Details

sample1.2s

Algorithm

intervals

Results

955.0ms	161×	body	1280	valid
150.0ms	69×	body	640	valid
16.0ms	16×	body	320	valid
6.0ms	8×	body	160	valid
1.0ms	2×	body	80	valid

simplify94.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.1b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.7b	(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`acos-asin` `cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
6.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
11.0ms	(cos (- lambda1 lambda2))

series300.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
48.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
10.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
33.0ms	(cos (- lambda1 lambda2))

simplify4.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	4228
3	1385
2	530
1	300
0	172

prune831.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b	(* (sin lambda1) (sin lambda2))
1.0b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `fma-udef` `sin-mult`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
15.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
11.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

416.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
40.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
68.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	5002
3	1732
2	600
1	262
0	131

prune937.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.6b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.4b	(exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2)))))
0.9b	(log (exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.0b	(acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

20.0ms	(* (sin lambda2) (sin lambda1))
4.0ms	(exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2)))))
6.0ms	(log (exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin lambda2) (sin lambda1))
35.0ms	(exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2)))))
14.0ms	(log (exp (acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))))
19.0ms	(acos (fma (cos phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify3.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
6	4279
5	2314
4	1207
3	677
2	322
1	179
0	112

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.6b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
0.2b	(* (sin lambda1) (sin lambda2))
1.0b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
2.6b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 71

Calls

4 calls:

16.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
21.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
9.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
71.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
54.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
4	2715
3	1038
2	425
1	213
0	124

prune782.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.6b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample22.4s

Algorithm

intervals

Results

15.6s	4788×	body	1280	valid
4.6s	2070×	body	640	valid
1.4s	730×	body	320	valid
226.0ms	272×	body	160	valid
83.0ms	16×	body	2560	valid
46.0ms	126×	body	80	valid