Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	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: 7.8b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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)

series80.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ x0 (- 1.0 x1))
47.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify56.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (42.0ms)

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

prune156.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (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))

series175.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (cbrt x0) (- 1.0 x1))
89.0ms	(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

prune178.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
0.5b	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
0.8b	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
6.3b	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 203

Calls

4 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
9.0ms	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
9.0ms	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
5.0ms	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (cbrt x0) (- 1.0 x1))
325.0ms	(/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0))
125.0ms	(pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1)))
148.0ms	(log (/ (pow (exp (pow x0 2/3)) (/ (cbrt x0) (- 1.0 x1))) (exp x0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	929	2386
1	3632	2269
2	5002	2250

prune659.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
5.6b	(+ (log (/ 1 (sqrt (exp x0)))) (fma (/ (cbrt x0) (- 1.0 x1)) (pow x0 2/3) (log (/ 1 (sqrt (exp x0))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
48×	`times-frac`
36×	`add-cube-cbrt`
22×	`associate-+l+` `log-prod`
18×	`cbrt-prod`
11×	`fma-def`
9×	`sqrt-prod` `log-pow`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `pow-flip` `associate-/l*`
5×	`associate-/r*`
4×	`add-exp-log` `sqrt-pow1`
3×	`exp-prod` `add-cbrt-cube` `add-log-exp`
2×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `log-div` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `div-exp` `clear-num` `sum-log` `flip--` `flip-+` `fma-udef` `inv-pow`

Counts

2 → 107

Calls

2 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
25.0ms	(+ (log (/ 1 (sqrt (exp x0)))) (fma (/ (cbrt x0) (- 1.0 x1)) (pow x0 2/3) (log (/ 1 (sqrt (exp x0))))))

series216.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (cbrt x0) (- 1.0 x1))
134.0ms	(+ (log (/ 1 (sqrt (exp x0)))) (fma (/ (cbrt x0) (- 1.0 x1)) (pow x0 2/3) (log (/ 1 (sqrt (exp x0))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	499	1161
1	1673	1108
2	5002	1054

prune369.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.2b

regimes63.0ms

Accuracy

48.5% (1.1b remaining)

Error of 4.4b against oracle of 3.3b and baseline of 5.4b

bsearch28.0ms

Steps

Iters	Range		Point
4	1.855	2.985	1.8749218749999998

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	52
1	43	52

end0.0ms

sample679.0ms

Algorithm

intervals

Results

275.0ms	8000×	body	80	valid
254.0ms	8000×	pre	80	true