Details

Time bar (total: 40.1s)

sample605.0ms

Algorithm
intervals
Results
359.0ms107×body1280valid
99.0ms60×body640valid
29.0ms25×body320valid
19.0ms58×body80valid
9.0ms6×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

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

rewrite48.0ms

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

series640.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin theta) (sin delta))
270.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
302.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.2s

Counts
84 → 84
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01571824
13381678
212651533
done50001485

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
54×add-sqr-sqrt
46×*-un-lft-identity
44×add-cube-cbrt
42×unpow-prod-down cube-prod
28×sqr-pow
22×cube-mult unpow3
12×fma-neg
8×difference-of-squares
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×asin-acos pow-pow pow-exp rem-cube-cbrt
1×difference-cubes cube-div pow-to-exp sub-neg flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 177
Calls
4 calls:
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
50.0ms
(- (pow (cos delta) 3) (pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3))
10.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

series1.1s

Counts
4 → 12
Calls
4 calls:
14.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
7.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
759.0ms
(- (pow (cos delta) 3) (pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3))
356.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

simplify4.0s

Counts
189 → 189
Iterations

Useful iterations: done (3.9s)

IterNodesCost
027115825
177710419
244286866
done50006865

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize119.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×fma-neg prod-diff
11×pow1
6×add-exp-log unpow-prod-down cube-prod add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×swap-sqr associate-*r* associate-*l*
2×cube-mult asin-acos unpow3 pow3 pow-prod-down sqr-pow
1×difference-cubes pow2 sub-neg flip3-- pow-plus diff-log prod-exp pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod sqr-sin sin-mult unswap-sqr
Counts
4 → 88
Calls
4 calls:
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
224.0ms
(- (pow (cos delta) 3) (* (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin phi1)) (sin phi1))))
24.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
8.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
749.0ms
(- (pow (cos delta) 3) (* (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin phi1)) (sin phi1))))
239.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

simplify2.8s

Counts
100 → 100
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01846077
15475468
233562852
done50002848

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cos delta) 6)
0.6b
(pow (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) 3)
0.6b
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
0.7b
(pow (sin phi1) 6)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
12×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
10×add-exp-log unpow-prod-down
9×pow-pow
8×add-cbrt-cube
5×pow-exp
4×expm1-log1p-u pow-to-exp cube-prod log1p-expm1-u add-log-exp sqr-pow
3×rem-cube-cbrt
2×cube-mult unpow3
1×cube-div pow2 pow-plus pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod sin-mult
Counts
4 → 92
Calls
4 calls:
7.0ms
(pow (cos delta) 6)
9.0ms
(pow (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) 3)
13.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
4.0ms
(pow (sin phi1) 6)

series876.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(pow (cos delta) 6)
301.0ms
(pow (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) 3)
445.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
59.0ms
(pow (sin phi1) 6)

simplify2.2s

Counts
104 → 104
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01652010
14991750
222051305
done50011298

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes545.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
032117
141117
done41117

end0.0ms

sample19.8s

Algorithm
intervals
Results
11.8s3241×body1280valid
4.8s1770×body640valid
1.4s695×body320valid
918.0ms1993×body80valid
271.0ms301×body160valid