Details

Time bar (total: 17.2s)

sample258.0ms

Algorithm
intervals
Results
153.0ms97×body1280valid
53.0ms55×body640valid
14.0ms72×body80valid
10.0ms18×body320valid
5.0ms14×body160valid

simplify10.0ms

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

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)))))))

rewrite40.0ms

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:
12.0ms
(* (sin theta) (sin delta))
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(* (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)))))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
141.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
161.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify104.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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)))
0.3b
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (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))))))
0.3b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
39×times-frac
36×*-un-lft-identity
32×difference-of-squares
28×add-cube-cbrt
26×sqr-pow
13×associate-/l*
12×add-exp-log unpow-prod-down cube-prod add-cbrt-cube
10×pow1
6×pow-unpow
4×difference-cubes expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod fma-udef associate-/l/
1×cbrt-undiv cube-div distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub div-exp clear-num *-commutative flip-- div-inv sin-mult unswap-sqr
Counts
4 → 144
Calls
4 calls:
13.0ms
(* (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)))
62.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (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))))))
3.0ms
(pow (cos delta) 3)
13.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.1s

Counts
4 → 12
Calls
4 calls:
276.0ms
(* (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)))
1.5s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (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))))))
30.0ms
(pow (cos delta) 3)
218.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify78.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09297418
150017023

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

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)

rewrite21.0ms

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×expm1-log1p-u pow-to-exp pow-pow pow-exp add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 76
Calls
4 calls:
9.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 4)
4.0ms
(pow (sin phi1) 5)
4.0ms
(pow (sin phi1) 6)

series135.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sin phi1) 4)
33.0ms
(pow (sin phi1) 4)
37.0ms
(pow (sin phi1) 5)
38.0ms
(pow (sin phi1) 6)

simplify150.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (145.0ms)

IterNodesCost
0223319
1789292
23555284
35001282

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

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)
2.6b
(log (exp (pow (sin phi1) 6)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×pow-unpow
8×pow1 log-pow
7×add-exp-log exp-prod
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp log-prod pow-pow pow-exp
1×rem-log-exp
Counts
4 → 78
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 5)
8.0ms
(pow (sin phi1) 6)
8.0ms
(log (exp (pow (sin phi1) 6)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sin phi1) 4)
37.0ms
(pow (sin phi1) 5)
41.0ms
(pow (sin phi1) 6)
37.0ms
(log (exp (pow (sin phi1) 6)))

simplify162.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0259333
1859301
23824295
35001295

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes681.0ms

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
0111108
1111108

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s3152×body1280valid
1.7s1792×body640valid
427.0ms686×body320valid
346.0ms2055×body80valid
127.0ms315×body160valid