Details

sample94.0ms

Algorithm

intervals

Results

41.0ms	91×	body	1280	valid
22.0ms	172×	body	80	valid
12.0ms	38×	body	640	valid
5.0ms	25×	body	320	valid
3.0ms	15×	body	160	valid

simplify19.0ms

Calls

1 calls:

Slowest

19.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(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))

series51.0ms

Calls

1 calls:

Slowest

51.0ms

(expm1 (* a x))

simplify341.0ms

Calls

4 calls:

Slowest

299.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
21.0ms	(- (exp (* a x)) 1)
17.0ms	(- (exp (* a x)) 1)
2.0ms	(* a x)

prune144.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

10.3b	(cbrt (expm1 (* a x)))
10.3b	(cbrt (expm1 (* a x)))
10.3b	(cbrt (expm1 (* a x)))
0.3b	(* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))

rewrite22.0ms

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

16.0ms	(* (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)))

series502.0ms

Calls

4 calls:

Slowest

145.0ms	(* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))
134.0ms	(cbrt (expm1 (* a x)))
125.0ms	(cbrt (expm1 (* a x)))
98.0ms	(cbrt (expm1 (* a x)))

simplify1.8s

Calls

41 calls:

Slowest

409.0ms	(+ (* 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)))))))))
406.0ms	(+ (* 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)))))))))
387.0ms	(+ (* 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))))))))))
48.0ms	(pow (pow (- (exp (* a x)) 1) 2) 1/3)

prune745.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b	(cbrt (expm1 (* a x)))
10.3b	(cbrt (expm1 (* a x)))
10.3b	(cbrt (expm1 (* a x)))
10.3b	(cbrt (expm1 (* a x)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series422.0ms

Calls

4 calls:

Slowest

114.0ms	(cbrt (expm1 (* a x)))
113.0ms	(cbrt (expm1 (* a x)))
104.0ms	(cbrt (expm1 (* a x)))
91.0ms	(cbrt (expm1 (* a x)))

simplify1.6s

Calls

24 calls:

Slowest

353.0ms	(+ (* 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)))))))))
352.0ms	(+ (* 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)))))))))
329.0ms	(+ (* 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)))))))))
295.0ms	(+ (* 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)))))))))
41.0ms	(pow (- (exp (* a x)) 1) 1/3)

prune780.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

17.3b	(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)))
0.0b	(expm1 (* a x))

rewrite42.0ms

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

15.0ms	(* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x)))
15.0ms	(cbrt (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))
10.0ms	(* (expm1 (* a x)) (expm1 (* a x)))
0.0ms	(expm1 (* a x))

series211.0ms

Calls

4 calls:

Slowest

62.0ms	(* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x)))
55.0ms	(expm1 (* a x))
53.0ms	(* (expm1 (* a x)) (expm1 (* a x)))
42.0ms	(cbrt (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))))

simplify1.9s

Calls

46 calls:

Slowest

288.0ms	(+ (* 7/12 (* (pow a 4) (pow x 4))) (+ (* (pow a 3) (pow x 3)) (* (pow a 2) (pow x 2))))
276.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
244.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
209.0ms	(+ (* 3/2 (* (pow a 4) (pow x 4))) (+ (* 5/4 (* (pow a 5) (pow x 5))) (* (pow a 3) (pow x 3))))
115.0ms	(* (* (* (* (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))))

prune849.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2708×	body	1280	valid
781.0ms	1332×	body	640	valid
309.0ms	5383×	body	80	valid
128.0ms	768×	body	320	valid
48.0ms	433×	body	160	valid