Details

sample1.1s

Algorithm

intervals

Results

624.0ms	162×	body	1280	valid
194.0ms	66×	body	640	valid
31.0ms	20×	body	320	valid
9.0ms	1×	body	2560	valid
4.0ms	5×	body	160	valid
1.0ms	3×	body	80	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	39
3	39
2	38
1	27
0	17

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.3b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.1b	(cos (- lambda1 lambda2))

rewrite26.0ms

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))))
16.0ms	(cos (- lambda1 lambda2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
24.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
39.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
4	3233
3	1101
2	480
1	286
0	172

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.3b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.2b	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.3b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.7b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite25.0ms

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:

11.0ms	(* (sin phi2) (sin phi1))
0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
12.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin phi2) (sin phi1))
376.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
48.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.6s

Counts

77 → 77

Iterations

Iter	Nodes
4	4440
3	1360
2	546
1	251
0	130

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.2b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* R (log1p (expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
0.5b	(expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.7b	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

rewrite25.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `expm1-log1p` `sin-mult` `expm1-udef`

Counts

4 → 66

Calls

4 calls:

17.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* R (log1p (expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
0.0ms	(expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin phi1) (sin phi2))
104.0ms	(* R (log1p (expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
70.0ms	(expm1 (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
10.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify2.3s

Counts

78 → 78

Iterations

Iter	Nodes
5	3231
4	1690
3	921
2	405
1	196
0	115

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(* R (log1p (- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)))
0.4b	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.5b	(- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)
0.7b	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-log-exp`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l`
2×	`acos-asin` `difference-of-squares`
1×	`expm1-def` `sub-neg` `flip3--` `exp-diff` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr` `rem-exp-log`

Counts

4 → 79

Calls

4 calls:

11.0ms	(* R (log1p (- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)))
4.0ms	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
11.0ms	(- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)
1.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* R (log1p (- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)))
29.0ms	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
58.0ms	(- (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))) 1)
10.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify12.3s

Counts

91 → 91

Iterations

Iter	Nodes
5	6281
4	1904
3	871
2	434
1	236
0	134

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.1b

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
2	33
1	33
0	28

end0.0ms

sample24.8s

Algorithm

intervals

Results

18.2s	4747×	body	1280	valid
4.8s	2174×	body	640	valid
979.0ms	670×	body	320	valid
221.0ms	287×	body	160	valid
128.0ms	14×	body	2560	valid
43.0ms	110×	body	80	valid