Details

sample239.0ms

Algorithm

intervals

Results

102.0ms	83×	body	1280	valid
43.0ms	76×	body	640	valid
39.0ms	300×	body	80	valid
18.0ms	43×	body	320	valid
7.0ms	24×	body	160	valid

simplify280.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

279.0ms

(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize25.0ms

Local error

Found 3 expressions with local error:

3.7b	(- (exp l) (exp (- l)))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

Slowest

72.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
54.0ms	(* J (- (exp l) (exp (- l))))
26.0ms	(- (exp l) (exp (- l)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

111.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
102.0ms	(* J (- (exp l) (exp (- l))))
52.0ms	(- (exp l) (exp (- l)))

simplify8.6s

Counts

80 → 108

Calls

80 calls:

Slowest

653.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
326.0ms	(* (* (* (* J (- (exp l) (exp (- l)))) (* J (- (exp l) (exp (- l))))) (* J (- (exp l) (exp (- l))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
275.0ms	(* J (- (exp l) (exp (* -1 l))))
267.0ms	(* (* J (- (pow (exp l) 3) (pow (exp (- l)) 3))) (cos (/ K 2)))
263.0ms	(+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
0.0b	(* l (fma 1/3 (* l l) 2))
0.0b	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

Slowest

25.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
7.0ms	(* l (fma 1/3 (* l l) 2))
6.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

series523.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

221.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
172.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
130.0ms	(* l (fma 1/3 (* l l) 2))

simplify7.9s

Counts

42 → 76

Calls

42 calls:

Slowest

1.1s	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
494.0ms	(fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))
484.0ms	(cbrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
481.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
455.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize61.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
0.1b	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
0.0b	(* l (fma 1/3 (* l l) 2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

Slowest

31.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
23.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
10.0ms	(* l (fma 1/3 (* l l) 2))

series474.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

225.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
136.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
112.0ms	(* l (fma 1/3 (* l l) 2))

simplify7.4s

Counts

40 → 74

Calls

40 calls:

Slowest

829.0ms	(* (* (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
740.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
498.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))
471.0ms	(+ (log (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (log (cos (/ K 2))))
466.0ms	(sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.2b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))

rewrite18.0ms

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

12.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

266.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
159.0ms	(cbrt (cos (/ K 2)))
144.0ms	(cbrt (cos (/ K 2)))
135.0ms	(cbrt (cos (/ K 2)))

simplify2.0s

Counts

65 → 97

Calls

65 calls:

Slowest

402.0ms	(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
230.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
207.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
184.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
154.0ms	(pow (pow (cos (* 1/2 K)) 2) 1/3)

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes513.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.6s	2595×	body	1280	valid
2.4s	2616×	body	640	valid
1.9s	8518×	body	80	valid
1.4s	1435×	body	320	valid
347.0ms	749×	body	160	valid