Details

sample142.0ms

Algorithm

intervals

Results

67.0ms	260×	body	10240	exit
34.0ms	94×	body	1280	valid
20.0ms	84×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	20×	body	80	valid

simplify48.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(fma 1 1 (exp (+ x x)))
0.8b	(/ (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	(expm1 (+ x x))
0.0ms	(fma 1 1 (exp (+ x x)))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series108.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(expm1 (+ x x))
21.0ms	(fma 1 1 (exp (+ x x)))
69.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify82.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (76.0ms)

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

prune150.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(fma 1 1 (exp (+ x x)))
0.2b	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
0.8b	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1` `log1p-expm1-u`
4×	`cbrt-undiv` `expm1-log1p-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`expm1-log1p` `pow-flip` `associate-/r/` `fma-udef` `inv-pow` `expm1-udef`

Counts

4 → 128

Calls

4 calls:

0.0ms	(expm1 (+ x x))
0.0ms	(fma 1 1 (exp (+ x x)))
5.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
2.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(expm1 (+ x x))
20.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
67.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	401	1494
1	1795	1297
2	5001	1209

prune246.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(expm1 (+ x x))
7.0ms	(/ 1 (+ (exp (* 2 x)) 1))
6.0ms	(+ (exp (* 2 x)) 1)
18.0ms	(* (/ 1 (+ (exp (* 2 x)) 1)) (expm1 (+ x x)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(expm1 (+ x x))
23.0ms	(/ 1 (+ (exp (* 2 x)) 1))
10.0ms	(+ (exp (* 2 x)) 1)
51.0ms	(* (/ 1 (+ (exp (* 2 x)) 1)) (expm1 (+ x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	331	819
1	1630	653
2	5002	650

prune226.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

localize13.0ms

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))

series167.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(- x (* 1/3 (pow x 3)))
54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
35.0ms	(* 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

prune155.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

regimes19.0ms

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	17	7
1	19	7
2	19	7

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	7562×	body	10240	exit
1.2s	3242×	body	1280	valid
571.0ms	2402×	body	640	valid
202.0ms	1254×	body	320	valid
77.0ms	668×	body	160	valid
33.0ms	434×	body	80	valid