Details

analyze1.3s (30.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (27.7%)

Results

1.0s	8255×	body	128	valid
94.0ms	727×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series60.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

46.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
15.0ms	(/.f64 t (-.f64 a z))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

3.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune76.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	2.7b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
	23.4b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
	25.1b	(fma.f64 (/.f64 y a) t x)

Compiler

Compiled 2385 to 753 computations (68.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 t (/.f64 1 (-.f64 a z)))
✓	2.6b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)

series62.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

36.0ms	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
16.0ms	(*.f64 t (/.f64 1 (-.f64 a z)))
9.0ms	(/.f64 1 (-.f64 a z))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 99

Calls

3 calls:

7.0ms	(*.f64 t (/.f64 1 (-.f64 a z)))
4.0ms	(/.f64 1 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)

simplify94.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

762×	`associate-/l*_binary64`
755×	`fma-def_binary64`
291×	`cancel-sign-sub-inv_binary64`
228×	`associate-/r/_binary64`
178×	`sub-neg_binary64`

Counts

219 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	4220
1	577	4080
2	2119	3398
3	5241	3398

prune126.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	197	5	202

Error

Counts

202 → 5

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	2.7b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
	23.4b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
	25.1b	(fma.f64 (/.f64 y a) t x)

Compiler

Compiled 4171 to 1556 computations (62.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	10.7b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series89.0ms (2%)

Counts

3 → 144

Calls

3 calls:

44.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
36.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
6.0ms	(*.f64 (-.f64 y z) t)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
6.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
5.0ms	(*.f64 (-.f64 y z) t)

simplify147.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
587×	`cancel-sign-sub-inv_binary64`
313×	`sub-neg_binary64`
179×	`fma-neg_binary64`
159×	`associate-/l*_binary64`

Counts

216 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	5006
1	725	4379
2	2654	3966
3	4886	3964
4	5000	3964
5	4974	3964

prune123.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	188	5	193

Error

Counts

193 → 5

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	2.7b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
	23.4b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
▶	0.8b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))

Compiler

Compiled 4385 to 1255 computations (71.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	0.9b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))

series95.0ms (2.2%)

Counts

3 → 144

Calls

3 calls:

43.0ms	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
32.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
20.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

11.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
7.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
2.0ms	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))

simplify137.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

809×	`cancel-sign-sub-inv_binary64`
481×	`sub-neg_binary64`
214×	`associate--l+_binary64`
213×	`fma-neg_binary64`
205×	`+-commutative_binary64`

Counts

266 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	6572
1	979	6464
2	3690	6005
3	5272	6005

prune159.0ms (3.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	243	5	248

Error

Counts

248 → 5

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	2.7b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
✓	0.8b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
	18.7b	(+.f64 x (*.f64 t (neg.f64 (+.f64 (/.f64 y z) -1))))

Compiler

Compiled 6197 to 1797 computations (71% saved)

regimes278.0ms (6.4%)

Accuracy

Total 1.2b remaining (98.7%)

Threshold costs 0b (0%)

Counts

46 → 1

Compiler

Compiled 4811 to 3068 computations (36.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	22	16
3	24	16
4	25	16
5	25	16

end76.0ms (1.7%)

Compiler: Compiled 111 to 71 computations (36% saved)

Details

analyze1.3s (30.2%)

sample1.2s (27.7%)

simplify118.0ms (2.7%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series60.0ms (1.4%)

rewrite7.0ms (0.2%)

simplify73.0ms (1.7%)

prune76.0ms (1.8%)

localize10.0ms (0.2%)

series62.0ms (1.4%)

rewrite18.0ms (0.4%)

simplify94.0ms (2.2%)

prune126.0ms (2.9%)

localize8.0ms (0.2%)

series89.0ms (2%)

rewrite22.0ms (0.5%)

simplify147.0ms (3.4%)

prune123.0ms (2.8%)

localize8.0ms (0.2%)

series95.0ms (2.2%)

rewrite31.0ms (0.7%)

simplify137.0ms (3.2%)

prune159.0ms (3.6%)

regimes278.0ms (6.4%)

simplify2.0ms (0.1%)

end76.0ms (1.7%)

Profiling