Details

sample523.0ms

Algorithm

intervals

Results

159.0ms	81×	body	2560	valid
150.0ms	112×	body	1280	valid
146.0ms	67×	body	10240	exit
25.0ms	36×	body	640	valid
16.0ms	323×	pre	80	true
4.0ms	7×	body	320	valid
3.0ms	16×	body	80	valid
2.0ms	4×	body	160	valid

simplify670.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

670.0ms

(/ (* 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: 57.8b

localize53.0ms

Local error

Found 4 expressions with local error:

4.3b	(- (exp (* (+ a b) eps)) 1)
3.9b	(- (exp (* b eps)) 1)
1.3b	(- (exp (* a eps)) 1)
0.7b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
10×	`add-log-exp` `difference-of-squares`
9×	`flip3--` `flip--`
7×	`associate-r` `associate-l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
4×	`frac-times` `insert-posit16`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

Slowest

85.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
25.0ms	(- (exp (* a eps)) 1)
22.0ms	(- (exp (* b eps)) 1)
13.0ms	(- (exp (* (+ a b) eps)) 1)

series209.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(- (exp (* (+ a b) eps)) 1)
57.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
49.0ms	(- (exp (* b eps)) 1)
37.0ms	(- (exp (* a eps)) 1)

simplify12.7s

Counts

66 → 102

Calls

66 calls:

Slowest

634.0ms	(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
457.0ms	(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))
451.0ms	(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
426.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
410.0ms	(* (- (exp (* eps b)) 1) (- (exp (* a eps)) 1))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 46.2b

localize82.0ms

Local error

Found 4 expressions with local error:

4.3b	(- (exp (* (+ a b) eps)) 1)
3.9b	(- (exp (* b eps)) 1)
3.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
3.0b	(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-/r/` `add-log-exp`
7×	`associate-r`
6×	`pow1` `flip3-+` `associate-*r/` `add-cube-cbrt` `flip-+` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `sub-neg` `div-exp` `associate-*l/` `insert-posit16`
3×	`difference-of-sqr-1` `associate-l` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `pow-prod-down` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

Slowest

3.7s	(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
783.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
17.0ms	(- (exp (* (+ a b) eps)) 1)
12.0ms	(- (exp (* b eps)) 1)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
169.0ms	(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
75.0ms	(- (exp (* (+ a b) eps)) 1)
37.0ms	(- (exp (* b eps)) 1)

simplify20.5s

Counts

77 → 113

Calls

77 calls:

Slowest

1.3s	(* (+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))) (+ (exp (* b eps)) 1))
1.2s	(* (* (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))) (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1)))
749.0ms	(* (+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))) (+ (exp (* b eps)) 1))
636.0ms	(* (- (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps))))) (- (pow (exp (* b eps)) 3) (pow 1 3)))
588.0ms	(+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))))

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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

10.0ms

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

series17.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

17.0ms

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

simplify222.0ms

Counts

16 → 23

Calls

16 calls:

Slowest

25.0ms	(* (exp (/ 1 a)) (exp (/ 1 b)))
20.0ms	(+ (/ 1 a) (/ 1 b))
17.0ms	(+ (/ 1 b) (/ 1 a))
17.0ms	(+ (/ 1 a) (/ 1 b))
17.0ms	(+ (/ 1 a) (/ 1 b))

prune201.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

14.3b

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

rewrite34.0ms

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

33.0ms

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

series68.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

68.0ms

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

simplify732.0ms

Counts

19 → 29

Calls

19 calls:

Slowest

300.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
182.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
53.0ms	(- (log (+ b a)) (+ (log a) (log b)))
50.0ms	(- (log (+ b a)) (log (* a b)))
31.0ms	(- (* b b) (* a a))

prune231.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.0b and baseline of 3.4b

bsearch1.0ms

end0.0ms

sample19.8s

Algorithm

intervals

Results

6.3s	2609×	body	2560	valid
5.8s	3405×	body	1280	valid
4.4s	2011×	body	10240	exit
1.4s	1042×	body	640	valid
974.0ms	10013×	pre	80	true
286.0ms	366×	body	320	valid
118.0ms	455×	body	80	valid
83.0ms	125×	body	160	valid