Details

sample133.0ms

Algorithm

intervals

Results

99.0ms	148×	body	10240	exit
13.0ms	256×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.3b	(/ (exp a) (+ (exp a) (exp b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

18.0ms	(+ (exp a) (exp b))
40.0ms	(/ (exp a) (+ (exp a) (exp b)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (exp a) (exp b))
87.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify5.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
4	2463
3	987
2	502
1	184
0	82

prune462.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.2b	(expm1 (/ (exp a) (+ (exp a) (exp b))))
0.3b	(/ (exp a) (+ (exp a) (exp b)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
5×	`add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`add-exp-log` `associate-/r*` `log1p-expm1-u`
3×	`pow1` `expm1-log1p-u` `fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `expm1-log1p` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `expm1-udef`

Counts

3 → 63

Calls

3 calls:

23.0ms	(+ (exp a) (exp b))
1.0ms	(expm1 (/ (exp a) (+ (exp a) (exp b))))
50.0ms	(/ (exp a) (+ (exp a) (exp b)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (exp a) (exp b))
144.0ms	(expm1 (/ (exp a) (+ (exp a) (exp b))))
79.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify4.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	3440
3	1357
2	603
1	225
0	101

prune623.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 2 expressions with local error:

0.0b	(log1p (fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1))
0.2b	(fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`expm1-log1p-u`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

2 → 21

Calls

2 calls:

1.0ms	(log1p (fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1))
1.0ms	(fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1)

series413.0ms

Counts

2 → 6

Calls

2 calls:

272.0ms	(log1p (fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1))
140.0ms	(fma (exp 1/2) (fma b -1/4 (fma 1/4 a 1)) -1)

simplify5.2s

Counts

27 → 27

Iterations

Iter	Nodes
done	5000
4	4037
3	1035
2	362
1	148
0	65

prune254.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))
0.0b	(log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1)))
0.2b	(fma (fma 1/4 (- a b) 1) (sqrt E) -1)
0.2b	(expm1 (log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log1p-udef` `log1p-expm1`
1×	`expm1-log1p` `fma-udef` `expm1-udef`

Counts

4 → 43

Calls

4 calls:

1.0ms	(log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))
1.0ms	(log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1)))
1.0ms	(fma (fma 1/4 (- a b) 1) (sqrt E) -1)
1.0ms	(expm1 (log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))))

series4.7s

Counts

4 → 12

Calls

4 calls:

300.0ms	(log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))
1.7s	(log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1)))
157.0ms	(fma (fma 1/4 (- a b) 1) (sqrt E) -1)
2.5s	(expm1 (log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))))

simplify4.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
2	1448
1	414
0	157

prune581.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes376.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.8s	3467×	body	10240	exit
498.0ms	8000×	body	80	valid