Details

sample169.0ms

Algorithm

intervals

Results

52.0ms	279×	body	80	valid
50.0ms	27×	body	1280	valid
31.0ms	37×	body	640	valid
12.0ms	24×	body	320	valid
3.0ms	10×	body	160	valid

simplify370.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

369.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize32.0ms

Local error

Found 4 expressions with local error:

4.6b	(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))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

Slowest

26.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
9.0ms	(cos (/ (+ phi2 phi1) 2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

670.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
535.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
123.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
25.0ms	(cos (/ (+ phi2 phi1) 2))

simplify3.5s

Counts

34 → 79

Calls

34 calls:

Slowest

505.0ms	(* (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (* R R) R))
404.0ms	(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
310.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
273.0ms	(- (+ (* 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))))))
271.0ms	(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize39.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ phi2 phi1) 2))
0.5b	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.3b	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.2b	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

16.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
0.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
75.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
53.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
36.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Counts

27 → 71

Calls

27 calls:

Slowest

426.0ms	(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
387.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
315.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
298.0ms	(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
182.0ms	(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ phi2 phi1) 2))
0.5b	(expm1 (cos (/ (+ phi2 phi1) 2)))
0.3b	(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.3b	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

Slowest

14.0ms	(cos (/ (+ phi2 phi1) 2))
1.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
1.0ms	(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(log1p (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
77.0ms	(expm1 (cos (/ (+ phi2 phi1) 2)))
52.0ms	(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
33.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

15 → 58

Calls

15 calls:

Slowest

352.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
309.0ms	(- (log 2) (+ (* 1/8 (* phi1 phi2)) (* 1/16 (pow phi2 2))))
297.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
248.0ms	(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))
40.0ms	(log (+ (cos (* 1/2 (+ phi1 phi2))) 1))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.0b

localize54.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ phi2 phi1) 2))
4.6b	(cos (/ (+ phi2 phi1) 2))
4.6b	(cos (/ (+ phi2 phi1) 2))
0.7b	(* (expm1 (cos (/ (+ phi2 phi1) 2))) (expm1 (cos (/ (+ phi2 phi1) 2))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

Slowest

16.0ms	(cos (/ (+ phi2 phi1) 2))
16.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))
11.0ms	(* (expm1 (cos (/ (+ phi2 phi1) 2))) (expm1 (cos (/ (+ phi2 phi1) 2))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(* (expm1 (cos (/ (+ phi2 phi1) 2))) (expm1 (cos (/ (+ phi2 phi1) 2))))
38.0ms	(cos (/ (+ phi2 phi1) 2))
34.0ms	(cos (/ (+ phi2 phi1) 2))
24.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.6s

Counts

33 → 70

Calls

33 calls:

Slowest

414.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
375.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
317.0ms	(- (+ (pow E 2) (+ (* 1/2 (* E (* phi1 phi2))) (+ (* 1/4 (* E (pow phi2 2))) 1))) (+ (* 1/2 (* (pow E 2) (* phi1 phi2))) (+ (* 2 E) (* 1/4 (* (pow E 2) (pow phi2 2))))))
294.0ms	(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
275.0ms	(pow (- (exp (cos (* 1/2 (+ phi1 phi2)))) 1) 2)

prune1.3s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 3.0b

regimes978.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch4.0ms

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.1s	8375×	body	80	valid
1.6s	811×	body	1280	valid
1.4s	1313×	body	640	valid
1.1s	754×	body	320	valid
174.0ms	370×	body	160	valid