Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	31	9
1	59	9
2	90	9
3	116	7
4	130	7
5	148	7
6	188	7
7	264	7
8	304	7
9	377	7
10	580	7
11	851	7
12	1402	7
13	2787	7
14	3168	7
15	4321	7
16	5001	7

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
0.1b	(fma x (fma 0.04481 x 0.99229) 1.0)
0.1b	(* 0.70711 (fma 0.27061 x 2.30753))
12.2b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

1.0ms	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
1.0ms	(fma x (fma 0.04481 x 0.99229) 1.0)
3.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
4.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
25.0ms	(fma x (fma 0.04481 x 0.99229) 1.0)
54.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
74.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	272	452
1	1121	382
2	5002	382

prune220.0ms

Filtered

77 candidates to 59 candidates (76.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 0b

Counts

79 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.70711 (fma 0.27061 x 2.30753))
0.1b	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
11.1b	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
12.2b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac` `associate-/r*`
12×	`add-exp-log` `unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `rem-cbrt-cube` `div-inv` `associate-/l` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

3.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
2.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
2.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
7.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
55.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
26.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
77.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	392	766
1	1802	690
2	5001	675

prune385.0ms

Filtered

129 candidates to 74 candidates (57.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	130	2	132

Merged error: 0b

Counts

132 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b	(expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
11.1b	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
12.2b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
12.6b	(log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `cube-prod` `associate-/r*`
2×	`cbrt-undiv` `div-exp`
1×	`cube-mult` `log1p-udef` `expm1-log1p` `frac-2neg` `pow1/3` `unpow3` `log1p-expm1` `prod-exp` `clear-num` `rem-cbrt-cube` `cbrt-unprod` `div-inv` `associate-/l*` `expm1-udef` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

1.0ms	(expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
4.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
7.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
1.0ms	(log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
38.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
214.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
92.0ms	(log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

simplify61.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	606	847
1	2783	718
2	5002	701

prune280.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	2	82

Merged error: 0b

Counts

82 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))
1.1b	(pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3))
11.1b	(cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3)))
12.2b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

43×	`unpow-prod-down`
33×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac` `associate-/r*`
12×	`add-exp-log` `pow-unpow`
9×	`sqr-pow`
7×	`add-cbrt-cube`
6×	`sqrt-prod`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp`
2×	`cbrt-undiv` `pow-pow` `div-exp`
1×	`frac-2neg` `pow1/3` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

4.0ms	(pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))
2.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3))
3.0ms	(cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3)))
8.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))))

series2.2s

Counts

4 → 12

Calls

4 calls:

406.0ms	(pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))
203.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3))
623.0ms	(cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3)))
946.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (pow (fma x (fma 0.04481 x 0.99229) 1.0) (sqrt 3)) (sqrt 3))))

simplify110.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1091	2089
1	4931	1866
2	5001	1866

prune777.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	128	2	130

Merged error: 0b

Counts

130 → 2

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample400.0ms

Algorithm

intervals

Results

299.0ms

8000×

body

valid