Details

Time bar (total: 44.4s)

sample607.0ms

Algorithm
intervals
Results
390.0ms100×body1280valid
108.0ms55×body640valid
33.0ms27×body320valid
24.0ms64×body80valid
8.0ms10×body160valid

simplify134.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
02233
13632
26132
37332
47532
done7532

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize510.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite72.0ms

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:
25.0ms
(* (sin theta) (sin delta))
26.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (sin theta) (sin delta))
240.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
15.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
281.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01581747
13381677
213091498
done50001485

prune856.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×add-exp-log
18×add-cube-cbrt *-un-lft-identity
13×add-cbrt-cube
11×pow1 associate-*r*
10×prod-exp
9×times-frac
6×sin-mult add-log-exp
5×associate-*l/ unswap-sqr
4×expm1-log1p-u unpow-prod-down associate-*l* cos-mult cbrt-unprod log1p-expm1-u associate-/l/
3×swap-sqr associate-/r* associate-/l*
2×pow2 pow-to-exp flip3-- pow-prod-down pow-exp *-commutative frac-sub flip-- unpow2 sub-div sqr-pow
1×cbrt-undiv sub-neg sqr-cos frac-2neg pow-plus fma-neg diff-log div-sub div-exp prod-diff associate--l+ clear-num pow-sqr pow-prod-up sqr-sin div-inv
Counts
4 → 115
Calls
4 calls:
57.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
77.0ms
(* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))
81.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
29.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
274.0ms
(* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))
576.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
257.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify4.4s

Counts
127 → 127
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02597326
17536635
247405868
done50005868

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×add-exp-log
18×add-cube-cbrt *-un-lft-identity
13×add-cbrt-cube
11×pow1 associate-*l*
10×prod-exp
9×times-frac
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down associate-*r* cbrt-unprod log1p-expm1-u add-log-exp
3×swap-sqr associate-/r* associate-/l*
2×pow2 pow-to-exp pow-prod-down pow-exp *-commutative sin-mult unpow2 sqr-pow
1×cbrt-undiv frac-2neg pow-plus associate-*r/ div-exp clear-num pow-sqr pow-prod-up fma-udef sqr-sin div-inv
Counts
4 → 101
Calls
4 calls:
7.0ms
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
48.0ms
(* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
27.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
309.0ms
(* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
249.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
632.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify2.1s

Counts
113 → 113
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02186211
15745831
227525029
done50024129

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize147.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(* (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))))
10.5b
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
10.5b
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
28×pow1
18×sqrt-pow1
16×add-sqr-sqrt
13×pow-prod-down
12×add-cube-cbrt *-un-lft-identity
10×pow2 pow1/2
8×add-exp-log add-cbrt-cube
7×swap-sqr associate-*r* associate-*l* associate-*l/ pow-prod-up sin-mult
6×sqrt-div sqrt-prod
5×pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
1×frac-times sqrt-unprod associate-*r/ rem-square-sqrt sqr-sin
Counts
4 → 103
Calls
4 calls:
25.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
257.0ms
(* (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))))
54.0ms
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
51.0ms
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

series1.0s

Counts
4 → 12
Calls
4 calls:
210.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
293.0ms
(* (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))))
311.0ms
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
233.0ms
(sqrt (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

simplify1.4s

Counts
115 → 115
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01295625
13264067
215773339
done50002154

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes711.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02774
13774
24274
done4274

end0.0ms

sample20.9s

Algorithm
intervals
Results
12.6s3125×body1280valid
4.6s1867×body640valid
1.3s723×body320valid
1.2s1974×body80valid
356.0ms311×body160valid