Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify142.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r` `associate-l`
12×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`*-commutative` `unswap-sqr`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`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` `div-inv`

Counts

4 → 109

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)
4.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
10.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

series222.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
29.0ms	(fma x (fma 0.04481 x 0.99229) 1.0)
49.0ms	(* 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))

simplify57.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	401	922
1	1617	852
2	5002	852

prune332.0ms

Filtered

121 candidates to 94 candidates (77.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0b

Counts

123 → 3

localize17.0ms

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)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
168×	`cbrt-prod`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
112×	`add-cube-cbrt`
51×	`associate-r` `associate-l`
45×	`unpow-prod-down` `cube-prod`
17×	`*-commutative` `unswap-sqr`
15×	`cube-mult` `unpow3` `associate-/r*` `add-cbrt-cube` `sqr-pow`
12×	`add-exp-log` `associate-/l*`
7×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod`
2×	`div-exp` `prod-exp` `rem-cbrt-cube` `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` `div-inv` `rem-cube-cbrt`

Counts

4 → 296

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)
3.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
12.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
50.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
25.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
73.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

simplify106.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	771	3176
1	3191	2955
2	5001	2916

prune507.0ms

Filtered

308 candidates to 129 candidates (41.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	309	2	311

Merged error: 0b

Counts

311 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
11.1b	(cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
12.2b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
24.1b	(log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
66×	`add-sqr-sqrt`
52×	`add-cube-cbrt` `*-un-lft-identity`
42×	`cbrt-prod`
21×	`associate-r` `associate-l`
12×	`add-cbrt-cube` `associate-/l*`
9×	`add-exp-log`
7×	`*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`pow1` `cbrt-undiv` `add-log-exp`
2×	`expm1-log1p` `div-exp` `cbrt-unprod`
1×	`log1p-udef` `frac-2neg` `pow1/3` `log1p-expm1` `prod-exp` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 144

Calls

4 calls:

1.0ms	(expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
1.0ms	(cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
8.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
1.0ms	(log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))

series971.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
268.0ms	(cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
426.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (expm1 (log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
111.0ms	(log1p (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1191	2862
1	5001	2563

prune676.0ms

Filtered

156 candidates to 130 candidates (83.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	156	2	158

Merged error: 0b

Counts

158 → 2

localize19.0ms

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

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

Counts

4 → 114

Calls

4 calls:

1.0ms	(expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
3.0ms	(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)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
25.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
215.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (expm1 (log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))))
94.0ms	(log1p (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

simplify93.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	758	1617
1	3712	1209
2	5002	1190

prune447.0ms

Filtered

126 candidates to 96 candidates (76.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	126	2	128

Merged error: 0b

Counts

128 → 2

regimes15.0ms

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

sample356.0ms

Algorithm

intervals

Results

266.0ms

8000×

body

valid