Details

sample100.0ms

Algorithm

intervals

Results

49.0ms	124×	body	1280	valid
20.0ms	80×	body	640	valid
13.0ms	272×	body	80	overflowed
5.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid
1.0ms	10×	body	80	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (46.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(expm1 (+ x x))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

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

series106.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
18.0ms	(expm1 (+ x x))
67.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382

prune142.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.0b	(expm1 (log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

0.0ms	(expm1 (+ x x))
0.0ms	(log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.0ms	(expm1 (log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(expm1 (+ x x))
119.0ms	(log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
185.0ms	(expm1 (log1p (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
66.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify100.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	202	626
1	700	561
2	3181	540
3	5001	538

prune184.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(log1p (* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1))))
0.0b	(/ 1 (+ (exp (* 2 x)) 1))
0.7b	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`div-exp` `prod-exp` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `log1p-udef` `pow-flip` `frac-2neg` `log1p-expm1` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 110

Calls

4 calls:

4.0ms	(+ (exp (* 2 x)) 1)
0.0ms	(log1p (* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1))))
7.0ms	(/ 1 (+ (exp (* 2 x)) 1))
18.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp (* 2 x)) 1)
108.0ms	(log1p (* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1))))
17.0ms	(/ 1 (+ (exp (* 2 x)) 1))
52.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify46.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	357	915
1	1749	761
2	5001	707

prune260.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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:

2.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
6.0ms	(* 1/3 (pow x 3))

series164.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(- x (* 1/3 (pow x 3)))
50.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
40.0ms	(* 1/3 (pow x 3))

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5001	292

prune149.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes36.0ms

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	13	8
1	15	8
2	15	8

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	3300×	body	1280	valid
595.0ms	2453×	body	640	valid
349.0ms	7515×	body	80	overflowed
193.0ms	1234×	body	320	valid
64.0ms	618×	body	160	valid
23.0ms	395×	body	80	valid