Details

Time bar (total: 15.6s)

sample268.0ms

Algorithm
intervals
Results
164.0ms99×body1280valid
56.0ms60×body640valid
15.0ms24×body320valid
10.0ms63×body80valid
4.0ms10×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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
(* (* (cos phi1) (sin delta)) (cos theta))
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))))))
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:
8.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(* (sin phi1) (sin (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)))))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
154.0ms
(* (sin phi1) (sin (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)))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0305974
11167862
25002860

prune374.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
12×*-un-lft-identity
10×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
8×difference-of-squares sqr-pow
6×unpow-prod-down pow-unpow cube-prod add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod sin-mult
1×difference-cubes cube-div sub-neg flip3-- diff-log *-commutative flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 87
Calls
4 calls:
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(- (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)
3.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.2s

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
755.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
32.0ms
(pow (cos delta) 3)
239.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify105.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
05241539
127721462
250011450

prune665.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.6b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.6b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
6.6b
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×sin-mult add-log-exp
3×cbrt-prod pow-unpow cbrt-div pow1/3
2×pow-pow pow-exp rem-cube-cbrt
1×cube-div cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod pow-prod-down prod-exp cbrt-unprod sqr-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
2.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
241.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
325.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
320.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
321.0ms
(cbrt (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify181.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02371105
1823965
24662946
35001946

prune599.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))
0.3b
(pow (cos delta) 3)
0.4b
(pow (sin phi1) 3)
0.6b
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
3×cube-div cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×difference-cubes sub-neg flip3-- flip3-+ diff-log associate-*r/ pow-prod-down frac-add cos-mult sin-cos-mult flip-- flip-+
Counts
4 → 85
Calls
4 calls:
18.0ms
(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))
1.0ms
(pow (cos delta) 3)
2.0ms
(pow (sin phi1) 3)
12.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

series987.0ms

Counts
4 → 12
Calls
4 calls:
748.0ms
(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))
32.0ms
(pow (cos delta) 3)
30.0ms
(pow (sin phi1) 3)
176.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

simplify139.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (130.0ms)

IterNodesCost
06501056
13631932
25002919

prune585.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes497.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05259
15259

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3089×body1280valid
1.7s1857×body640valid
441.0ms692×body320valid
373.0ms2067×body80valid
118.0ms295×body160valid