Details

sample88.0ms

Algorithm

intervals

Results

42.0ms	92×	body	1280	valid
13.0ms	39×	body	640	valid
12.0ms	169×	body	80	valid
5.0ms	24×	body	320	valid
2.0ms	11×	body	160	valid

simplify92.0ms

Calls

1 calls:

Slowest

92.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize18.0ms

Local error

Found 2 expressions with local error:

3.5b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`exp-prod`
11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr` `rem-exp-log`

Calls

2 calls:

Slowest

48.0ms	(- (exp (* a x)) 1)
13.0ms	(exp (* a x))

series75.0ms

Calls

2 calls:

Slowest

52.0ms	(- (exp (* a x)) 1)
22.0ms	(exp (* a x))

simplify1.9s

Calls

27 calls:

Slowest

229.0ms	(/ (exp (exp (* a x))) (exp 1))
218.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
183.0ms	(exp (* a (* (cbrt x) (cbrt x))))
144.0ms	(- (sqrt (exp (* a x))) 1)
140.0ms	(+ (sqrt (exp (* a x))) (sqrt 1))

prune461.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

14.6b	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
1.8b	(* x (* (* a 1/6) (* (* a x) (* a x))))
1.5b	(* (* a 1/6) (* (* a x) (* a x)))
0.3b	(* a 1/6)

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

311×	`associate-r`
301×	`add-sqr-sqrt`
187×	`unswap-sqr`
142×	`associate-l`
128×	`*-un-lft-identity`
100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
45×	`*-commutative`
43×	`distribute-lft-out`
40×	`swap-sqr` `add-cube-cbrt`
28×	`distribute-rgt-out`
12×	`distribute-rgt1-in`
9×	`add-log-exp`
4×	`insert-posit16`
3×	`sum-log`
2×	`+-commutative` `associate-+l+`
1×	`flip3-+` `flip-+`

Calls

4 calls:

Slowest

3.3s	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
483.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
137.0ms	(* (* a 1/6) (* (* a x) (* a x)))
5.0ms	(* a 1/6)

series328.0ms

Calls

4 calls:

Slowest

146.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
80.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
68.0ms	(* (* a 1/6) (* (* a x) (* a x)))
34.0ms	(* a 1/6)

simplify1.1m

Calls

366 calls:

Slowest

947.0ms	(* (* (cbrt a) 1/6) (* (* a x) (* a x)))
910.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
818.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* (* a x) (* a x))) (* (* a x) (* a x)))))
747.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x)))))
703.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))))

prune3.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (sqrt (exp (* a x))) 1)
0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(sqrt (exp (* a x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
30×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
14×	`sqrt-pow1` `add-cube-cbrt`
11×	`add-log-exp`
9×	`associate-r` `associate-l`
7×	`sqrt-prod`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
3×	`exp-to-pow` `*-commutative` `unswap-sqr`
2×	`difference-of-sqr-1` `distribute-lft-out--` `rem-exp-log`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `diff-log` `flip--`

Calls

4 calls:

Slowest

47.0ms	(- (sqrt (exp (* a x))) 1)
18.0ms	(sqrt (exp (* a x)))
18.0ms	(exp (* a x))
15.0ms	(exp (* a x))

series168.0ms

Calls

4 calls:

Slowest

85.0ms	(- (sqrt (exp (* a x))) 1)
39.0ms	(sqrt (exp (* a x)))
22.0ms	(exp (* a x))
22.0ms	(exp (* a x))

simplify4.0s

Calls

72 calls:

Slowest

238.0ms	(exp (* a (* (cbrt x) (cbrt x))))
232.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
186.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
184.0ms	(exp (* a (* (cbrt x) (cbrt x))))
171.0ms	(exp (* a (* (cbrt x) (cbrt x))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (sqrt (exp (* a x))) 1)
3.5b	(- (sqrt (exp (* a x))) 1)
3.5b	(- (sqrt (exp (* a x))) 1)
0.0b	(cbrt (- (sqrt (exp (* a x))) 1))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
16×	`sqrt-prod` `difference-of-squares`
11×	`cbrt-prod`
10×	`add-log-exp`
8×	`difference-of-sqr-1` `distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Calls

4 calls:

Slowest

60.0ms	(- (sqrt (exp (* a x))) 1)
60.0ms	(- (sqrt (exp (* a x))) 1)
33.0ms	(cbrt (- (sqrt (exp (* a x))) 1))
30.0ms	(- (sqrt (exp (* a x))) 1)

series412.0ms

Calls

4 calls:

Slowest

179.0ms	(cbrt (- (sqrt (exp (* a x))) 1))
82.0ms	(- (sqrt (exp (* a x))) 1)
77.0ms	(- (sqrt (exp (* a x))) 1)
74.0ms	(- (sqrt (exp (* a x))) 1)

simplify8.9s

Calls

67 calls:

Slowest

516.0ms	(cbrt (- (pow (sqrt (exp (* a x))) 3) (pow 1 3)))
383.0ms	(pow (- (sqrt (exp (* a x))) 1) 1/3)
369.0ms	(pow (- (sqrt (exp (* a x))) 1) 1/3)
218.0ms	(cbrt (- (* (sqrt (exp (* a x))) (sqrt (exp (* a x)))) (* 1 1)))
207.0ms	(+ (* 1/8 (* (pow a 2) (pow x 2))) (+ (* 1/2 (* a x)) (* 1/48 (* (pow a 3) (pow x 3)))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes300.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.9b

bsearch12.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	2585×	body	1280	valid
424.0ms	5531×	body	80	valid
341.0ms	1334×	body	640	valid
187.0ms	780×	body	320	valid
46.0ms	402×	body	160	valid