Details

sample400.0ms

Algorithm

intervals

Results

136.0ms	75×	body	10240	exit
109.0ms	75×	body	2560	valid
102.0ms	111×	body	1280	valid
16.0ms	35×	body	640	valid
8.0ms	331×	pre	80	true
4.0ms	11×	body	320	valid
2.0ms	20×	body	80	valid
1.0ms	4×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2307
4	629
3	237
2	95
1	40
0	17

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.2b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* a eps)) 1.0)
7.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite95.0ms

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:

57.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* b eps)) 1.0)
11.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series214.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
58.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.6s

Counts

150 → 150

Iterations

Iter	Nodes
done	5007
2	1672
1	539
0	221

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.5b

localize95.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps)))) (- (exp (* b eps)) 1.0)))
7.2b	(- (exp (* (+ a b) eps)) 1.0)
17.7b	(* (* (* a a) 1/2) (* eps eps))
18.8b	(fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-cbrt-cube` `add-exp-log`
25×	`pow1`
19×	`prod-exp` `cbrt-unprod`
15×	`pow-prod-down`
13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`associate-/r/` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `associate-r` `associate-l` `-commutative` `fma-udef` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

40.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps)))) (- (exp (* b eps)) 1.0)))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
100.0ms	(* (* (* a a) 1/2) (* eps eps))
1.0ms	(fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps))))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps)))) (- (exp (* b eps)) 1.0)))
71.0ms	(- (exp (* (+ a b) eps)) 1.0)
51.0ms	(* (* (* a a) 1/2) (* eps eps))
135.0ms	(fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps))))

simplify4.1s

Counts

107 → 107

Iterations

Iter	Nodes
done	5509
2	2898
1	696
0	241

prune745.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite45.0ms

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:

42.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify3.9s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
5	4525
4	1680
3	692
2	316
1	110
0	42

prune274.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt a) (cbrt a))
0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

9.0ms	(* (cbrt a) (cbrt a))
1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series1.1s

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (cbrt a) (cbrt a))
278.0ms	(cbrt a)
264.0ms	(cbrt a)
261.0ms	(cbrt a)

simplify3.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	4108
3	1072
2	382
1	140
0	65

prune455.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes308.0ms

Accuracy

0% (3.5b remaining)

Error of 3.6b against oracle of 0.1b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample13.9s

Algorithm

intervals

Results

5.4s	2622×	body	2560	valid
3.4s	1934×	body	10240	exit
3.0s	3375×	body	1280	valid
707.0ms	1048×	body	640	valid
701.0ms	9935×	pre	80	true
111.0ms	356×	body	320	valid
45.0ms	479×	body	80	valid
26.0ms	121×	body	160	valid