Details

sample76.0ms

Algorithm

intervals

Results

34.0ms	85×	body	1280	valid
12.0ms	44×	body	640	valid
11.0ms	200×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify64.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

64.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

Slowest

11.0ms	(- (exp (* a x)) 1)
4.0ms	(exp (* a x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

50.0ms	(- (exp (* a x)) 1)
14.0ms	(exp (* a x))

simplify1.3s

Counts

16 → 34

Calls

16 calls:

Slowest

221.0ms	(/ (exp (exp (* a x))) (exp 1))
167.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
140.0ms	(- (sqrt (exp (* a x))) (sqrt 1))
134.0ms	(- (sqrt (exp (* a x))) 1)
121.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))

prune311.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

12.3b	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
2.3b	(* x (* (* a 1/6) (* (* a x) (* a x))))
1.8b	(* (* a 1/6) (* (* a x) (* a x)))
0.3b	(* a 1/6)

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

Slowest

186.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
120.0ms	(* (* a 1/6) (* (* a x) (* a x)))
74.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
10.0ms	(* a 1/6)

series286.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
75.0ms	(* x (* (* a 1/6) (* (* a x) (* a x))))
56.0ms	(* (* a 1/6) (* (* a x) (* a x)))
15.0ms	(* a 1/6)

simplify27.8s

Counts

91 → 132

Calls

91 calls:

Slowest

1.0s	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x)))))
801.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* (* a x) (* a x))) (* (* a x) (* a x)))))
752.0ms	(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) 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)))))
709.0ms	(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))))

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(exp (* a x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 46

Calls

4 calls:

Slowest

61.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
5.0ms	(exp (* a x))
4.0ms	(exp (* a x))
4.0ms	(exp (* a x))

series111.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

43.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
24.0ms	(exp (* a x))
23.0ms	(exp (* a x))
22.0ms	(exp (* a x))

simplify1.3s

Counts

22 → 58

Calls

22 calls:

Slowest

423.0ms	(/ (exp (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp 1))
195.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
190.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
136.0ms	(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
123.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))

prune714.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
2.9b	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
2.9b	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
0.1b	(cbrt (- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`cbrt-prod` `sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 53

Calls

4 calls:

Slowest

75.0ms	(cbrt (- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1))
68.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
58.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
56.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)

series282.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(cbrt (- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1))
46.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
44.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)
37.0ms	(- (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x)))) 1)

simplify4.2s

Counts

20 → 65

Calls

20 calls:

Slowest

519.0ms	(+ (* 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)))))))))
432.0ms	(/ (exp (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp 1))
416.0ms	(pow (- (exp (* a x)) 1) 1/3)
392.0ms	(/ (exp (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp 1))
390.0ms	(/ (exp (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp 1))

prune903.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes483.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch12.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	2704×	body	1280	valid
423.0ms	1304×	body	640	valid
320.0ms	5363×	body	80	valid
138.0ms	757×	body	320	valid
49.0ms	402×	body	160	valid