Details

sample618.0ms

Algorithm

intervals

Results

230.0ms	95×	body	2560	valid
177.0ms	100×	body	1280	valid
132.0ms	60×	body	10240	exit
27.0ms	31×	body	640	valid
16.0ms	316×	pre	80	true
10.0ms	17×	body	320	valid
2.0ms	4×	body	160	valid
1.0ms	9×	body	80	valid

simplify317.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

316.0ms

(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.5b

localize43.0ms

Local error

Found 4 expressions with local error:

5.3b	(- (exp (* (+ a b) eps)) 1)
4.7b	(- (exp (* a eps)) 1)
1.9b	(- (exp (* b eps)) 1)
0.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity`
10×	`flip3--` `flip--` `add-log-exp`
8×	`associate-/r/`
6×	`difference-of-squares`
4×	`frac-times` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `add-cube-cbrt` `cbrt-unprod` `insert-posit16`
3×	`sub-neg` `diff-log` `difference-of-sqr-1` `distribute-lft-out--`
2×	`associate-*l/` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l`

Counts

4 → 83

Calls

4 calls:

Slowest

51.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
27.0ms	(- (exp (* (+ a b) eps)) 1)
14.0ms	(- (exp (* a eps)) 1)
11.0ms	(- (exp (* b eps)) 1)

series381.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

238.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
64.0ms	(- (exp (* (+ a b) eps)) 1)
42.0ms	(- (exp (* b eps)) 1)
37.0ms	(- (exp (* a eps)) 1)

simplify15.4s

Counts

54 → 95

Calls

54 calls:

Slowest

1.6s	(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
1.4s	(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* a eps)) 1)) (- (exp (* a eps)) 1)) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1))))
1.3s	(/ (* (* (* eps eps) eps) (* (* (- (exp (* (+ a b) eps)) 1) (- (exp (* (+ a b) eps)) 1)) (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* a eps)) 1)) (- (exp (* a eps)) 1)) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1))))
1.3s	(/ (* (* (* eps eps) eps) (* (* (- (exp (* (+ a b) eps)) 1) (- (exp (* (+ a b) eps)) 1)) (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
806.0ms	(+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1)))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16`

Counts

1 → 20

Calls

1 calls:

Slowest

13.0ms

(+ (/ 1 a) (/ 1 b))

series26.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

26.0ms

(+ (/ 1 a) (/ 1 b))

simplify186.0ms

Counts

16 → 23

Calls

16 calls:

Slowest

23.0ms	(* (exp (/ 1 a)) (exp (/ 1 b)))
17.0ms	(+ (/ 1 a) (/ 1 b))
15.0ms	(+ (/ 1 a) (/ 1 b))
15.0ms	(+ (* 1 b) (* a 1))
14.0ms	(+ (/ 1 a) (/ 1 b))

prune181.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

15.3b

(/ (+ b a) (* a b))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-cbrt-cube` `add-exp-log`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out` `associate-/l/`
1×	`pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 26

Calls

1 calls:

Slowest

20.0ms

(/ (+ b a) (* a b))

series58.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

58.0ms

(/ (+ b a) (* a b))

simplify617.0ms

Counts

19 → 29

Calls

19 calls:

Slowest

232.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
181.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
41.0ms	(- (log (+ b a)) (log (* a b)))
40.0ms	(- (log (+ b a)) (+ (log a) (log b)))
24.0ms	(+ (pow b 3) (pow a 3))

prune212.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

10.1b	(* (/ 1 a) (/ (+ b a) b))
0.0b	(/ (+ b a) b)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`times-frac`
26×	`add-exp-log` `add-cube-cbrt`
16×	`add-cbrt-cube` `associate-r`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp`
7×	`distribute-lft-out`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`pow1` `cbrt-unprod` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

2 → 94

Calls

2 calls:

Slowest

23.0ms	(* (/ 1 a) (/ (+ b a) b))
13.0ms	(/ (+ b a) b)

series105.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

68.0ms	(* (/ 1 a) (/ (+ b a) b))
37.0ms	(/ (+ b a) b)

simplify4.2s

Counts

93 → 100

Calls

93 calls:

Slowest

330.0ms	(* (/ (* (* 1 1) 1) (* (* a a) a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
329.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b))
297.0ms	(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
179.0ms	(+ (- 0 (log a)) (- (log (+ b a)) (log b)))
173.0ms	(* (/ 1 a) (/ (+ b a) b))

prune831.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes200.0ms

Accuracy

93% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 3.4b

bsearch14.0ms

end0.0ms

sample19.8s

Algorithm

intervals

Results

6.2s	3375×	body	1280	valid
5.9s	2590×	body	2560	valid
4.9s	2013×	body	10240	exit
1.4s	1047×	body	640	valid
594.0ms	10013×	pre	80	true
227.0ms	389×	body	320	valid
80.0ms	143×	body	160	valid
78.0ms	456×	body	80	valid