Details

sample502.0ms

Algorithm

intervals

Results

164.0ms	83×	body	2560	valid
125.0ms	107×	body	1280	valid
94.0ms	56×	body	10240	exit
71.0ms	38×	body	640	valid
9.0ms	312×	pre	80	true
4.0ms	9×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	3×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2045
4	572
3	224
2	95
1	40
0	17

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.6b

localize47.0ms

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)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `*-un-lft-identity` `flip3--` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`frac-times` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `add-cube-cbrt` `cbrt-unprod`
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 → 73

Calls

4 calls:

41.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
19.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)

series449.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
59.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* a eps)) 1.0)
57.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5121
2	2046
1	481
0	174

prune648.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+`

Counts

1 → 19

Calls

1 calls:

38.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify3.6s

Counts

22 → 22

Iterations

Iter	Nodes
done	5000
5	3767
4	1436
3	568
2	270
1	102
0	40

prune102.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2))
3.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2)) (* eps a)) (- (exp (* b eps)) 1.0)))
5.3b	(- (exp (* (+ a b) eps)) 1.0)
13.9b	(* (* a (* a a)) (* eps (* eps eps)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

68×	`pow1`
52×	`add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
31×	`prod-exp` `cbrt-unprod`
16×	`pow-prod-up`
8×	`associate-/r/` `add-log-exp`
6×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `flip3-+` `pow-plus` `div-exp` `associate-*r/` `add-cube-cbrt` `flip-+`
2×	`pow2` `cube-unmult` `associate-*l/` `pow-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `times-frac` `diff-log` `associate-r` `associate-l` `-commutative` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

303.0ms	(+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2))
1.4s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2)) (* eps a)) (- (exp (* b eps)) 1.0)))
22.0ms	(- (exp (* (+ a b) eps)) 1.0)
109.0ms	(* (* a (* a a)) (* eps (* eps eps)))

series1.5s

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2))
1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2)) (* eps a)) (- (exp (* b eps)) 1.0)))
59.0ms	(- (exp (* (+ a b) eps)) 1.0)
92.0ms	(* (* a (* a a)) (* eps (* eps eps)))

simplify3.8s

Counts

112 → 112

Iterations

Iter	Nodes
done	5010
2	3960
1	789
0	251

prune719.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps))))
4.2b	(* (/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps))) (/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.3b	(- (exp (* (+ a b) eps)) 1.0)
16.0b	(/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps)))

rewrite7.1s

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
47×	`times-frac`
31×	`associate-r`
30×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
15×	`associate-l`
11×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`associate-/r` `flip3-+` `flip-+` `div-inv` `associate-/l`
2×	`flip3--` `flip--`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 124

Calls

4 calls:

324.0ms	(+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps))))
4.6s	(* (/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps))) (/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* b eps)) 1.0)))
20.0ms	(- (exp (* (+ a b) eps)) 1.0)
2.1s	(/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps)))

series1.6s

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps))))
1.2s	(* (/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps))) (/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* b eps)) 1.0)))
73.0ms	(- (exp (* (+ a b) eps)) 1.0)
186.0ms	(/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps)))

simplify3.3s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	3675
1	929
0	297

prune990.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes340.0ms

Accuracy

92.3% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.4b

bsearch4.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	27

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.3s	2561×	body	2560	valid
3.7s	1858×	body	10240	exit
3.6s	3424×	body	1280	valid
997.0ms	1121×	body	640	valid
829.0ms	9862×	pre	80	true
179.0ms	317×	body	320	valid
101.0ms	123×	body	160	valid
44.0ms	458×	body	80	valid