Details

sample136.0ms

Algorithm

intervals

Results

57.0ms	269×	body	80	valid
24.0ms	38×	body	640	valid
23.0ms	24×	body	1280	valid
8.0ms	19×	body	320	valid
5.0ms	14×	body	160	valid

simplify233.0ms

Calls

1 calls:

Slowest

233.0ms

(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi2 phi1) 2))
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`associate-l/` `-commutative`
1×	`hypot-udef` `flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`

Calls

4 calls:

Slowest

12.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
5.0ms	(cos (/ (+ phi2 phi1) 2))
0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series948.0ms

Calls

4 calls:

Slowest

455.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
373.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
86.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
34.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Calls

24 calls:

Slowest

364.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
338.0ms	(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
307.0ms	(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
271.0ms	(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* phi1 (* R phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)) (/ (* phi1 (* lambda2 (* R phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))))))
201.0ms	(+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* R (* phi1 phi2)) (* lambda1 (cos (* 1/2 (+ phi1 phi2))))) (/ (* R (* lambda2 (* phi1 phi2))) (* (pow lambda1 2) (cos (* 1/2 (+ phi1 phi2)))))))

prune937.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize3.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi2 phi1) 2))
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`associate-l/` `-commutative`
1×	`hypot-udef` `flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`

Calls

4 calls:

Slowest

6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.0ms	(cos (/ (+ phi2 phi1) 2))
1.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series926.0ms

Calls

4 calls:

Slowest

466.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
371.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
69.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
19.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Calls

25 calls:

Slowest

356.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
351.0ms	(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
301.0ms	(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* R (* lambda2 (* phi1 phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))) (/ (* R (* phi1 phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)))))
243.0ms	(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
203.0ms	(+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* phi1 (* R phi2)) (* lambda1 (cos (* 1/2 (+ phi1 phi2))))) (/ (* phi1 (* lambda2 (* R phi2))) (* (pow lambda1 2) (cos (* 1/2 (+ phi1 phi2)))))))

prune907.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi2 phi1) 2))
0.4b	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.2b	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.2b	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `expm1-udef`

Calls

4 calls:

Slowest

7.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
2.0ms	(cos (/ (+ phi2 phi1) 2))
0.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series245.0ms

Calls

4 calls:

Slowest

118.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
55.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
53.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
19.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.1s

Calls

24 calls:

Slowest

333.0ms	(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
304.0ms	(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
299.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
283.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
184.0ms	(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi2 phi1) 2))
2.5b	(cos (/ (+ phi2 phi1) 2))
2.5b	(cos (/ (+ phi2 phi1) 2))
0.5b	(cbrt (cos (/ (+ phi2 phi1) 2)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Calls

4 calls:

Slowest

2.0ms	(cos (/ (+ phi2 phi1) 2))
2.0ms	(cos (/ (+ phi2 phi1) 2))
2.0ms	(cos (/ (+ phi2 phi1) 2))
1.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))

series161.0ms

Calls

4 calls:

Slowest

114.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))
17.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))
14.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.5s

Calls

15 calls:

Slowest

344.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
334.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
315.0ms	(- 1 (+ (* 1/12 (* phi1 phi2)) (* 1/24 (pow phi2 2))))
283.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
42.0ms	(pow (cos (* 1/2 (+ phi1 phi2))) 1/3)

prune928.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

regimes900.0ms

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch2.0ms

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.1s	8425×	body	80	valid
1.5s	1283×	body	640	valid
1.2s	788×	body	1280	valid
1.1s	731×	body	320	valid
554.0ms	338×	body	160	valid