Details

sample209.0ms

Algorithm

intervals

Results

72.0ms	154×	body	160	valid
41.0ms	254×	body	80	nan
35.0ms	510×	pre	80	true
23.0ms	45×	body	320	valid
10.0ms	57×	body	80	valid

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.2b	(- (* b b) (* (* 4 a) c))
37.8b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
53.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
24.0ms	(- (* b b) (* (* 4 a) c))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
147.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
52.0ms	(- (* b b) (* (* 4 a) c))
121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

simplify2.7s

Counts

106 → 106

Iterations

Iter	Nodes
3	5277
2	1370
1	435
0	166

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune45.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2 (/ (* a c) b)) (* 2 a))
0.3b	(/ (* a c) b)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 57

Calls

2 calls:

27.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
14.0ms	(/ (* a c) b)

series58.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
27.0ms	(/ (* a c) b)

simplify15.1s

Counts

63 → 63

Iterations

Iter	Nodes
3	14724
2	1741
1	332
0	113

prune525.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (/ (* a c) b))
0.2b	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
0.3b	(/ (* a c) b)
0.3b	(expm1 (log1p (/ (* a c) b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
5×	`expm1-log1p-u` `prod-exp` `cbrt-unprod`
4×	`pow1` `associate-/r*` `times-frac` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 72

Calls

4 calls:

1.0ms	(log1p (/ (* a c) b))
23.0ms	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
16.0ms	(/ (* a c) b)
0.0ms	(expm1 (log1p (/ (* a c) b)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(log1p (/ (* a c) b))
114.0ms	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
22.0ms	(/ (* a c) b)
122.0ms	(expm1 (log1p (/ (* a c) b)))

simplify13.1s

Counts

84 → 84

Iterations

Iter	Nodes
3	9315
2	1413
1	360
0	146

prune706.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 5.3b

regimes722.0ms

Accuracy

11.2% (6.4b remaining)

Error of 11.6b against oracle of 5.3b and baseline of 12.4b

bsearch75.0ms

Steps

Iters	Range		Point
4	0.012192119033112701	0.016950738658885803	0.01334404880395557

simplify17.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.4s	4853×	body	160	valid
1.1s	8303×	body	80	nan
947.0ms	16303×	pre	80	true
661.0ms	1355×	body	320	valid
581.0ms	1792×	body	80	valid