Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	134×	pre	10240	exit
4.0ms	256×	body	80	valid
3.0ms	122×	pre	80	true

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ x0 (- 1.0 x1))
7.3b	(- (/ x0 (- 1.0 x1)) x0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
76×	`times-frac`
69×	`add-cube-cbrt`
63×	`prod-diff`
21×	`fma-neg`
18×	`difference-of-squares`
17×	`distribute-lft-out--`
10×	`associate-/r/`
6×	`flip3--` `flip--`
5×	`associate-/r*` `div-inv`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num`

Counts

2 → 140

Calls

2 calls:

5.0ms	(/ x0 (- 1.0 x1))
41.0ms	(- (/ x0 (- 1.0 x1)) x0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ x0 (- 1.0 x1))
47.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify57.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	421	1434
1	1527	945
2	5001	894

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
6.4b	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
72×	`sqrt-prod`
57×	`*-un-lft-identity`
54×	`times-frac`
29×	`add-cube-cbrt`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
9×	`associate-/r*`
6×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 95

Calls

2 calls:

12.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
0.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series508.0ms

Counts

2 → 6

Calls

2 calls:

168.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
341.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	363	1223
1	1306	1140
2	5002	1106

prune186.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
21×	`add-cube-cbrt`
18×	`cbrt-prod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`associate-/r*`
4×	`add-exp-log`
3×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 67

Calls

2 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series181.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (cbrt x0) (- 1.0 x1))
93.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify36.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	307	589
1	1046	558
2	5001	548

prune182.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
0.7b	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
18×	`cbrt-prod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`add-exp-log` `associate-/r*`
4×	`pow1` `exp-prod` `add-cbrt-cube`
3×	`expm1-log1p-u` `log-prod` `exp-sum` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `log-pow` `flip--` `fma-udef` `div-inv` `rem-exp-log`

Counts

3 → 84

Calls

3 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
1.0ms	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series456.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (cbrt x0) (- 1.0 x1))
277.0ms	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
91.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify39.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	338	821
1	1104	767
2	5002	729

prune249.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.3b

regimes75.0ms

Accuracy

54.7% (1.1b remaining)

Error of 5.5b against oracle of 4.4b and baseline of 6.8b

bsearch20.0ms

Steps

Iters	Range		Point
4	1.855	2.985	2.9451562499999997

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	23
1	28	23

end0.0ms

sample748.0ms

Algorithm

intervals

Results

399.0ms	4069×	pre	10240	exit
144.0ms	8000×	body	80	valid
61.0ms	3931×	pre	80	true