Details

sample539.0ms

Algorithm

intervals

Results

305.0ms	114×	body	1280	valid
157.0ms	75×	body	640	valid
35.0ms	35×	body	320	valid
10.0ms	15×	body	160	valid
5.0ms	17×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	23
2	23
1	20
0	14

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.4b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 65

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
10.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

series244.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
175.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms	(cos (- lambda1 lambda2))
33.0ms	(sin (- lambda1 lambda2))

simplify3.2s

Counts

77 → 77

Iterations

Iter	Nodes
5	4322
4	1564
3	745
2	408
1	283
0	176

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
2.7b	(sin (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sin-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×	`sub-neg` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
11.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
16.0ms	(sin (- lambda1 lambda2))

series440.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
72.0ms	(* (sin lambda1) (sin lambda2))
314.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
42.0ms	(sin (- lambda1 lambda2))

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
4	5834
3	1557
2	627
1	331
0	188

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

19.0ms	(* (sin lambda1) (cos lambda2))
63.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
14.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series549.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (cos lambda2))
168.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
61.0ms	(* (sin lambda1) (sin lambda2))
252.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.7s

Counts

96 → 96

Iterations

Iter	Nodes
3	3430
2	1062
1	387
0	168

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
0.2b	(* (sin lambda2) (sin lambda1))
0.5b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
0.6b	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

rewrite19.0ms

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-prod` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `associate-l` `fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

2.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
11.0ms	(* (sin lambda2) (sin lambda1))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
4.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

403.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
75.0ms	(* (sin lambda2) (sin lambda1))
295.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
283.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
4	4621
3	1355
2	518
1	238
0	120

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes894.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample17.5s

Algorithm

intervals

Results

11.0s	3557×	body	1280	valid
4.5s	2398×	body	640	valid
1.1s	925×	body	320	valid
260.0ms	400×	body	160	valid
201.0ms	720×	body	80	valid