Details

sample1.3s

Algorithm

intervals

Results

886.0ms	146×	body	1280	valid
140.0ms	75×	body	640	valid
36.0ms	7×	body	160	valid
25.0ms	22×	body	320	valid
2.0ms	6×	body	80	valid

simplify60.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

60.0ms

(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize75.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (- lambda1 lambda2))
0.5b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* (sin phi2) (sin phi1))

rewrite48.0ms

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` `sin-mult` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

Slowest

22.0ms	(cos (- lambda1 lambda2))
21.0ms	(* (sin phi2) (sin phi1))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

264.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
62.0ms	(* (sin phi2) (sin phi1))
61.0ms	(cos (- lambda1 lambda2))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify1.5s

Counts

35 → 78

Calls

35 calls:

Slowest

335.0ms	(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
137.0ms	(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
134.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
77.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))
76.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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:

Slowest

11.0ms	(* (sin phi2) (sin phi1))
5.0ms	(* 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))))
0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series935.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

482.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
382.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
54.0ms	(* (sin phi2) (sin phi1))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify5.7s

Counts

33 → 77

Calls

33 calls:

Slowest

397.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
380.0ms	(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
378.0ms	(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
370.0ms	(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
363.0ms	(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.0b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

Slowest

21.0ms	(* (sin phi2) (sin phi1))
11.0ms	(* R (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.0ms	(fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

395.0ms	(fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))
84.0ms	(* (sin phi2) (sin phi1))
49.0ms	(* R (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
18.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify5.6s

Counts

33 → 77

Calls

33 calls:

Slowest

368.0ms	(* (* (* R R) R) (* (* (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))) (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))) (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
345.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
344.0ms	(* (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))) R)
344.0ms	(* (* (* (sin phi2) (sin phi2)) (sin phi2)) (* (* (sin phi1) (sin phi1)) (sin phi1)))
343.0ms	(* R (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.4b	(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
0.4b	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.2b	(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

15.0ms	(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
3.0ms	(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
2.0ms	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

40.0ms	(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
39.0ms	(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
19.0ms	(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
18.0ms	(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))

simplify12.0s

Counts

45 → 88

Calls

45 calls:

Slowest

375.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))
371.0ms	(* (* (* R R) R) (* (* (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))) (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))) (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))))
370.0ms	(+ (log R) (log (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))))
366.0ms	(* (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))) R)
365.0ms	(exp (sqrt (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))

prune2.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.9b

regimes1.2s

Accuracy

0% (0.5b remaining)

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

bsearch11.0ms

end0.0ms

sample24.9s

Algorithm

intervals

Results

16.7s	4784×	body	1280	valid
6.4s	2135×	body	640	valid
918.0ms	677×	body	320	valid
206.0ms	260×	body	160	valid
95.0ms	13×	body	2560	valid
78.0ms	132×	body	80	valid