Details

sample809.0ms

Algorithm

intervals

Results

528.0ms	159×	body	1280	valid
139.0ms	61×	body	640	valid
26.0ms	23×	body	320	valid
5.0ms	7×	body	160	valid
2.0ms	6×	body	80	valid

simplify49.0ms

Counts: 1 → 1

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize58.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (- lambda1 lambda2))
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
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×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

Slowest

456.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
62.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
40.0ms	(cos (- lambda1 lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.3s

Counts: 90 → 90

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))

rewrite52.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 76

Calls

4 calls:

Slowest

22.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

91.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
73.0ms	(* (sin lambda1) (sin lambda2))
65.0ms	(* (sin phi1) (sin phi2))
29.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.5s

Counts: 88 → 88

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))
0.4b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))))
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))) R)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

Slowest

9.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))) R)
3.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))))
2.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))) R)
51.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2)))))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))
15.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (* (sin phi1) (sin phi2))))))

simplify3.3s

Counts: 82 → 82

prune2.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.7b

localize116.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin lambda2))
0.7b	(cbrt (sin lambda2))
0.7b	(cbrt (sin lambda2))
0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))

rewrite34.0ms

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:

Slowest

24.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
3.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series600.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

168.0ms	(cbrt (sin lambda2))
168.0ms	(cbrt (sin lambda2))
144.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
119.0ms	(cbrt (sin lambda2))

simplify2.3s

Counts: 97 → 97

prune2.2s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.7b

regimes2.1s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch6.0ms

end0.0ms

sample23.8s

Algorithm

intervals

Results

17.2s	4825×	body	1280	valid
4.9s	2040×	body	640	valid
954.0ms	704×	body	320	valid
254.0ms	285×	body	160	valid
100.0ms	12×	body	2560	valid
51.0ms	136×	body	80	valid