Details

sample581.0ms

Algorithm

intervals

Results

200.0ms	73×	body	10240	exit
174.0ms	84×	body	2560	valid
136.0ms	112×	body	1280	valid
20.0ms	25×	body	640	valid
16.0ms	329×	pre	80	true
7.0ms	13×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	13×	body	80	valid

simplify315.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

315.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize68.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (exp (* (+ a b) eps)) 1)
4.5b	(- (exp (* a eps)) 1)
2.9b	(- (exp (* b eps)) 1)
0.2b	(* (- (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

102.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
15.0ms	(- (exp (* (+ a b) eps)) 1)
14.0ms	(- (exp (* b eps)) 1)
12.0ms	(- (exp (* a eps)) 1)

series273.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
79.0ms	(- (exp (* (+ a b) eps)) 1)
57.0ms	(- (exp (* b eps)) 1)
55.0ms	(- (exp (* a eps)) 1)

simplify12.5s

Counts

66 → 102

Calls

66 calls:

Slowest

725.0ms	(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
503.0ms	(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))
451.0ms	(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
388.0ms	(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
388.0ms	(* (- (exp (* eps b)) 1) (- (exp (* a eps)) 1))

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.5b

localize83.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (exp (* (+ a b) eps)) 1)
4.5b	(- (exp (* a eps)) 1)
3.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
2.2b	(* eps (* b (* (* eps b) (* eps b))))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
29×	`pow1`
23×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`add-cube-cbrt`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `insert-posit16` `difference-of-squares`
3×	`flip3-+` `associate-l` `flip-+`
2×	`sub-neg` `diff-log` `difference-of-sqr-1` `associate-*l/` `distribute-lft-out--` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

Slowest

256.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
204.0ms	(* eps (* b (* (* eps b) (* eps b))))
15.0ms	(- (exp (* (+ a b) eps)) 1)
12.0ms	(- (exp (* a eps)) 1)

series1.8s

Counts

4 → 12

Calls

4 calls:

Slowest

1.7s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
74.0ms	(* eps (* b (* (* eps b) (* eps b))))
50.0ms	(- (exp (* (+ a b) eps)) 1)
36.0ms	(- (exp (* a eps)) 1)

simplify13.5s

Counts

68 → 109

Calls

68 calls:

Slowest

835.0ms	(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))))))
737.0ms	(* (+ (exp (* a eps)) 1) (+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))))))
516.0ms	(/ (exp (exp (* a eps))) (exp 1))
461.0ms	(+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
438.0ms	(* (* (* eps eps) eps) (* (* (* b b) b) (* (* (* (* eps eps) eps) (* (* b b) b)) (* (* (* eps b) (* eps b)) (* eps b)))))

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

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

21.0ms

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

series25.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

25.0ms

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

simplify219.0ms

Counts

16 → 23

Calls

16 calls:

Slowest

25.0ms	(* (exp (/ 1 a)) (exp (/ 1 b)))
22.0ms	(+ (/ 1 a) (/ 1 b))
18.0ms	(+ (/ 1 a) (/ 1 b))
17.0ms	(+ (/ 1 a) (/ 1 b))
17.0ms	(+ (/ 1 a) (/ 1 b))

prune227.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

12.2b

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

rewrite19.0ms

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

18.0ms

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

series59.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

59.0ms

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

simplify670.0ms

Counts

19 → 29

Calls

19 calls:

Slowest

239.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
175.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
47.0ms	(+ (pow b 3) (pow a 3))
42.0ms	(- (log (+ b a)) (+ (log a) (log b)))
40.0ms	(- (* b b) (* a a))

prune233.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes189.0ms

Accuracy

0% (3.3b remaining)

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

bsearch2.0ms

end0.0ms

sample19.9s

Algorithm

intervals

Results

6.4s	2550×	body	2560	valid
5.2s	3502×	body	1280	valid
4.7s	1991×	body	10240	exit
1.7s	1016×	body	640	valid
965.0ms	9995×	pre	80	true
228.0ms	356×	body	320	valid
116.0ms	457×	body	80	valid
48.0ms	123×	body	160	valid