Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample871.0ms (22.3%)

Infinites

0% of outputs are infinite.

Results

681.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	4.1b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	29.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series56.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
8.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
8.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
5.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
3.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
294×	`fma-neg_binary64`
248×	`associate-/r*_binary64`

Counts

136 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2837
1	356	2636
2	1254	2600
3	4560	2600
4	5037	2600

prune105.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	4	137

Error

0.3b

Counts

137 → 4

Alt Table

Status	Error	Program
	30.5b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))))
	33.0b	-1
	31.2b	1
▶	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))))

Compiler

Compiled 4083 to 2133 computations (47.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	0.0b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))))
✓	20.9b	(/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
✓	23.3b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series147.0ms (3.8%)

Counts

3 → 72

Calls

3 calls:

65.0ms

(-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))) (/.f64 (*.f64 (*.f64 y 4) y) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))))

58.0ms

(/.f64 (*.f64 (*.f64 y 4) y) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))

24.0ms

(/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))

rewrite60.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`prod-diff_binary64`
67×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
48×	`associate-/r/_binary64`

Counts

3 → 172

Calls

3 calls:

16.0ms

(-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))) (/.f64 (*.f64 (*.f64 y 4) y) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))))

10.0ms

(/.f64 (*.f64 (*.f64 y 4) y) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))

5.0ms

(/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))

simplify286.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
284×	`distribute-neg-frac_binary64`
195×	`sub-neg_binary64`
182×	`associate-/l*_binary64`

Counts

244 → 307

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	15319
1	887	11002
2	3252	8719
3	4878	8719
4	4894	8719

prune420.0ms (10.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	360	1	361
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	361	4	365

Error

0.3b

Counts

365 → 4

Alt Table

Status	Error	Program
✓	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))))
▶	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4)))))))
	31.2b	1
	33.0b	-1

Compiler

Compiled 21466 to 11704 computations (45.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4)))))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	20.9b	(/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4))))
	23.3b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series80.0ms (2%)

Counts

3 → 72

Calls

3 calls:

31.0ms

(-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4)))))))

24.0ms

(/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4))))

24.0ms

(expm1.f64 (log1p.f64 (/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`prod-diff_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
16×	`times-frac_binary64`

Counts

3 → 92

Calls

3 calls:

10.0ms

(-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4)))))))

5.0ms

(/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4))))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (*.f64 y (*.f64 y 4)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

simplify160.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
410×	`fma-neg_binary64`
392×	`associate-/r/_binary64`
320×	`associate-/l/_binary64`
306×	`cancel-sign-sub-inv_binary64`

Counts

164 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	7349
1	555	5759
2	2037	5095
3	4841	5095
4	4979	5095

prune261.0ms (6.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	224	4	228

Error

0.3b

Counts

228 → 4

Alt Table

Status	Error	Program
✓	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))))
✓	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4)))))))
▶	31.2b	1
	33.0b	-1

Compiler

Compiled 11706 to 6732 computations (42.5% saved)

localize0.0ms (0%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.3b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (/.f64 (.f64 (.f64 y 4) y) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))))
✓	30.5b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))) (expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 y 4)) (fma.f64 x x (.f64 y (.f64 y 4)))))))
✓	31.2b	1
	33.0b	-1

Compiler

Compiled 69 to 42 computations (39.1% saved)

regimes1.0s (26.1%)

Accuracy

Total 11.8b remaining (97.2%)

Threshold costs 0b (0%)

Counts

98 → 5

Compiler

Compiled 14316 to 8672 computations (39.4% saved)

bsearch67.0ms (1.7%)

Steps

Iters	Range		Point
9	1.0139683234247327e+138	1.5631059904905651e+147	1.53922962851806e+147
5	1.411795836989264e-153	3.649414678791937e-153	1.9388453121044746e-153
8	-4.132173779288115e-121	-1.2422370898486311e-123	-2.5067818285457853e-122
10	-1.0938974287607881e+169	-1.4976561051222266e+159	-1.511705281598505e+159

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	109
1	47	109
2	52	109
3	62	109
4	67	109
5	70	109
6	71	109
7	69	109

end93.0ms (2.4%)

Compiler: Compiled 223 to 132 computations (40.8% saved)

Details

analyze4.0ms (0.1%)

sample871.0ms (22.3%)

simplify104.0ms (2.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series56.0ms (1.4%)

rewrite17.0ms (0.4%)

simplify88.0ms (2.2%)

prune105.0ms (2.7%)

localize10.0ms (0.3%)

series147.0ms (3.8%)

rewrite60.0ms (1.5%)

simplify286.0ms (7.3%)

prune420.0ms (10.7%)

localize13.0ms (0.3%)

series80.0ms (2%)

rewrite25.0ms (0.7%)

simplify160.0ms (4.1%)

prune261.0ms (6.7%)

localize0.0ms (0%)

prune4.0ms (0.1%)

regimes1.0s (26.1%)

bsearch67.0ms (1.7%)

simplify7.0ms (0.2%)

end93.0ms (2.4%)

Profiling