Details

Time bar (total: 40.9s)

sample570.0ms

Algorithm
intervals
Results
348.0ms93×body1280valid
111.0ms60×body640valid
32.0ms21×body320valid
25.0ms71×body80valid
9.0ms11×body160valid

simplify85.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
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×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 72
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
13.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (sin theta) (sin delta))
254.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
248.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify940.0ms

Counts
84 → 84
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01641747
13561677
213261531
done50001485

prune966.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))
0.2b
(* (sin theta) (sin delta))
0.2b
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1))
0.4b
(- (cos delta) (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
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 unswap-sqr
1×sub-neg flip3-- diff-log fma-udef flip-- sin-mult
Counts
4 → 71
Calls
4 calls:
1.0ms
(fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))
19.0ms
(* (sin theta) (sin delta))
12.0ms
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1))
6.0ms
(- (cos delta) (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))
65.0ms
(* (sin theta) (sin delta))
261.0ms
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1))
300.0ms
(- (cos delta) (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (sin phi1)))

simplify988.0ms

Counts
83 → 83
Iterations

Useful iterations: done (984.0ms)

IterNodesCost
01401562
13111495
213241364
done50011354

prune991.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))
0.3b
(/ (- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
0.3b
(- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2)))
0.4b
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×add-exp-log
18×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube
11×pow1 associate-*r*
10×prod-exp
9×times-frac
6×add-log-exp
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down associate-*l* cbrt-unprod log1p-expm1-u
3×associate-/r* swap-sqr associate-/l*
2×pow2 pow-to-exp flip3-- pow-prod-down pow-exp *-commutative fma-udef flip-- unpow2 sqr-pow associate-/l/
1×distribute-rgt-in cbrt-undiv sqr-cos clear-num sub-neg frac-2neg distribute-lft-in pow-plus fma-neg diff-log div-sub div-exp prod-diff associate--l+ pow-sqr pow-prod-up div-inv
Counts
4 → 110
Calls
4 calls:
38.0ms
(* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))
25.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
25.0ms
(- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2)))
13.0ms
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))))

series2.2s

Counts
4 → 12
Calls
4 calls:
289.0ms
(* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))
1.1s
(/ (- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
568.0ms
(- (* (cos delta) (cos delta)) (* (* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta)))) (pow (sin phi1) 2)))
267.0ms
(* (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))))

simplify2.7s

Counts
122 → 122
Iterations

Useful iterations: 2 (887.0ms)

IterNodesCost
02496395
17374595
248434098
done50004098

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))
0.3b
(/ (fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2)))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
0.4b
(pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2)
0.5b
(fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
19×add-exp-log
18×*-un-lft-identity add-cube-cbrt
17×unpow-prod-down
16×unswap-sqr
11×unpow2 sqr-pow
9×times-frac prod-exp
8×add-cbrt-cube associate-*r* associate-*l*
7×pow-to-exp pow-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* associate-/l*
1×cbrt-undiv clear-num pow-pow frac-2neg div-exp pow-prod-down *-commutative cbrt-unprod fma-udef div-inv
Counts
4 → 112
Calls
4 calls:
30.0ms
(* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))
8.0ms
(/ (fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2)))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
4.0ms
(pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2)
1.0ms
(fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))))

series2.4s

Counts
4 → 12
Calls
4 calls:
315.0ms
(* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))
1.2s
(/ (fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2)))) (fma (sin phi1) (fma (cos delta) (sin phi1) (* (* (cos theta) (cos phi1)) (sin delta))) (cos delta)))
242.0ms
(pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2)
648.0ms
(fma (cos delta) (cos delta) (- (* (pow (fma (cos phi1) (* (cos theta) (sin delta)) (* (sin phi1) (cos delta))) 2) (pow (sin phi1) 2))))

simplify2.2s

Counts
124 → 124
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02364657
16264479
230513984
done50003980

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes700.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03058
14558
24758
done4758

end0.0ms

sample21.1s

Algorithm
intervals
Results
11.1s3157×body1280valid
6.0s1870×body640valid
1.4s695×body320valid
1.0s1966×body80valid
813.0ms312×body160valid