Details

Time bar (total: 12.8s)

sample268.0ms

Algorithm
intervals
Results
160.0ms98×body1280valid
51.0ms54×body640valid
22.0ms25×body320valid
11.0ms66×body80valid
5.0ms13×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(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
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:
5.0ms
(* (sin theta) (sin delta))
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))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series378.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin theta) (sin delta))
149.0ms
(* (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))))
179.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune471.0ms

Filtered
84 candidates to 66 candidates (78.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New741084
Fresh000
Picked101
Done000
Total751085

Merged error: 0.0b

Counts
85 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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×asin-acos pow-unpow
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 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))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series240.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
221.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify156.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0185939
1692822
24182822
35001822

prune485.0ms

Filtered
67 candidates to 52 candidates (77.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New65267
Fresh189
Picked101
Done000
Total671077

Merged error: 0.0b

Counts
77 → 10

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log unpow-prod-down pow-unpow cube-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div
2×cube-mult pow-to-exp asin-acos pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×flip3-+ associate-*r/ frac-add cos-mult sin-cos-mult flip-+
Counts
4 → 73
Calls
4 calls:
3.0ms
(pow (cos delta) 3)
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

series210.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (cos delta) 3)
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
167.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

simplify63.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0365890
11704760
25001749

prune579.0ms

Filtered
85 candidates to 58 candidates (68.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New84185
Fresh189
Picked011
Done000
Total851095

Merged error: 0.0b

Counts
95 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×fma-neg
2×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos log1p-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 81
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
6.0ms
(* (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))))
5.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
146.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
222.0ms
(- (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03611973
111511353
250011344

prune422.0ms

Filtered
93 candidates to 67 candidates (72.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New92193
Fresh178
Picked011
Done011
Total9310103

Merged error: 0.0b

Counts
103 → 10

regimes394.0ms

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
04052
14552
24552

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.3s3137×body1280valid
1.7s1828×body640valid
446.0ms711×body320valid
363.0ms1992×body80valid
139.0ms332×body160valid