Details

sample452.0ms

Algorithm

intervals

Results

130.0ms	74×	body	2560	valid
129.0ms	58×	body	10240	exit
120.0ms	102×	body	1280	valid
31.0ms	43×	body	640	valid
12.0ms	314×	pre	80	true
4.0ms	10×	body	320	valid
3.0ms	22×	body	80	valid
1.0ms	5×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
5	4110
4	689
3	215
2	98
1	43
0	17

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 56.6b

localize39.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.4b	(- (exp (* b eps)) 1)
5.8b	(- (exp (* a eps)) 1)
7.1b	(- (exp (* (+ a b) eps)) 1)

rewrite103.0ms

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:

67.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
11.0ms	(- (exp (* b eps)) 1)
11.0ms	(- (exp (* a eps)) 1)
13.0ms	(- (exp (* (+ a b) eps)) 1)

series212.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
39.0ms	(- (exp (* b eps)) 1)
50.0ms	(- (exp (* a eps)) 1)
72.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	4122
2	1252
1	378
0	154

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 43.3b

localize77.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))
4.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))))
5.8b	(- (exp (* a eps)) 1)
7.1b	(- (exp (* (+ a b) eps)) 1)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

429.0ms	(+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))
541.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))))
15.0ms	(- (exp (* a eps)) 1)
14.0ms	(- (exp (* (+ a b) eps)) 1)

series1.9s

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))
1.6s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* (* (* eps 1/6) (* (* eps b) (* eps b))) b) (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)))))
32.0ms	(- (exp (* a eps)) 1)
64.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
2	3308
1	673
0	213

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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:

21.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.3s

Counts

23 → 23

Iterations

Iter	Nodes
5	2804
4	1255
3	582
2	281
1	103
0	41

prune226.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 163

Calls

4 calls:

69.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
13.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
14.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
14.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
133.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
138.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
137.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

simplify1.2s

Counts

175 → 175

Iterations

Iter	Nodes
3	3019
2	1070
1	411
0	180

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes253.0ms

Accuracy

0% (3.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	6

end0.0ms

sample20.7s

Algorithm

intervals

Results

6.9s	2610×	body	2560	valid
5.8s	3408×	body	1280	valid
5.4s	2104×	body	10240	exit
1.0s	1088×	body	640	valid
558.0ms	320×	body	320	valid
516.0ms	10106×	pre	80	true
109.0ms	453×	body	80	valid
47.0ms	123×	body	160	valid