Details

Time bar (total: 16.9s)

sample291.0ms

Algorithm
intervals
Results
204.0ms121×body1280valid
46.0ms52×body640valid
9.0ms57×body80valid
9.0ms15×body320valid
4.0ms11×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (sin delta)) (cos theta))
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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg prod-diff
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
5.0ms
(* (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)))))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
156.0ms
(* (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))))
180.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03381246
112941093
250011088

prune523.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(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))
0.4b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
57×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
45×unpow-prod-down cube-prod
29×sqr-pow
23×cube-mult unpow3
12×fma-neg
8×pow1 add-exp-log add-cbrt-cube difference-of-squares
6×pow-unpow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-pow pow-exp rem-cube-cbrt
2×pow-to-exp
1×difference-cubes cube-div sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 192
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
17.0ms
(- (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)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.0s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
748.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms
(pow (cos delta) 3)
237.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify171.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
07046457
132624820
250014818

prune866.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(fma (* (cos delta) (cos delta)) (cos delta) (- (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×asin-acos 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 fma-udef sin-mult sqr-pow
Counts
4 → 55
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series986.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
744.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
229.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify62.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
03781117
11830973
25001972

prune829.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.4b
(fma (* (cos delta) (cos delta)) (cos delta) (- (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))))
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.1b
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod
21×unpow-prod-down cube-prod
11×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-exp add-cbrt-cube
7×pow1 cube-mult unpow3 sqr-pow
6×pow-unpow
5×cube-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow sin-mult rem-cube-cbrt
2×prod-exp
1×cbrt-div pow1/3 pow-prod-down rem-cbrt-cube cbrt-unprod fma-udef
Counts
4 → 108
Calls
4 calls:
4.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))))
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
4.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series2.1s

Counts
4 → 12
Calls
4 calls:
911.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
730.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))))
229.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
222.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify96.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
05282408
125212172
250012163

prune747.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes447.0ms

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
04888
14888

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.2s3155×body1280valid
1.7s1815×body640valid
437.0ms706×body320valid
343.0ms2010×body80valid
118.0ms314×body160valid