Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
6.0ms	26×	body	2560	valid
4.0ms	22×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	14	17
1	28	16
2	40	16
3	47	16
4	49	16
5	51	16
6	52	16
done	52	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
18.0ms	(+ (* (* 4.0 p) p) (* x x))
51.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
35.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	136	1755
1	294	1489
2	840	1391
3	2380	1379
done	5001	1375

prune378.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
4.4b	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
70×	`add-cube-cbrt`
66×	`prod-diff`
59×	`times-frac`
34×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l*` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

17.0ms	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
9.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
52.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
62.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
60.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.1s

Counts

152 → 152

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	261	7025
1	600	6162
2	1498	4542
done	5001	3662

prune546.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
4.4b	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
70×	`add-cube-cbrt`
66×	`prod-diff`
59×	`times-frac`
34×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l*` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

17.0ms	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
10.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- 1.0 (/ x (sqrt (fma 4.0 (pow p 2) (pow x 2)))))
60.0ms	(/ (* x x) (fma 4.0 (pow p 2) (pow x 2)))
58.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
64.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.1s

Counts

152 → 152

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	261	7025
1	600	6162
2	1498	4542
done	5001	3662

prune581.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ 1.0 (* (/ (/ (* (cbrt x) (cbrt x)) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
15.7b	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 61

Calls

4 calls:

7.0ms	(+ 1.0 (* (/ (/ (* (cbrt x) (cbrt x)) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
1.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
2.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ 1.0 (* (/ (/ (* (cbrt x) (cbrt x)) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2))))) (/ (cbrt x) (cbrt (sqrt (fma 4.0 (pow p 2) (pow x 2)))))))
62.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
58.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))
61.0ms	(sqrt (fma 4.0 (pow p 2) (pow x 2)))

simplify1.2s

Counts

73 → 73

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	61	1469
1	143	1350
2	462	799
3	1936	722
done	5000	685

prune329.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.5b

regimes121.0ms

Accuracy

0% (0.2b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	50
1	26	50
done	26	50

end0.0ms

sample878.0ms

Algorithm

intervals

Results

218.0ms	5998×	body	80	valid
178.0ms	822×	body	2560	valid
106.0ms	613×	body	1280	valid
100.0ms	8000×	pre	80	true
44.0ms	326×	body	640	valid
18.0ms	177×	body	320	valid
4.0ms	64×	body	160	valid