Details

sample114.0ms

Algorithm

intervals

Results

49.0ms	269×	body	10240	exit
33.0ms	108×	body	1280	valid
15.0ms	80×	body	640	valid
4.0ms	33×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	14×	body	80	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (44.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
1.2b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv` `expm1-udef`

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series88.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343

prune115.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
0.0b	(pow (+ (exp (* 2 x)) 1) 3)
1.2b	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 161

Calls

4 calls:

4.0ms	(+ (exp (* 2 x)) 1)
6.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
6.0ms	(pow (+ (exp (* 2 x)) 1) 3)
15.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp (* 2 x)) 1)
10.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
30.0ms	(pow (+ (exp (* 2 x)) 1) 3)
55.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

simplify68.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	378	1647
1	1691	1481
2	5001	1423

prune299.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b	(- x (* 1/3 (pow x 3)))
0.1b	(* 1/3 (pow x 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 63

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
2.0ms	(- x (* 1/3 (pow x 3)))
10.0ms	(* 1/3 (pow x 3))

series169.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
78.0ms	(- x (* 1/3 (pow x 3)))
36.0ms	(* 1/3 (pow x 3))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5002	292

prune160.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.1b	(* 1/3 (pow x 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`pow1` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `log1p-udef` `expm1-log1p` `unpow3` `log1p-expm1` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef`

Counts

4 → 65

Calls

4 calls:

0.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
7.0ms	(* 1/3 (pow x 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
50.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
153.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
40.0ms	(* 1/3 (pow x 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	306	465
1	1191	409
2	5001	389

prune199.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.1b

regimes20.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	20	8
2	20	8

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	7817×	body	10240	exit
985.0ms	3247×	body	1280	valid
470.0ms	2518×	body	640	valid
138.0ms	1189×	body	320	valid
46.0ms	615×	body	160	valid
16.0ms	431×	body	80	valid