Details

sample97.0ms

Algorithm

intervals

Results

28.0ms	341×	body	80	valid
27.0ms	53×	body	1280	valid
15.0ms	45×	body	640	valid
5.0ms	75×	body	80	overflowed
3.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (38.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.6b	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `times-frac` `associate-l/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
1.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (- 1.0 eps) x)
26.0ms	(* (+ 1.0 eps) x)
48.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
239.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	462	738
1	1805	635
2	5002	628

prune299.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 5.7b

Counts

98 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
3.8b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.2b	(/ (pow x 3) eps)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
12×	`cube-prod` `associate-/l*`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqr-pow`
4×	`cube-mult` `unpow3` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `div-exp` `associate-l` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 106

Calls

3 calls:

9.0ms	(* 0.5 (pow x 2))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0ms	(/ (pow x 3) eps)

series98.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* 0.5 (pow x 2))
46.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms	(/ (pow x 3) eps)

simplify61.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5001	451

prune251.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	107	13	120

Merged error: 5.7b

Counts

120 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
3.8b	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
43.3b	(cbrt (pow x 3))
43.3b	(cbrt (pow x 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
24×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
13×	`associate-/r*`
12×	`add-cbrt-cube`
6×	`cbrt-undiv` `unpow-prod-down` `cube-prod` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`cube-mult` `pow1/3` `unpow3` `prod-exp` `rem-cbrt-cube` `cbrt-unprod` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef` `associate-/l*`

Counts

4 → 104

Calls

4 calls:

11.0ms	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
1.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
2.0ms	(cbrt (pow x 3))
2.0ms	(cbrt (pow x 3))

series173.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
85.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
15.0ms	(cbrt (pow x 3))
17.0ms	(cbrt (pow x 3))

simplify86.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	388	603
1	2652	494
2	5002	480

prune297.0ms

Filtered

116 candidates to 79 candidates (68.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 2.1b

Counts

129 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
3.2b	(log (exp x))
3.6b	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
43.3b	(cbrt (pow x 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`associate-/r*`
12×	`cbrt-prod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `log-prod` `exp-prod` `cube-prod` `div-inv`
2×	`prod-exp` `cbrt-unprod`
1×	`cube-mult` `frac-2neg` `pow1/3` `unpow3` `rem-log-exp` `clear-num` `associate-/r/` `rem-cbrt-cube` `fma-udef` `associate-/l*` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

10.0ms	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
2.0ms	(log (exp x))
1.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.0ms	(cbrt (pow x 3))

series144.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
8.0ms	(log (exp x))
77.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
16.0ms	(cbrt (pow x 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	432	605
1	2783	478
2	5002	464

prune279.0ms

Filtered

110 candidates to 79 candidates (71.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 2.1b

Counts

118 → 6

regimes92.0ms

Accuracy

96.2% (0.6b remaining)

Error of 2.2b against oracle of 1.6b and baseline of 17.8b

bsearch2.0ms

Steps

Iters	Range		Point
0	6.262145176279688e-07	6.47571746699048e-07	6.368931321635083e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	50
1	59	50
2	59	50

end0.0ms

sample2.7s

Algorithm

intervals

Results

925.0ms	1729×	body	1280	valid
745.0ms	10160×	body	80	valid
420.0ms	1288×	body	640	valid
142.0ms	1986×	body	80	overflowed
138.0ms	618×	body	320	valid
52.0ms	336×	body	160	valid

Details

sample97.0ms

simplify40.0ms

prune10.0ms

localize17.0ms

rewrite32.0ms

series346.0ms

simplify50.0ms

prune299.0ms

localize10.0ms

rewrite19.0ms

series98.0ms

simplify61.0ms

prune251.0ms

localize14.0ms

rewrite20.0ms

series173.0ms

simplify86.0ms

prune297.0ms

localize21.0ms

rewrite19.0ms

series144.0ms

simplify89.0ms

prune279.0ms

regimes92.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling