Details

analyze921.0ms (12.4%)

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)

sample1.6s (21%)

Results

964.0ms	8256×	body	128	valid
359.0ms	3083×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune4.0ms (0.1%)

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	6.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series38.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

31.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
7.0ms	(-.f64 t (*.f64 z z))

rewrite119.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

524×	`prod-diff_binary64`
397×	`fma-udef_binary64`
355×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`

Counts

2 → 119

Calls

2 calls:

116.0ms	(-.f64 t (*.f64 z z))
116.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	232	24
2	2678	24
3	4790	24
4	4815	24
5	4945	24
0	0	0
1	0	0

simplify204.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-neg-in_binary64`
686×	`fma-def_binary64`
678×	`cube-prod_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

191 → 139

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	29	1087
1	85	941
2	200	869
3	491	869
4	1080	869
5	1887	869
6	2612	869
7	3173	869
8	3184	869
9	3382	869
10	3546	869
11	3731	749
12	3361	749
13	3932	749
14	4622	749
15	4884	749

prune116.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	8	140

Error

5.6b

Counts

140 → 8

Alt Table

Status	Error	Program
	32.7b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)
	41.6b	(pow.f64 x 2)
	17.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
	37.2b	(.f64 4 (.f64 y t))
	40.5b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	6.7b	(fma.f64 y (.f64 4 (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t)) (*.f64 x x))
▶	6.5b	(fma.f64 y (.f64 4 (fma.f64 z (neg.f64 z) t)) (.f64 x x))
	7.7b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2))

Compiler

Compiled 2977 to 1233 computations (58.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.1b	(fma.f64 y (.f64 4 (fma.f64 z (neg.f64 z) t)) (.f64 x x))

series36.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

36.0ms

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

rewrite46.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

849×	`log1p-expm1-u_binary64`
849×	`expm1-log1p-u_binary64`
176×	`prod-diff_binary64`
109×	`add-sqr-sqrt_binary64`
102×	`add-cbrt-cube_binary64`

Counts

1 → 23

Calls

1 calls:

45.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	222	15
2	2231	15
3	5435	15
0	0	0
1	0	0

simplify194.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

708×	`distribute-rgt-neg-in_binary64`
678×	`cube-prod_binary64`
657×	`fma-def_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

71 → 38

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	27	940
1	81	794
2	192	722
3	465	722
4	1047	722
5	1855	722
6	2608	722
7	3162	722
8	3174	722
9	3372	722
10	3536	722
11	3721	644
12	3351	644
13	3922	644
14	4612	644
15	4874	644

prune27.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	38	8	46

Error

5.6b

Counts

46 → 8

Alt Table

Status	Error	Program
	32.7b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)
	41.6b	(pow.f64 x 2)
	17.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
	37.2b	(.f64 4 (.f64 y t))
	40.5b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
▶	6.7b	(fma.f64 y (.f64 4 (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t)) (*.f64 x x))
✓	6.5b	(fma.f64 y (.f64 4 (fma.f64 z (neg.f64 z) t)) (.f64 x x))
	7.7b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2))

Compiler

Compiled 805 to 420 computations (47.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)
✓	6.1b	(fma.f64 y (.f64 4 (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t)) (*.f64 x x))

series662.0ms (8.9%)

Counts

4 → 84

Calls

4 calls:

446.0ms	(fma.f64 y (.f64 4 (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t)) (*.f64 x x))
107.0ms	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2))
68.0ms	(cbrt.f64 z)
40.0ms	(pow.f64 (cbrt.f64 z) 2)

rewrite67.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

599×	`log-prod_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
216×	`prod-diff_binary64`
210×	`log-pow_binary64`

Counts

4 → 98

Calls

4 calls:

63.0ms	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2))
63.0ms	(pow.f64 (cbrt.f64 z) 2)
63.0ms	(cbrt.f64 z)
63.0ms	(fma.f64 y (.f64 4 (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t)) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	301	31
2	2930	29
3	5136	29
0	0	0
1	0	0

simplify119.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
698×	`fma-def_binary64`
688×	`unswap-sqr_binary64`
501×	`associate-l_binary64`
417×	`cancel-sign-sub-inv_binary64`

Counts

182 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	1274
1	127	1116
2	301	1038
3	731	1038
4	1920	1038
5	4022	1038
6	4276	1038
7	4852	1038
8	4871	1038

prune96.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	152	5	157

Error

0.0b

Counts

157 → 5

Alt Table

Status	Error	Program
	40.5b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	24.5b	(fma.f64 z (.f64 y (.f64 z -4)) (*.f64 x x))
	32.7b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)
✓	6.5b	(fma.f64 y (.f64 4 (fma.f64 z (neg.f64 z) t)) (.f64 x x))
▶	7.7b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2))

Compiler

Compiled 3167 to 1512 computations (52.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2)
✓	1.8b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	6.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series680.0ms (9.2%)

Counts

3 → 144

Calls

3 calls:

453.0ms

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

189.0ms

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

37.0ms

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

rewrite133.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

516×	`prod-diff_binary64`
384×	`fma-udef_binary64`
251×	`fma-def_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`

Counts

3 → 81

Calls

3 calls:

130.0ms

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

130.0ms

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

130.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	292	56
2	3127	56
3	4988	56
4	4971	56
5	4943	56
0	0	0
1	0	0

simplify194.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

225 → 259

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	767	12551
1	2739	12277
2	5028	12277

prune683.0ms (9.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	444	0	444
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	444	5	449

Error

0.0b

Counts

449 → 5

Alt Table

Status	Error	Program
	40.5b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	24.5b	(fma.f64 z (.f64 y (.f64 z -4)) (*.f64 x x))
	32.7b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)
✓	6.5b	(fma.f64 y (.f64 4 (fma.f64 z (neg.f64 z) t)) (.f64 x x))
✓	7.7b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2))

Compiler

Compiled 29635 to 18449 computations (37.7% saved)

regimes1.2s (16.6%)

Accuracy

Total 0.2b remaining (77.6%)

Threshold costs 0.2b (77.6%)

Counts

58 → 3

Compiler

Compiled 12692 to 8450 computations (33.4% saved)

bsearch79.0ms (1.1%)

Steps

Iters	Range		Point
6	2.1948801667368868e+117	1.1685855108965993e+121	9.433316727882347e+117
10	-6.685254609558345e+163	-3.722081791026493e+151	-6.038238978544222e+153

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	29	57
2	31	57
3	32	57
4	32	57

end90.0ms (1.2%)

Compiler: Compiled 188 to 111 computations (41% saved)

Details

analyze921.0ms (12.4%)

sample1.6s (21%)

simplify64.0ms (0.9%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series38.0ms (0.5%)

rewrite119.0ms (1.6%)

simplify204.0ms (2.8%)

prune116.0ms (1.6%)

localize8.0ms (0.1%)

series36.0ms (0.5%)

rewrite46.0ms (0.6%)

simplify194.0ms (2.6%)

prune27.0ms (0.4%)

localize11.0ms (0.2%)

series662.0ms (8.9%)

rewrite67.0ms (0.9%)

simplify119.0ms (1.6%)

prune96.0ms (1.3%)

localize11.0ms (0.1%)

series680.0ms (9.2%)

rewrite133.0ms (1.8%)

simplify194.0ms (2.6%)

prune683.0ms (9.2%)

regimes1.2s (16.6%)

bsearch79.0ms (1.1%)

simplify4.0ms (0%)

end90.0ms (1.2%)

Profiling