Details

sample567.0ms

Algorithm

intervals

Results

287.0ms	93×	body	1280	valid
184.0ms	60×	body	640	valid
25.0ms	21×	body	320	valid
24.0ms	71×	body	80	valid
8.0ms	11×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	75
4	75
3	73
2	61
1	36
0	22

prune53.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

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

rewrite38.0ms

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:

10.0ms	(* (sin theta) (sin delta))
19.0ms	(* (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))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin theta) (sin delta))
252.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
256.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify919.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1303
1	353
0	162

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`asin-acos`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
4.0ms	(/ (fma (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (pow (sin phi1) 2)) (- (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))) (* (cos delta) (cos delta))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (cos delta)))
0.0ms	(fma (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (pow (sin phi1) 2)) (- (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))) (* (cos delta) (cos delta)))

series1.8s

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
7.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
1.1s	(/ (fma (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (pow (sin phi1) 2)) (- (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))) (* (cos delta) (cos delta))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (cos delta)))
621.0ms	(fma (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (pow (sin phi1) 2)) (- (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))) (* (cos delta) (cos delta)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1674
1	370
0	155

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l` `sin-mult` `associate-/l` `associate-/l/`
2×	`flip3-+` `frac-add` `associate-*r/` `cos-mult` `flip-+`
1×	`pow2` `cbrt-undiv` `+-commutative` `asin-acos` `sqr-cos` `associate-+r+` `clear-num` `sum-log` `fma-def` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

1.0ms	(asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))
74.0ms	(/ (+ (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (cos delta) (cos delta))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (cos delta)))
25.0ms	(+ (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (cos delta) (cos delta)))
18.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

10.0ms	(asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))
1.0s	(/ (+ (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (cos delta) (cos delta))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (cos delta)))
531.0ms	(+ (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (cos delta) (cos delta)))
209.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	3266
1	640
0	229

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize247.0ms

Local error

Found 4 expressions with local error:

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

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*r/`
25×	`pow1`
24×	`add-sqr-sqrt`
21×	`sin-mult`
18×	`*-un-lft-identity` `cos-mult` `add-cube-cbrt`
16×	`associate-/l/`
15×	`add-cbrt-cube` `add-exp-log`
10×	`associate-*l/`
9×	`swap-sqr` `associate-r` `associate-l` `frac-sub`
8×	`frac-times`
5×	`sub-div`
4×	`expm1-log1p-u` `times-frac` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-sin` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3--` `div-sub` `div-inv` `flip--`

Counts

4 → 129

Calls

4 calls:

489.0ms	(/ (- (* (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1)))))))) (* (* (cos delta) (cos delta)) (* (cos delta) (cos delta)))) (* (fma (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (cos delta)) (- (fma (pow (sin phi1) 2) (* (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)))))) (pow (cos delta) 2)))))
10.0ms	(* (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))))))
10.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))
13.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))

series3.6s

Counts

4 → 12

Calls

4 calls:

2.9s	(/ (- (* (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))) (* (- (pow (sin phi1) 2)) (* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1)))))))) (* (* (cos delta) (cos delta)) (* (cos delta) (cos delta)))) (* (fma (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (cos delta)) (- (fma (pow (sin phi1) 2) (* (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)))))) (pow (cos delta) 2)))))
213.0ms	(* (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))))))
220.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))
221.0ms	(* (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))) (sin (asin (fma (cos phi1) (* (sin delta) (cos theta)) (* (cos delta) (sin phi1))))))

simplify584.0ms

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
1	1037
0	315

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	127
1	127
0	86

end0.0ms

sample21.0s

Algorithm

intervals

Results

11.6s	3157×	body	1280	valid
5.5s	1870×	body	640	valid
1.8s	1966×	body	80	valid
991.0ms	695×	body	320	valid
283.0ms	312×	body	160	valid