6b
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
18×add-cube-cbrt prod-diff
13×log-pow
11×pow1
9×add-log-exp
6×add-exp-log log-prod add-cbrt-cube
4×expm1-log1p-u exp-prod exp-to-pow log1p-expm1-u
3×fma-neg associate-*r* associate-*l* associate--r+
2×distribute-lft-out--
1×sub-neg asin-acos flip3-- diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult difference-of-squares unswap-sqr
Counts
4 → 88
Calls
4 calls:
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))))
6.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
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))))
181.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
150.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify146.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
03282628
19571860
249451838
350011808

prune545.0ms

Pruning

9 alts after pruning (9 fresh and 0 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))))
0.4b
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.4b
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.7b
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×times-frac
8×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* associate-/r* associate-/l*
1×cbrt-undiv pow2 asin-acos frac-2neg pow-plus div-exp pow-prod-down prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin div-inv sin-mult unswap-sqr
Counts
4 → 78
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (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))))
808.0ms
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
146.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
499.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify65.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04073418
115832987
250012850

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2)))) (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.4b
(pow (sin phi1) 3)
0.5b
(pow (sin phi1) 4)
0.6b
(- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
33×add-cube-cbrt
24×prod-diff
19×unpow-prod-down
9×times-frac
8×add-exp-log fma-neg associate-*r/
7×add-cbrt-cube sqr-pow
6×pow1 pow-unpow add-log-exp
5×unpow2
4×expm1-log1p-u log1p-expm1-u associate-/l/ difference-of-squares
3×flip3-- cube-prod associate-/r* flip-- associate-/l*
2×pow-to-exp pow-pow pow-exp cos-mult frac-sub
1×cbrt-undiv cube-mult sub-neg frac-2neg diff-log unpow3 div-sub div-exp clear-num fma-udef div-inv associate--r+ distribute-lft-out-- rem-cube-cbrt
Counts
4 → 130
Calls
4 calls:
136.0ms
(/ (- (- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2)))) (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
1.0ms
(pow (sin phi1) 3)
1.0ms
(pow (sin phi1) 4)
13.0ms
(- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2))))

series991.0ms

Counts
4 → 12
Calls
4 calls:
694.0ms
(/ (- (- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2)))) (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
35.0ms
(pow (sin phi1) 3)
30.0ms
(pow (sin phi1) 4)
231.0ms
(- (pow (cos delta) 2) (fma (* (pow (sin phi1) 2) (pow (cos phi1) 2)) (* (pow (cos theta) 2) (pow (sin delta) 2)) (* (pow (sin phi1) 4) (pow (cos delta) 2))))

simplify128.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
07095605
132654039
250024031

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes643.0ms

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 (0.0ms)

IterNodesCost
069139
169139

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.2s3096×body1280valid
1.8s1890×body640valid
476.0ms727×body320valid
343.0ms1980×body80valid
123.0ms307×body160valid