Details

sample296.0ms

Algorithm

intervals

Results

86.0ms	75×	body	2560	valid
70.0ms	75×	body	10240	exit
65.0ms	111×	body	1280	valid
40.0ms	35×	body	640	valid
8.0ms	331×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	20×	body	80	valid
1.0ms	4×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.9b

localize51.0ms

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)

rewrite133.0ms

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:

90.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
11.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
51.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* a eps)) 1.0)
75.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.8s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2587
1	540
0	221

prune982.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.5b

localize65.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
7.2b	(- (exp (* (+ a b) eps)) 1.0)
14.7b	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
17.3b	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

42.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
0.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
0.0ms	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.4s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
87.0ms	(- (exp (* (+ a b) eps)) 1.0)
136.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
118.0ms	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

simplify3.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	3138
1	580
0	207

prune753.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite36.0ms

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:

35.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify2.6s

Counts

37 → 37

Iterations

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

prune236.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

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)

rewrite26.0ms

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:

18.0ms	(* (cbrt a) (cbrt a))
1.0ms	(cbrt a)
1.0ms	(cbrt a)
2.0ms	(cbrt a)

series1.1s

Counts

4 → 12

Calls

4 calls:

275.0ms	(* (cbrt a) (cbrt a))
242.0ms	(cbrt a)
301.0ms	(cbrt a)
297.0ms	(cbrt a)

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	725
1	142
0	65

prune555.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes293.0ms

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

sample15.6s

Algorithm

intervals

Results

5.5s	2622×	body	2560	valid
3.7s	1934×	body	10240	exit
3.4s	3375×	body	1280	valid
1.1s	1048×	body	640	valid
789.0ms	9935×	pre	80	true
393.0ms	121×	body	160	valid
126.0ms	356×	body	320	valid
85.0ms	479×	body	80	valid