Details

sample671.0ms

Algorithm

intervals

Results

365.0ms	92×	body	1280	valid
144.0ms	69×	body	640	valid
74.0ms	68×	body	80	valid
30.0ms	16×	body	320	valid
8.0ms	11×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

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

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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 phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms	(* (sin theta) (sin delta))
7.0ms	(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)))))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
61.0ms	(* (sin theta) (sin delta))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
264.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.6s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1311
1	353
0	162

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize210.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
16×	`sin-mult`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`cos-mult`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-/l/`
6×	`frac-sub` `add-log-exp`
5×	`associate-l/` `associate-r/` `difference-of-squares`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `associate-/l*` `sub-div`
3×	`frac-times` `associate-/r*`
2×	`pow-plus` `flip3--` `associate-/r/` `flip--`
1×	`pow2` `cbrt-undiv` `asin-acos` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `prod-diff` `associate--l+` `*-commutative` `flip-+` `div-inv`

Counts

4 → 115

Calls

4 calls:

3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
72.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
68.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
42.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.4s	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
252.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
795.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify3.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	4435
1	792
0	271

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize220.0ms

Local error

Found 4 expressions with local error:

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

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

157×	`pow1`
83×	`pow-prod-down`
54×	`add-cbrt-cube` `add-exp-log`
35×	`prod-exp` `cbrt-unprod`
19×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow-sqr` `pow-prod-up`
12×	`times-frac`
6×	`add-log-exp`
5×	`pow-plus` `associate-*r/` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `sin-mult` `associate-/l*`
3×	`associate-/r*` `prod-diff`
2×	`pow2` `flip3--` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--` `associate-/l/`
1×	`frac-times` `cbrt-undiv` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `associate-*l/` `associate--l+` `fma-udef` `div-inv` `associate--r+`

Counts

4 → 158

Calls

4 calls:

44.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
27.0ms	(/ (- (* (cos delta) (cos delta)) (fma (* (* (sin delta) (cos phi1)) (* (sin delta) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (fma (* (cos theta) (* (* (* (cos delta) (cos phi1)) (sin delta)) (* (* (sin phi1) (sin phi1)) (sin phi1)))) 2 (* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1))))))) (fma (cos delta) (* (sin phi1) (sin phi1)) (fma (sin delta) (* (* (cos theta) (cos phi1)) (sin phi1)) (cos delta))))
124.0ms	(* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1))))
18.0ms	(- (* (cos delta) (cos delta)) (fma (* (* (sin delta) (cos phi1)) (* (sin delta) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (fma (* (cos theta) (* (* (* (cos delta) (cos phi1)) (sin delta)) (* (* (sin phi1) (sin phi1)) (sin phi1)))) 2 (* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1)))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
1.0s	(/ (- (* (cos delta) (cos delta)) (fma (* (* (sin delta) (cos phi1)) (* (sin delta) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (fma (* (cos theta) (* (* (* (cos delta) (cos phi1)) (sin delta)) (* (* (sin phi1) (sin phi1)) (sin phi1)))) 2 (* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1))))))) (fma (cos delta) (* (sin phi1) (sin phi1)) (fma (sin delta) (* (* (cos theta) (cos phi1)) (sin phi1)) (cos delta))))
117.0ms	(* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1))))
566.0ms	(- (* (cos delta) (cos delta)) (fma (* (* (sin delta) (cos phi1)) (* (sin delta) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (fma (* (cos theta) (* (* (* (cos delta) (cos phi1)) (sin delta)) (* (* (sin phi1) (sin phi1)) (sin phi1)))) 2 (* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1)))))))

simplify1.7s

Counts

170 → 170

Iterations

Iter	Nodes
done	5001
1	877
0	293

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize237.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))) (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))))
14.5b	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
14.5b	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
14.5b	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`cbrt-prod` `pow1`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `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 → 69

Calls

4 calls:

91.0ms	(* (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))) (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))))
22.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
34.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
23.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))

series656.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))) (cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))))
163.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
178.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))
162.0ms	(cbrt (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))))

simplify1.6s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1099
1	230
0	88

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes799.0ms

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	58
1	58
0	42

end0.0ms

sample18.5s

Algorithm

intervals

Results

10.6s	3149×	body	1280	valid
3.9s	1864×	body	640	valid
1.4s	683×	body	320	valid
1.3s	1995×	body	80	valid
622.0ms	309×	body	160	valid