Details

Time bar (total: 12.6s)

sample265.0ms

Algorithm
intervals
Results
154.0ms95×body1280valid
55.0ms62×body640valid
22.0ms31×body320valid
10.0ms60×body80valid
3.0ms8×body160valid

simplify10.0ms

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: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:
15.0ms
(* (sin theta) (sin delta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin theta) (sin delta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
167.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
191.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify102.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune499.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
0.4b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.5b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.6b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg associate-*r* associate-*l* prod-diff
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
21.0ms
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
8.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series401.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
188.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
38.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify47.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03181880
111581703
250011692

prune551.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow pow1/3 rem-cbrt-cube
1×pow-to-exp pow-pow pow-exp rem-cube-cbrt
Counts
4 → 94
Calls
4 calls:
4.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series60.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify139.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01121720
13941653
228001643
350011643

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
3.4b
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
6.6b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
6.6b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
2×cube-mult unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 70
Calls
4 calls:
1.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
3.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
3.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series170.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
90.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))
8.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify72.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
01161257
13571196
221711195
350021187

prune526.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes409.0ms

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
04480
14480

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.0s3107×body1280valid
1.7s1866×body640valid
432.0ms728×body320valid
335.0ms2001×body80valid
125.0ms298×body160valid