Details

sample101.0ms

Algorithm

intervals

Results

30.0ms	69×	body	10240	exit
23.0ms	55×	body	1280	valid
16.0ms	307×	body	80	valid
11.0ms	43×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
32×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
19×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 176

Calls

4 calls:

42.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms	(* (- 1.0 eps) x)
10.0ms	(* (+ 1.0 eps) x)
26.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
28.0ms	(* (- 1.0 eps) x)
28.0ms	(* (+ 1.0 eps) x)
187.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1368	3921
1	5002	3693

prune490.0ms

Filtered

188 candidates to 105 candidates (55.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 1 expressions with local error:

7.2b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify29.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	42	89
1	136	78
2	722	78
3	5002	75

prune54.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series42.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	49	82
1	132	67
2	534	67
3	3076	67
4	5001	67

prune45.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

7.2b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
0.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
0.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
142.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
150.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
147.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	190	752
1	639	693
2	2777	627
3	5001	621

prune240.0ms

Filtered

61 candidates to 58 candidates (95.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

regimes102.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.7b

bsearch150.0ms

Steps

Iters	Range		Point
10	0.3394070361140097	2696347712.967018	199.93447332075127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	26
1	65	26
2	65	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

762.0ms	1923×	body	10240	exit
751.0ms	1721×	body	1280	valid
537.0ms	9984×	body	80	valid
318.0ms	1276×	body	640	valid
109.0ms	645×	body	320	valid
37.0ms	334×	body	160	valid