Details

Time bar (total: 13.1s)

sample267.0ms

Algorithm
intervals
Results
178.0ms108×body1280valid
47.0ms55×body640valid
11.0ms68×body80valid
10.0ms17×body320valid
3.0ms8×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin theta) (sin delta)) (cos phi1))
0.3b
(* (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 sin-mult
1×sub-neg asin-acos flip3-- diff-log associate-*l/ flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
9.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
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)))))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
157.0ms
(* (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))))
183.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03631254
112761101
250011096

prune459.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (* (sin theta) (sin delta)))
0.3b
(* (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)))))))

rewrite18.0ms

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-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-neg prod-diff
2×*-commutative sin-mult
1×sub-neg asin-acos flip3-- diff-log associate-*r/ flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
8.0ms
(* (cos phi1) (* (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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (cos phi1) (* (sin theta) (sin delta)))
160.0ms
(* (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))))
181.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify128.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
03531252
111571099
248211094
350011089

prune450.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg pow1/3 prod-diff
1×sub-neg flip3-- diff-log flip--
Counts
4 → 59
Calls
4 calls:
3.0ms
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(cbrt (sin phi1))
1.0ms
(cbrt (sin phi1))
1.0ms
(cbrt (sin phi1))

series481.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
100.0ms
(cbrt (sin phi1))
99.0ms
(cbrt (sin phi1))
99.0ms
(cbrt (sin phi1))

simplify171.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (159.0ms)

IterNodesCost
0238977
1806814
24537740
35001719

prune462.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos phi1))
0.3b
(cbrt (cos phi1))
0.3b
(cbrt (cos phi1))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg pow1/3 prod-diff
1×sub-neg flip3-- diff-log flip--
Counts
4 → 59
Calls
4 calls:
1.0ms
(cbrt (cos phi1))
1.0ms
(cbrt (cos phi1))
1.0ms
(cbrt (cos phi1))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (cos phi1))
102.0ms
(cbrt (cos phi1))
102.0ms
(cbrt (cos phi1))
183.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0210737
1613650
22276639
35002581

prune433.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes258.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03429
13429

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.3s3210×body1280valid
1.6s1783×body640valid
503.0ms2003×body80valid
426.0ms698×body320valid
129.0ms306×body160valid