Details

sample104.0ms

Algorithm

intervals

Results

30.0ms	62×	body	10240	exit
19.0ms	35×	body	1280	valid
14.0ms	49×	body	640	valid
7.0ms	121×	body	80	valid
7.0ms	35×	body	320	valid
3.0ms	78×	body	80	nan
3.0ms	1×	body	2560	valid
2.0ms	17×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	5×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	3×	body	160	nan

simplify222.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
3.1b	(+ (- 1.0 y) (* y (exp z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
12.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
157.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
77.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune351.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
3.6b	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
11.2b	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
2.0ms	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
3.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

series755.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt y)
188.0ms	(cbrt y)
278.0ms	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
112.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	289	815
1	1018	694
2	5002	633

prune325.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
11.2b	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
11.2b	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
11.2b	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
3.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
3.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
3.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

series652.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(log (+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y)))
118.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
119.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))
123.0ms	(+ (fma (sqrt 1.0) (sqrt 1.0) (- (* (cbrt y) (* (cbrt y) (cbrt y))))) (fma y (expm1 z) y))

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	259	1347
1	921	1103
2	5001	935

prune533.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1.0 (pow z 2))
2.3b	(fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2))))
5.8b	(/ y (/ 1.0 (pow z 2)))
6.0b	(/ (fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2)))) t)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
118×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down`
39×	`associate-/r*`
21×	`add-exp-log`
16×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
11×	`div-exp`
9×	`associate-/l*`
7×	`div-inv`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-exp`
1×	`associate-/r/` `fma-udef`

Counts

4 → 224

Calls

4 calls:

4.0ms	(/ 1.0 (pow z 2))
0.0ms	(fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2))))
9.0ms	(/ y (/ 1.0 (pow z 2)))
2.0ms	(/ (fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2)))) t)

series428.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1.0 (pow z 2))
137.0ms	(fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2))))
38.0ms	(/ y (/ 1.0 (pow z 2)))
221.0ms	(/ (fma 1/2 (/ y (/ 1.0 (pow z 2))) (fma (/ z 1.0) y (log (pow (sqrt 1.0) 2)))) t)

simplify91.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	766	1970
1	3256	1759
2	5001	1750

prune885.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

regimes524.0ms

Accuracy

76.6% (4.0b remaining)

Error of 8.5b against oracle of 4.6b and baseline of 21.5b

bsearch155.0ms

Steps

Iters	Range		Point
8	3.7682752778021148e-62	1.3117471561541868e-59	1.0673077358209968e-59
8	-1.3142528534888108e-15	-1.2804377133427356e-18	-3.2580599270527733e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	44	26

end0.0ms

sample3.1s

Algorithm

intervals

Results

758.0ms	1419×	body	1280	valid
748.0ms	1499×	body	10240	exit
474.0ms	1589×	body	640	valid
221.0ms	3571×	body	80	valid
176.0ms	939×	body	320	valid
95.0ms	2510×	body	80	nan
79.0ms	61×	body	2560	valid
51.0ms	257×	body	640	nan
49.0ms	454×	body	160	valid
36.0ms	117×	body	1280	nan
27.0ms	208×	body	320	nan
9.0ms	107×	body	160	nan