Details

sample377.0ms

Algorithm

intervals

Results

131.0ms	73×	body	10240	exit
118.0ms	90×	body	2560	valid
74.0ms	105×	body	1280	valid
13.0ms	29×	body	640	valid
8.0ms	329×	pre	80	true
4.0ms	11×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	5×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.6b

localize61.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.1b	(- (exp (* b eps)) 1.0)
3.4b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite167.0ms

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:

91.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
24.0ms	(- (exp (* b eps)) 1.0)
22.0ms	(- (exp (* a eps)) 1.0)
25.0ms	(- (exp (* (+ a b) eps)) 1.0)

series255.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
53.0ms	(- (exp (* b eps)) 1.0)
55.0ms	(- (exp (* a eps)) 1.0)
68.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2587
1	540
0	221

prune949.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 48.4b

localize40.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))) (- (exp (* b eps)) 1.0)))
5.4b	(- (exp (* (+ a b) eps)) 1.0)
11.2b	(fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a)))
13.3b	(fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))

rewrite81.0ms

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:

54.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))) (- (exp (* b eps)) 1.0)))
22.0ms	(- (exp (* (+ a b) eps)) 1.0)
0.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a)))
1.0ms	(fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))) (- (exp (* b eps)) 1.0)))
67.0ms	(- (exp (* (+ a b) eps)) 1.0)
143.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a)))
185.0ms	(fma (pow eps 3) (* 1/6 (pow a 3)) (* eps a))

simplify1.5s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
2	3136
1	574
0	205

prune904.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite44.0ms

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:

40.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify2.2s

Counts

37 → 37

Iterations

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

prune223.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

15.5b

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

rewrite34.0ms

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×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

32.0ms

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

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

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

simplify2.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
3	2995
2	619
1	150
0	58

prune89.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

0% (3.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.5s

Algorithm

intervals

Results

5.1s	2615×	body	2560	valid
5.0s	3397×	body	1280	valid
3.5s	1968×	body	10240	exit
635.0ms	1066×	body	640	valid
360.0ms	9969×	pre	80	true
226.0ms	354×	body	320	valid
52.0ms	436×	body	80	valid
30.0ms	133×	body	160	valid