Details

sample310.0ms

Algorithm

intervals

Results

104.0ms	83×	body	2560	valid
96.0ms	107×	body	1280	valid
60.0ms	56×	body	10240	exit
15.0ms	38×	body	640	valid
7.0ms	312×	pre	80	true
2.0ms	9×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	3×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.3b	(- (exp (* b eps)) 1.0)
3.7b	(- (exp (* a eps)) 1.0)
5.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

48.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
17.0ms	(- (exp (* b eps)) 1.0)
11.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series403.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
42.0ms	(- (exp (* b eps)) 1.0)
42.0ms	(- (exp (* a eps)) 1.0)
56.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.1s

Counts

129 → 129

Iterations

Iter	Nodes
done	5020
2	2354
1	619
0	228

prune986.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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:

21.0ms

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

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify3.7s

Counts

37 → 37

Iterations

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

prune207.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))) (- (exp (* b eps)) 1.0)))
5.3b	(- (exp (* (+ a b) eps)) 1.0)
13.5b	(* (* 1/2 (* eps eps)) (* a a))
15.2b	(fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))

rewrite192.0ms

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:

68.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))) (- (exp (* b eps)) 1.0)))
23.0ms	(- (exp (* (+ a b) eps)) 1.0)
93.0ms	(* (* 1/2 (* eps eps)) (* a a))
1.0ms	(fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))) (- (exp (* b eps)) 1.0)))
61.0ms	(- (exp (* (+ a b) eps)) 1.0)
63.0ms	(* (* 1/2 (* eps eps)) (* a a))
230.0ms	(fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))

simplify3.8s

Counts

107 → 107

Iterations

Iter	Nodes
done	5056
2	2966
1	683
0	243

prune827.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

2.8b	(fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))
3.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (log1p (expm1 (fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))))) (- (exp (* b eps)) 1.0)))
3.6b	(* eps (* a (* (* a eps) (* a eps))))
5.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
29×	`pow1`
23×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`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` `associate-l` `flip--`
2×	`associate-/r/` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `associate-r` `-commutative` `fma-udef` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))
46.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (log1p (expm1 (fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))))) (- (exp (* b eps)) 1.0)))
211.0ms	(* eps (* a (* (* a eps) (* a eps))))
24.0ms	(- (exp (* (+ a b) eps)) 1.0)

series2.4s

Counts

4 → 12

Calls

4 calls:

190.0ms	(fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))
2.0s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (log1p (expm1 (fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))))) (- (exp (* b eps)) 1.0)))
97.0ms	(* eps (* a (* (* a eps) (* a eps))))
85.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify3.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5003
2	2468
1	606
0	218

prune824.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes216.0ms

Accuracy

0% (3.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample13.4s

Algorithm

intervals

Results

4.8s	2561×	body	2560	valid
3.6s	3424×	body	1280	valid
3.3s	1858×	body	10240	exit
850.0ms	1121×	body	640	valid
267.0ms	9862×	pre	80	true
157.0ms	317×	body	320	valid
64.0ms	123×	body	160	valid
44.0ms	458×	body	80	valid