Details

sample1.2s

Algorithm

intervals

Results

557.0ms	159×	body	1280	valid
99.0ms	50×	body	640	valid
30.0ms	24×	body	320	valid
7.0ms	17×	body	80	valid
5.0ms	6×	body	160	valid

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	80
4	80
3	77
2	47
1	28
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

22.0ms	(* (cos phi1) (sin phi2))
53.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series253.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi1) (sin phi2))
138.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
37.0ms	(sin (- lambda1 lambda2))

simplify2.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	3138
2	1015
1	452
0	226

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.3b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
39.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series451.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cos phi1) (sin phi2))
208.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
163.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	4753
2	1387
1	496
0	230

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize118.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `insert-posit16` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 101

Calls

4 calls:

103.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (sin lambda1) (sin lambda2))
72.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
74.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
60.0ms	(* (sin lambda1) (sin lambda2))
169.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
146.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify4.4s

Counts

113 → 113

Iterations

Iter	Nodes
3	9211
2	1716
1	448
0	175

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `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 → 85

Calls

4 calls:

12.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
1.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))

series459.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
116.0ms	(cbrt (sin lambda2))
111.0ms	(cbrt (sin lambda2))
100.0ms	(cbrt (sin lambda2))

simplify1.8s

Counts

97 → 97

Iterations

Iter	Nodes
4	4250
3	1199
2	433
1	180
0	81

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes663.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	39
1	39
0	28

end0.0ms

sample21.4s

Algorithm

intervals

Results

15.2s	4624×	body	1280	valid
4.6s	1925×	body	640	valid
851.0ms	573×	body	320	valid
285.0ms	667×	body	80	valid
174.0ms	211×	body	160	valid