Details

sample50.0ms

Algorithm

intervals

Results

28.0ms	90×	body	1280	valid
6.0ms	170×	body	80	valid
6.0ms	35×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	15×	body	160	valid

simplify17.0ms

Calls

1 calls:

Slowest

17.0ms

(- (exp (* a x)) 1)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(expm1 (* a x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

1 calls:

Slowest

0.0ms

(expm1 (* a x))

series41.0ms

Calls

1 calls:

Slowest

41.0ms

(expm1 (* a x))

simplify333.0ms

Calls

4 calls:

Slowest

260.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
37.0ms	(- (exp (* a x)) 1)
34.0ms	(- (exp (* a x)) 1)
2.0ms	(* a x)

prune149.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

9.8b	(cbrt (expm1 (* a x)))
9.8b	(cbrt (expm1 (* a x)))
9.8b	(cbrt (expm1 (* a x)))
0.3b	(* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

8.0ms	(* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))
1.0ms	(cbrt (expm1 (* a x)))
1.0ms	(cbrt (expm1 (* a x)))
1.0ms	(cbrt (expm1 (* a x)))

series507.0ms

Calls

4 calls:

Slowest

150.0ms	(* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))
130.0ms	(cbrt (expm1 (* a x)))
123.0ms	(cbrt (expm1 (* a x)))
105.0ms	(cbrt (expm1 (* a x)))

simplify1.7s

Calls

41 calls:

Slowest

375.0ms	(+ (* 1/6 (* a (* x (exp (* 1/3 (+ (log a) (log x))))))) (+ (exp (* 1/3 (+ (log a) (log x)))) (* 1/36 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (log a) (log x)))))))))
354.0ms	(+ (* 1/6 (* a (* x (exp (* 1/3 (+ (log a) (log x))))))) (+ (exp (* 1/3 (+ (log a) (log x)))) (* 1/36 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (log a) (log x)))))))))
354.0ms	(+ (* 1/6 (* a (* x (exp (* 1/3 (+ (log a) (log x))))))) (+ (exp (* 1/3 (+ (log a) (log x)))) (* 1/36 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (log a) (log x)))))))))
160.0ms	(+ (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))) (+ (* 1/3 (* a (* x (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x)))))))) (* 1/12 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))))))))
43.0ms	(pow (pow (- (exp (* a x)) 1) 2) 1/3)

prune842.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

18.4b	(cbrt (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))
0.1b	(* (expm1 (* a x)) (expm1 (* a x)))
0.1b	(* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x)))
0.1b	(expm1 (* a x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `associate-r` `pow-prod-up`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow2`
2×	`pow3` `*-commutative`
1×	`cbrt-prod` `expm1-log1p` `pow1/3` `rem-cbrt-cube` `expm1-udef`

Calls

4 calls:

Slowest

11.0ms	(* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x)))
7.0ms	(cbrt (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))
4.0ms	(* (expm1 (* a x)) (expm1 (* a x)))
0.0ms	(expm1 (* a x))

series237.0ms

Calls

4 calls:

Slowest

73.0ms	(* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x)))
63.0ms	(* (expm1 (* a x)) (expm1 (* a x)))
62.0ms	(cbrt (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))
39.0ms	(expm1 (* a x))

simplify1.8s

Calls

46 calls:

Slowest

280.0ms	(+ (* 3/2 (* (pow a 4) (pow x 4))) (+ (* 5/4 (* (pow a 5) (pow x 5))) (* (pow a 3) (pow x 3))))
269.0ms	(+ (* 7/12 (* (pow a 4) (pow x 4))) (+ (* (pow a 3) (pow x 3)) (* (pow a 2) (pow x 2))))
263.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
252.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
91.0ms	(* (* (* (* (expm1 (* a x)) (expm1 (* a x))) (* (expm1 (* a x)) (expm1 (* a x)))) (* (expm1 (* a x)) (expm1 (* a x)))) (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))

prune835.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

20.6b	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
20.6b	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
20.6b	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
18.4b	(cbrt (* (* (* (cbrt (* (expm1 (* a x)) (expm1 (* a x)))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (expm1 (* a x))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

61.0ms	(cbrt (* (* (* (cbrt (* (expm1 (* a x)) (expm1 (* a x)))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (expm1 (* a x))))
3.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
2.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
2.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))

series498.0ms

Calls

4 calls:

Slowest

161.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
146.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
141.0ms	(cbrt (* (expm1 (* a x)) (expm1 (* a x))))
49.0ms	(cbrt (* (* (* (cbrt (* (expm1 (* a x)) (expm1 (* a x)))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (expm1 (* a x))))

simplify1.3s

Calls

16 calls:

Slowest

333.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
192.0ms	(+ (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))) (+ (* 1/3 (* a (* x (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x)))))))) (* 1/12 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))))))))
176.0ms	(+ (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))) (+ (* 1/3 (* a (* x (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x)))))))) (* 1/12 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))))))))
175.0ms	(+ (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))) (+ (* 1/3 (* a (* x (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x)))))))) (* 1/12 (* (pow a 2) (* (pow x 2) (exp (* 1/3 (+ (* 2 (log a)) (* 2 (log x))))))))))
56.0ms	(cbrt (* (* (cbrt (* (expm1 (* a x)) (expm1 (* a x)))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))))

prune667.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	2691×	body	1280	valid
408.0ms	5364×	body	80	valid
401.0ms	1348×	body	640	valid
154.0ms	720×	body	320	valid
52.0ms	426×	body	160	valid