Details

Time bar (total: 35.4s)

sample590.0ms

Algorithm
intervals
Results
378.0ms99×body1280valid
105.0ms57×body640valid
37.0ms27×body320valid
24.0ms68×body80valid
4.0ms5×body160valid

simplify132.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (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))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite63.0ms

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:
14.0ms
(* (sin theta) (sin delta))
28.0ms
(* (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))))
17.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series643.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (sin theta) (sin delta))
250.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
311.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts
84 → 84
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01571824
13381678
212651533
done50001485

prune920.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite73.0ms

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
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip-- distribute-lft-out-- expm1-udef associate--r- difference-of-squares
Counts
4 → 81
Calls
4 calls:
27.0ms
(* (sin theta) (sin delta))
23.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
1.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
18.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series673.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (sin theta) (sin delta))
225.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
16.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
360.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify1.5s

Counts
93 → 93
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01772957
13692183
214931846
done50001637

prune754.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
44.0ms
(* (cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
2.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
2.0ms
(cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
305.0ms
(* (cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))
385.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
352.0ms
(cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))
320.0ms
(cbrt (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

simplify921.0ms

Counts
93 → 93
Iterations

Useful iterations: done (915.0ms)

IterNodesCost
01162838
12652625
29772398
done50012089

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3)))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
0.4b
(fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))))
0.8b
(pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))
7.0b
(cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-exp-log
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×cbrt-prod pow-pow pow1/3
1×cbrt-undiv pow-to-exp pow-unpow cbrt-div frac-2neg div-exp pow-exp clear-num fma-udef div-inv sin-mult sqr-pow
Counts
4 → 70
Calls
4 calls:
10.0ms
(/ (fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3)))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
1.0ms
(fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))))
14.0ms
(pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))
31.0ms
(cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3)))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
560.0ms
(fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))))
443.0ms
(pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3))
432.0ms
(cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

simplify1.5s

Counts
82 → 82
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01953867
14893628
220823280
done50003261

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes812.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02758
13758
23958
done3958

end0.0ms

sample19.0s

Algorithm
intervals
Results
11.4s3088×body1280valid
4.5s1863×body640valid
1.3s726×body320valid
938.0ms2010×body80valid
213.0ms313×body160valid