Details

sample477.0ms

Algorithm

intervals

Results

159.0ms	86×	body	2560	valid
109.0ms	71×	body	10240	exit
102.0ms	114×	body	1280	valid
64.0ms	33×	body	640	valid
8.0ms	327×	pre	80	true
2.0ms	16×	body	80	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4020
4	765
3	258
2	101
1	40
0	17

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* a eps)) 1.0)
3.6b	(- (exp (* b eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

103.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* a eps)) 1.0)
11.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series244.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
41.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* b eps)) 1.0)
70.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.8s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2610
1	540
0	221

prune883.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 49.6b

localize99.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)
9.5b	(fma (* 1/2 (* b b)) (* eps eps) (* b eps))
17.0b	(fma (* eps (* eps eps)) (* (* b (* b b)) 1/6) (fma (* 1/2 (* b b)) (* eps eps) (* b eps)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

13.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)
0.0ms	(fma (* 1/2 (* b b)) (* eps eps) (* b eps))
0.0ms	(fma (* eps (* eps eps)) (* (* b (* b b)) 1/6) (fma (* 1/2 (* b b)) (* eps eps) (* b eps)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (exp (* a eps)) 1.0)
66.0ms	(- (exp (* (+ a b) eps)) 1.0)
82.0ms	(fma (* 1/2 (* b b)) (* eps eps) (* b eps))
148.0ms	(fma (* eps (* eps eps)) (* (* b (* b b)) 1/6) (fma (* 1/2 (* b b)) (* eps eps) (* b eps)))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1255
1	341
0	151

prune802.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 48.6b

localize136.0ms

Local error

Found 4 expressions with local error:

2.5b	(fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))
3.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (log1p (expm1 (fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))))))
3.4b	(- (exp (* a eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `flip--`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))
53.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (log1p (expm1 (fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))))))
14.0ms	(- (exp (* a eps)) 1.0)
23.0ms	(- (exp (* (+ a b) eps)) 1.0)

series798.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))
532.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (log1p (expm1 (fma (* (* eps b) (* eps b)) 1/2 (* eps (+ b (* (* (* (* eps b) (* eps b)) b) 1/6))))))))
53.0ms	(- (exp (* a eps)) 1.0)
73.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.7s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2736
1	525
0	193

prune850.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

22.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify2.5s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
3	2236
2	439
1	110
0	42

prune176.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes248.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.2s

Algorithm

intervals

Results

4.7s	2042×	body	10240	exit
4.6s	2530×	body	2560	valid
4.0s	3494×	body	1280	valid
747.0ms	1075×	body	640	valid
492.0ms	10044×	pre	80	true
127.0ms	365×	body	320	valid
44.0ms	423×	body	80	valid
27.0ms	115×	body	160	valid