Details

Time bar (total: 16.5s)

sample251.0ms

Algorithm
intervals
Results
148.0ms97×body1280valid
54.0ms55×body640valid
12.0ms72×body80valid
10.0ms18×body320valid
5.0ms14×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.2b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite41.0ms

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:
12.0ms
(* (sin theta) (sin delta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
18.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
138.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
167.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune385.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
39×times-frac
35×*-un-lft-identity
32×difference-of-squares
27×add-cube-cbrt
26×sqr-pow
15×add-exp-log add-cbrt-cube
13×pow1 associate-/l*
12×unpow-prod-down cube-prod
7×associate-/r/ sin-mult
6×pow-unpow
5×flip3-+ frac-add cos-mult flip-+
4×difference-cubes frac-times associate-*r/ pow-prod-down prod-exp cbrt-unprod distribute-lft-out-- add-log-exp
3×pow-pow associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 associate-*l/ associate-/l/
1×cbrt-undiv cube-div distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub div-exp associate-*l* clear-num *-commutative flip-- div-inv
Counts
4 → 148
Calls
4 calls:
101.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (+ (* (* (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))) (* (cos delta) (cos delta))))
58.0ms
(* (* (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)))))) (cos delta)))
4.0ms
(pow (cos delta) 3)
10.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.3s

Counts
4 → 12
Calls
4 calls:
1.7s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (+ (* (* (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))) (* (cos delta) (cos delta))))
330.0ms
(* (* (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)))))) (cos delta)))
26.0ms
(pow (cos delta) 3)
220.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify87.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011398364
150017997

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 4)
0.4b
(pow (sin phi1) 4)
0.5b
(pow (sin phi1) 5)
0.6b
(pow (sin phi1) 6)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube add-log-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 5)
4.0ms
(pow (sin phi1) 6)

series141.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (sin phi1) 4)
28.0ms
(pow (sin phi1) 4)
37.0ms
(pow (sin phi1) 5)
44.0ms
(pow (sin phi1) 6)

simplify146.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (141.0ms)

IterNodesCost
0217295
1765268
23458264
35001256

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 4)
0.5b
(pow (sin phi1) 5)
0.6b
(pow (sin phi1) 6)
5.0b
(cbrt (pow (pow (sin phi1) 6) 3))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down
20×cbrt-prod
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×pow-unpow
7×pow1 add-exp-log cube-prod
6×sqr-pow
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow pow-exp
1×cube-mult pow1/3 unpow3 rem-cbrt-cube
Counts
4 → 80
Calls
4 calls:
8.0ms
(pow (sin phi1) 4)
4.0ms
(pow (sin phi1) 5)
3.0ms
(pow (sin phi1) 6)
6.0ms
(cbrt (pow (pow (sin phi1) 6) 3))

series149.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sin phi1) 4)
44.0ms
(pow (sin phi1) 5)
38.0ms
(pow (sin phi1) 6)
39.0ms
(cbrt (pow (pow (sin phi1) 6) 3))

simplify42.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0302375
11111308
25002306

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes727.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105108
1107108
2107108

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.0s3152×body1280valid
1.6s1792×body640valid
405.0ms686×body320valid
349.0ms2055×body80valid
128.0ms315×body160valid