Details

analyze908.0ms (4.2%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.4s (6.5%)

Results

929.0ms	8256×	body	128	valid
418.0ms	3064×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
159×	`associate-l_binary64`
152×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	77	17
3	302	17
4	829	17
5	1620	17
6	2745	17
7	3158	17
8	3307	17
9	3349	17
10	3365	17
11	3365	17

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

Compiler

Compiled 61 to 34 computations (44.3% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.8b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

series29.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

29.0ms

(fma.f64 y (*.f64 (-.f64 (*.f64 z z) t) -4) (*.f64 x x))

rewrite63.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`prod-diff_binary64`
233×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
182×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	230	17
2	2868	17

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

62.0ms

(fma.f64 y (*.f64 (-.f64 (*.f64 z z) t) -4) (*.f64 x x))

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
599×	`fma-neg_binary64`
387×	`cancel-sign-sub-inv_binary64`
310×	`distribute-rgt-neg-in_binary64`
284×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	940
1	81	794
2	229	722
3	597	722
4	1580	722
5	3145	722
6	4638	722

Stop Event

1×	node limit

Counts

74 → 42

prune30.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

0.1b

Counts

43 → 5

Alt Table

Status	Error	Program
▶	9.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
	34.9b	(/.f64 (-.f64 (.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))) (pow.f64 x 4)) (-.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (*.f64 x x)))
✓	8.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	23.9b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	29.1b	(exp.f64 (log.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))

Compiler

Compiled 835 to 426 computations (49% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
✓	1.7b	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
✓	7.8b	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

series15.3s (70.5%)

Counts

4 → 180

Calls

4 calls:

15.1s	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
133.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
33.0ms	(fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))
20.0ms	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

rewrite65.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

590×	`prod-diff_binary64`
236×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	291	66
2	3398	66

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

63.0ms	(fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))
63.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
63.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
63.0ms	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

simplify118.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

451×	`times-frac_binary64`
374×	`fma-def_binary64`
372×	`associate-/l*_binary64`
348×	`associate-/r*_binary64`
185×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	482	9338
1	1740	8880

Stop Event

1×	node limit

Counts

281 → 199

prune268.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	198	6	204

Error

0.1b

Counts

204 → 6

Alt Table

Status	Error	Program
▶	10.2b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))) 2) 3) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
	23.9b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	9.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
✓	8.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	34.9b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 y (.f64 -4 (-.f64 (.f64 z z) t))) 2)) (-.f64 (.f64 x x) (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))
	29.1b	(exp.f64 (log.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))

Compiler

Compiled 9710 to 6675 computations (31.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
✓	0.8b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))) 2) 3)
✓	1.7b	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))
✓	7.8b	(.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))

series705.0ms (3.3%)

Counts

4 → 180

Calls

4 calls:

411.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))) 2) 3)
151.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
124.0ms	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))
18.0ms	(.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))

rewrite74.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	355	75
2	4081	75

Stop Event

1×	node limit

Counts

4 → 100

Calls

4 calls:

72.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
72.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))) 2) 3)
72.0ms	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))))
72.0ms	(.f64 y (.f64 -4 (-.f64 (*.f64 z z) t)))

simplify221.0ms (1%)

Algorithm

1×	egg-herbie

Rules

420×	`*-commutative_binary64`
230×	`+-commutative_binary64`
230×	`sub-neg_binary64`
212×	`fma-def_binary64`
192×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1094	19200
1	4075	19020

Stop Event

1×	node limit

Counts

280 → 350

prune898.0ms (4.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	489	7	496

Error

0.0b

Counts

496 → 7

Alt Table

Status	Error	Program
✓	10.2b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))) 2) 3) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
▶	23.9b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	9.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
	41.9b	(.f64 (cbrt.f64 (pow.f64 (.f64 4 (-.f64 (.f64 t y) (.f64 (.f64 z z) y))) 2)) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (.f64 z z) t))))))
✓	8.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	34.9b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 y (.f64 -4 (-.f64 (.f64 z z) t))) 2)) (-.f64 (.f64 x x) (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))
	29.1b	(exp.f64 (log.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))

Compiler

Compiled 39850 to 26327 computations (33.9% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	0.2b	(.f64 z (.f64 z (*.f64 y -4)))

series29.0ms (0.1%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
13.0ms	(.f64 z (.f64 z (*.f64 y -4)))

rewrite76.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
198×	`prod-diff_binary64`
90×	`associate-r_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	181	24
2	2154	24

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

46.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
46.0ms	(.f64 z (.f64 z (*.f64 y -4)))

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
645×	`unswap-sqr_binary64`
326×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
252×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	738
1	32	684
2	80	684
3	225	684
4	672	684
5	1310	684
6	1997	684
7	3187	684

Stop Event

1×	node limit

Counts

98 → 44

prune40.0ms (0.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	43	8	51

Error

0.0b

Counts

51 → 8

Alt Table

Status	Error	Program
✓	9.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
	38.9b	(fma.f64 x x (exp.f64 (log.f64 (.f64 z (.f64 y (*.f64 -4 z))))))
✓	10.2b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))) 2) 3) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (*.f64 z z) t))))))
✓	23.9b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	41.9b	(.f64 (cbrt.f64 (pow.f64 (.f64 4 (-.f64 (.f64 t y) (.f64 (.f64 z z) y))) 2)) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 -4 (-.f64 (.f64 z z) t))))))
✓	8.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	34.9b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 y (.f64 -4 (-.f64 (.f64 z z) t))) 2)) (-.f64 (.f64 x x) (.f64 y (.f64 -4 (-.f64 (.f64 z z) t)))))
	43.2b	(pow.f64 (hypot.f64 x (.f64 z (sqrt.f64 (.f64 y -4)))) 2)

Compiler

Compiled 796 to 477 computations (40.1% saved)

regimes1.1s (5.2%)

Accuracy

Total 0.1b remaining (81.5%)

Threshold costs 0.1b (81.5%)

Counts

48 → 2

Compiler

Compiled 10659 to 7218 computations (32.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	25	40
2	30	40
3	32	40
4	33	40

Stop Event

1×

saturated

end144.0ms (0.7%)

Compiler: Compiled 248 to 151 computations (39.1% saved)

Details

analyze908.0ms (4.2%)

sample1.4s (6.5%)

simplify45.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0%)

series29.0ms (0.1%)

rewrite63.0ms (0.3%)

simplify56.0ms (0.3%)

prune30.0ms (0.1%)

localize12.0ms (0.1%)

series15.3s (70.5%)

rewrite65.0ms (0.3%)

simplify118.0ms (0.5%)

prune268.0ms (1.2%)

localize13.0ms (0.1%)

series705.0ms (3.3%)

rewrite74.0ms (0.3%)

simplify221.0ms (1%)

prune898.0ms (4.1%)

localize6.0ms (0%)

series29.0ms (0.1%)

rewrite76.0ms (0.3%)

simplify47.0ms (0.2%)

prune40.0ms (0.2%)

regimes1.1s (5.2%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end144.0ms (0.7%)

Profiling