Details

sample597.0ms

Algorithm

intervals

Results

373.0ms	107×	body	1280	valid
92.0ms	55×	body	640	valid
64.0ms	70×	body	80	valid
22.0ms	19×	body	320	valid
4.0ms	5×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	64
3	64
2	59
1	36
0	22

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize446.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

38.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
17.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
12.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
8.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
256.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
295.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.0s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
3	3382
2	1008
1	371
0	166

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize186.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
9×	`fma-neg` `prod-diff`
8×	`associate-*r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 98

Calls

4 calls:

66.0ms	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
263.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
255.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
308.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify2.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1651
1	369
0	166

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.2b	(* (sin phi1) (sin phi1))
0.3b	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
0.6b	(- (cos delta) (fma (* (sin phi1) (sin phi1)) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`prod-diff`
7×	`associate-l`
6×	`add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `*-commutative`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-sqr` `pow-prod-up` `fma-udef` `sqr-sin` `flip--` `sin-mult` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

20.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
13.0ms	(* (sin phi1) (sin phi1))
45.0ms	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
6.0ms	(- (cos delta) (fma (* (sin phi1) (sin phi1)) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
40.0ms	(* (sin phi1) (sin phi1))
140.0ms	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
303.0ms	(- (cos delta) (fma (* (sin phi1) (sin phi1)) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5002
2	1670
1	513
0	207

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
0.6b	(- (cos delta) (fma (- 1/2 (* 1/2 (cos (+ phi1 phi1)))) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))
1.6b	(- 1/2 (* 1/2 (cos (+ phi1 phi1))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`prod-diff`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`
1×	`fma-udef` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

19.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
42.0ms	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
13.0ms	(- (cos delta) (fma (- 1/2 (* 1/2 (cos (+ phi1 phi1)))) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))
10.0ms	(- 1/2 (* 1/2 (cos (+ phi1 phi1))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
167.0ms	(* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))
345.0ms	(- (cos delta) (fma (- 1/2 (* 1/2 (cos (+ phi1 phi1)))) (cos delta) (* (* (cos theta) (sin phi1)) (* (cos phi1) (sin delta)))))
64.0ms	(- 1/2 (* 1/2 (cos (+ phi1 phi1))))

simplify1.9s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1755
1	521
0	216

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes861.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample19.8s

Algorithm

intervals

Results

12.4s	3177×	body	1280	valid
4.3s	1820×	body	640	valid
963.0ms	726×	body	320	valid
926.0ms	1951×	body	80	valid
759.0ms	326×	body	160	valid