Details

analyze978.0ms (16.2%)

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)

sample1.5s (24.1%)

Results

1.0s	8256×	body	128	valid
352.0ms	2996×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify47.0ms (0.8%)

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

4.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.3b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

Compiler

Compiled 61 to 34 computations (44.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 z z) t)
✓	4.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

series31.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

27.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
4.0ms	(-.f64 (*.f64 z z) t)

rewrite55.0ms (0.9%)

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	24
1	230	24
2	2868	24

Stop Event

1×	node limit

Counts

2 → 122

Calls

2 calls:

53.0ms	(-.f64 (*.f64 z z) t)
53.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
629×	`fma-neg_binary64`
389×	`cancel-sign-sub-inv_binary64`
306×	`distribute-rgt-neg-in_binary64`
292×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1087
1	85	941
2	233	869
3	605	869
4	1611	869
5	3221	869
6	4735	869

Stop Event

1×	node limit

Counts

194 → 144

prune122.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	10	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Error

4.1b

Counts

145 → 10

Alt Table

Status	Error	Program
	24.6b	(fma.f64 y (.f64 (.f64 (-.f64 (pow.f64 z 4) (.f64 t t)) (/.f64 1 (fma.f64 z z t))) -4) (.f64 x x))
	15.5b	(fma.f64 x x (.f64 t (.f64 4 y)))
	4.5b	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))
	33.8b	(fma.f64 y (.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (neg.f64 t)) -4) (*.f64 x x))
	5.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 3)
▶	4.3b	(fma.f64 y (.f64 (fma.f64 z z (neg.f64 t)) -4) (.f64 x x))
	5.4b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))
	42.0b	(pow.f64 x 2)
	5.1b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 z z) t)) 3) -4) (*.f64 x x))
	35.1b	(.f64 4 (.f64 y t))

Compiler

Compiled 2940 to 1280 computations (56.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(fma.f64 y (.f64 (fma.f64 z z (neg.f64 t)) -4) (.f64 x x))

series27.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

27.0ms

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

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`log1p-expm1-u_binary64`
858×	`expm1-log1p-u_binary64`
229×	`prod-diff_binary64`
111×	`add-sqr-sqrt_binary64`
102×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	221	15
2	2623	15

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

42.0ms

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

simplify52.0ms (0.9%)

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

71 → 39

prune27.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Error

0.0b

Counts

49 → 6

Alt Table

Status	Error	Program
	26.8b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	15.5b	(fma.f64 x x (.f64 t (.f64 4 y)))
▶	4.5b	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))
	33.8b	(fma.f64 y (.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (neg.f64 t)) -4) (*.f64 x x))
✓	4.3b	(fma.f64 y (.f64 (fma.f64 z z (neg.f64 t)) -4) (.f64 x x))
	5.4b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))

Compiler

Compiled 774 to 394 computations (49.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (pow.f64 (cbrt.f64 z) 2))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)
✓	4.1b	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))

series567.0ms (9.4%)

Counts

4 → 84

Calls

4 calls:

374.0ms	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))
86.0ms	(pow.f64 (cbrt.f64 z) 2)
64.0ms	(*.f64 z (pow.f64 (cbrt.f64 z) 2))
42.0ms	(cbrt.f64 z)

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`prod-diff_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
146×	`add-sqr-sqrt_binary64`
139×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	302	35
2	3493	33

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

51.0ms	(*.f64 z (pow.f64 (cbrt.f64 z) 2))
51.0ms	(pow.f64 (cbrt.f64 z) 2)
51.0ms	(cbrt.f64 z)
51.0ms	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
688×	`unswap-sqr_binary64`
578×	`associate-l_binary64`
460×	`associate-r_binary64`
351×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	1266
1	129	1108
2	348	1030
3	989	1030
4	3273	1030

Stop Event

1×	node limit

Counts

163 → 101

prune102.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	127	6	133

Error

0.0b

Counts

133 → 6

Alt Table

Status	Error	Program
	26.8b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	15.5b	(fma.f64 x x (.f64 t (.f64 4 y)))
✓	4.5b	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))
	33.8b	(fma.f64 y (.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (neg.f64 t)) -4) (*.f64 x x))
✓	4.3b	(fma.f64 y (.f64 (fma.f64 z z (neg.f64 t)) -4) (.f64 x x))
▶	5.4b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))

Compiler

Compiled 2691 to 1245 computations (53.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
✓	1.0b	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
✓	4.1b	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

series430.0ms (7.1%)

Counts

4 → 180

Calls

4 calls:

232.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
147.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
30.0ms	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))
20.0ms	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

590×	`prod-diff_binary64`
245×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	71
1	313	71
2	3542	71

Stop Event

1×	node limit

Counts

4 → 81

Calls

4 calls:

61.0ms	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))
61.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
61.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
61.0ms	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))

simplify169.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

775×	`times-frac_binary64`
707×	`fma-def_binary64`
295×	`*-commutative_binary64`
159×	`sub-neg_binary64`
156×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	770	13046
1	2819	12772

Stop Event

1×	node limit

Counts

261 → 261

prune582.0ms (9.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	395	0	395
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	395	6	401

Error

0.0b

Counts

401 → 6

Alt Table

Status	Error	Program
	26.8b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	15.5b	(fma.f64 x x (.f64 t (.f64 4 y)))
✓	4.5b	(fma.f64 y (.f64 (fma.f64 (.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (neg.f64 t)) -4) (*.f64 x x))
	33.8b	(fma.f64 y (.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (neg.f64 t)) -4) (*.f64 x x))
✓	4.3b	(fma.f64 y (.f64 (fma.f64 z z (neg.f64 t)) -4) (.f64 x x))
✓	5.4b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2))

Compiler

Compiled 28564 to 18614 computations (34.8% saved)

regimes935.0ms (15.5%)

Accuracy

Total 0.3b remaining (86.8%)

Threshold costs 0.3b (86.8%)

Counts

59 → 3

Compiler

Compiled 12878 to 8350 computations (35.2% saved)

bsearch29.0ms (0.5%)

Steps

Iters	Range		Point
2	9.63658784865117e+135	2.8935849714929136e+140	2.1474743947097236e+139
6	-6.57601071846273e+121	-1.1584282867602942e+79	-1.1783638165363816e+89

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	30	57
2	32	57
3	33	57

Stop Event

1×

saturated

end99.0ms (1.6%)

Compiler: Compiled 205 to 124 computations (39.5% saved)

Details

analyze978.0ms (16.2%)

sample1.5s (24.1%)

simplify47.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series31.0ms (0.5%)

rewrite55.0ms (0.9%)

simplify56.0ms (0.9%)

prune122.0ms (2%)

localize8.0ms (0.1%)

series27.0ms (0.4%)

rewrite43.0ms (0.7%)

simplify52.0ms (0.9%)

prune27.0ms (0.4%)

localize13.0ms (0.2%)

series567.0ms (9.4%)

rewrite53.0ms (0.9%)

simplify72.0ms (1.2%)

prune102.0ms (1.7%)

localize13.0ms (0.2%)

series430.0ms (7.1%)

rewrite64.0ms (1.1%)

simplify169.0ms (2.8%)

prune582.0ms (9.6%)

regimes935.0ms (15.5%)

bsearch29.0ms (0.5%)

simplify7.0ms (0.1%)

end99.0ms (1.6%)

Profiling