Details

analyze14.0ms (0.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	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)

sample203.0ms (9.2%)

Algorithm

1×

intervals

Results

61.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify104.0ms (4.7%)

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

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

31.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.6b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 y 4)))
✓	4.2b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	31.0b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series39.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
10.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
8.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))

rewrite6.0ms (0.3%)

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`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
0.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
0.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))

simplify114.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
500×	`div-sub_binary64`
426×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-in_binary64`

Counts

121 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2496
1	221	2296
2	581	2284
3	2083	2266
4	4490	2230
5	5508	2230

prune77.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	4	112

Error

0.7b

Counts

112 → 4

Alt Table

Status	Error	Program
	31.6b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3))
	35.8b	(fma.f64 (pow.f64 (/.f64 x y) 4) -1/8 (fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1))
	33.3b	-1
▶	30.7b	1

Compiler

Compiled 2936 to 1416 computations (51.8% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

0.7b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	31.6b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3))
	35.8b	(fma.f64 (pow.f64 (/.f64 x y) 4) -1/8 (fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1))
	33.3b	-1
✓	30.7b	1

Compiler

Compiled 91 to 61 computations (33% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 y y) 4 (.f64 x x))
✓	0.0b	(pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)
✓	1.8b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	31.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x)))

series76.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)
22.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x)))
10.0ms	(fma.f64 (.f64 y y) 4 (.f64 x x))
9.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
13×	`cube-prod_binary64`

Counts

4 → 97

Calls

4 calls:

3.0ms	(pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)
2.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x)))
0.0ms	(fma.f64 (.f64 y y) 4 (.f64 x x))
0.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))

simplify141.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

956×	`times-frac_binary64`
649×	`log-prod_binary64`
469×	`fma-def_binary64`
357×	`unswap-sqr_binary64`
193×	`fma-neg_binary64`

Counts

193 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	5004
1	469	4683
2	1515	4579
3	4334	4555
4	5761	4555

prune96.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	135	4	139

Error

0.7b

Counts

139 → 4

Alt Table

Status	Error	Program
▶	31.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)) 3))
	35.8b	(fma.f64 (pow.f64 (/.f64 x y) 4) -1/8 (fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1))
	33.3b	-1
✓	30.7b	1

Compiler

Compiled 4100 to 2130 computations (48% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)
✓	0.0b	(pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)) 3)
	1.8b	(fma.f64 y (.f64 y -4) (.f64 x x))
	31.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x)))

series35.0ms (1.6%)

Counts

1 → 24

Calls

1 calls:

35.0ms

(pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (*.f64 y -4) (*.f64 x x)) (fma.f64 (*.f64 y y) 4 (*.f64 x x))) 3)) 3)

rewrite23.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`cbrt-prod_binary64`
61×	`cube-prod_binary64`
61×	`unpow-prod-down_binary64`
36×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`

Counts

1 → 91

Calls

1 calls:

8.0ms

(pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (*.f64 y -4) (*.f64 x x)) (fma.f64 (*.f64 y y) 4 (*.f64 x x))) 3)) 3)

simplify137.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

713×	`times-frac_binary64`
473×	`associate-/l*_binary64`
390×	`unswap-sqr_binary64`
335×	`fma-def_binary64`
317×	`log-div_binary64`

Counts

115 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	5129
1	426	4528
2	1208	4340
3	4605	4328
4	5378	4328

prune159.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	200	4	204

Error

0.7b

Counts

204 → 4

Alt Table

Status	Error	Program
✓	31.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 (.f64 y y) 4 (.f64 x x))) 3)) 3))
	35.8b	(fma.f64 (pow.f64 (/.f64 x y) 4) -1/8 (fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1))
	33.3b	-1
✓	30.7b	1

Compiler

Compiled 6860 to 3811 computations (44.4% saved)

regimes176.0ms (8%)

Accuracy

Total 12.5b remaining (97.3%)

Threshold costs 0b (0%)

Counts

10 → 3

Compiler

Compiled 1253 to 763 computations (39.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	54
1	28	54
2	27	54

end1.0ms (0%)

Compiler: Compiled 39 to 24 computations (38.5% saved)

sample734.0ms (33.4%)

Algorithm

1×

intervals

Results

459.0ms

8000×

body

128

valid

Compiler

Compiled 113 to 74 computations (34.5% saved)

Details

analyze14.0ms (0.6%)

sample203.0ms (9.2%)

simplify104.0ms (4.7%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series39.0ms (1.8%)

rewrite6.0ms (0.3%)

simplify114.0ms (5.2%)

prune77.0ms (3.5%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize12.0ms (0.6%)

series76.0ms (3.5%)

rewrite15.0ms (0.7%)

simplify141.0ms (6.4%)

prune96.0ms (4.3%)

localize16.0ms (0.7%)

series35.0ms (1.6%)

rewrite23.0ms (1.1%)

simplify137.0ms (6.2%)

prune159.0ms (7.2%)

regimes176.0ms (8%)

bsearch1.0ms (0%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample734.0ms (33.4%)

Profiling