Details

sample50.0ms

Algorithm

intervals

Results

25.0ms	63×	body	10240	exit
10.0ms	264×	body	80	valid
3.0ms	11×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.3b	(log (+ 1.0 (exp x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
3×	`pow1` `add-exp-log` `fma-def`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(+ 1.0 (exp x))
3.0ms	(log (+ 1.0 (exp x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ 1.0 (exp x))
64.0ms	(log (+ 1.0 (exp x)))

simplify102.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 4 (99.0ms)

Iter	Nodes	Cost
0	137	181
1	364	163
2	1024	163
3	3614	161
4	5001	159

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.3b	(log (+ (exp x) 1.0))
0.7b	(cbrt (pow (log (+ (exp x) 1.0)) 3))
0.7b	(pow (log (+ (exp x) 1.0)) 3)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`cube-mult` `log-div` `flip3-+` `unpow3` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
3.0ms	(log (+ (exp x) 1.0))
2.0ms	(cbrt (pow (log (+ (exp x) 1.0)) 3))
2.0ms	(pow (log (+ (exp x) 1.0)) 3)

series254.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
61.0ms	(log (+ (exp x) 1.0))
65.0ms	(cbrt (pow (log (+ (exp x) 1.0)) 3))
120.0ms	(pow (log (+ (exp x) 1.0)) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	269	526
1	1001	494
2	5001	485

prune215.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
0.7b	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
0.7b	(pow (log (+ (exp x) 1.0)) 3)
0.7b	(pow (log (+ (exp x) 1.0)) 3)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
28×	`sqrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down` `cube-prod`
14×	`pow1`
8×	`log-pow`
6×	`add-exp-log` `pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

2.0ms	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
2.0ms	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
2.0ms	(pow (log (+ (exp x) 1.0)) 3)
2.0ms	(pow (log (+ (exp x) 1.0)) 3)

series440.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
102.0ms	(cbrt (sqrt (pow (log (+ (exp x) 1.0)) 3)))
119.0ms	(pow (log (+ (exp x) 1.0)) 3)
118.0ms	(pow (log (+ (exp x) 1.0)) 3)

simplify39.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	233	1030
1	880	938
2	5001	908

prune289.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (log 2.0) 2)
1.0b	(pow (log 2.0) 3)
6.8b	(- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))
8.7b	(cbrt (+ (fma (* 1.5 (pow (log 2.0) 2)) x (pow (log 2.0) 3)) (- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down`
6×	`add-exp-log` `pow-unpow` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cbrt-prod` `expm1-log1p-u` `cube-prod` `associate-*r/` `log1p-expm1-u`
3×	`log-pow`
2×	`pow-to-exp` `cbrt-div` `pow-pow` `flip3-+` `pow-exp` `associate--l+` `frac-sub` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `cube-mult` `sub-neg` `flip3--` `distribute-lft-in` `fma-neg` `pow1/3` `diff-log` `unpow3` `prod-diff` `flip--` `distribute-lft-out` `unpow2` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

2.0ms	(pow (log 2.0) 2)
5.0ms	(pow (log 2.0) 3)
17.0ms	(- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))
38.0ms	(cbrt (+ (fma (* 1.5 (pow (log 2.0) 2)) x (pow (log 2.0) 3)) (- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))))

series1.4s

Counts

4 → 8

Calls

4 calls:

0.0ms	(pow (log 2.0) 2)
0.0ms	(pow (log 2.0) 3)
627.0ms	(- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))
736.0ms	(cbrt (+ (fma (* 1.5 (pow (log 2.0) 2)) x (pow (log 2.0) 3)) (- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	590	1455
1	3145	1367
2	5001	1360

prune381.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes52.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample1.7s

Algorithm

intervals

Results

982.0ms	2417×	body	10240	exit
311.0ms	8409×	body	80	valid
65.0ms	245×	body	640	valid
58.0ms	116×	body	1280	valid
30.0ms	189×	body	320	valid
10.0ms	107×	body	160	valid