Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
7.0ms	256×	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: 7.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.4b	(- (/ 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))
40.0ms	(- (/ x0 (- 1.0 x1)) x0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ x0 (- 1.0 x1))
42.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify55.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (43.0ms)

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

prune149.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
6.2b	(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))

series176.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (cbrt x0) (- 1.0 x1))
90.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (29.0ms)

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

prune170.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
0.8b	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.2b	(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))

series264.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (cbrt x0) (- 1.0 x1))
89.0ms	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
88.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (30.0ms)

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

prune244.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
0.7b	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
0.8b	(exp (log (log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))))
6.5b	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
68×	`add-sqr-sqrt` `*-un-lft-identity`
56×	`add-cube-cbrt`
36×	`pow-unpow`
29×	`log-prod`
27×	`unpow-prod-down`
15×	`cbrt-prod`
11×	`exp-prod`
9×	`sqr-pow`
8×	`pow1` `pow-pow`
7×	`add-exp-log` `associate-/l*`
6×	`div-exp` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `rem-log-exp` `exp-sum` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r*` `log-pow` `div-inv`
2×	`associate-/r/`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 164

Calls

4 calls:

8.0ms	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
8.0ms	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
2.0ms	(exp (log (log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))))
5.0ms	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
127.0ms	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
141.0ms	(exp (log (log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))))
148.0ms	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	809	2204
1	2914	2085
2	5001	2043

prune587.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.3b

regimes59.0ms

Accuracy

0% (2.2b remaining)

Error of 6.3b against oracle of 4.1b and baseline of 6.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample617.0ms

Algorithm

intervals

Results

257.0ms	8000×	body	80	valid
221.0ms	8000×	pre	80	true