Details

analyze1.3s (18.9%)

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
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.0s (29.9%)

Results

1.4s	8256×	body	128	valid
526.0ms	3243×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (/.f64 t y))
✓	0.4b	(/.f64 -1/3 z)
✓	2.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series31.0ms (0.5%)

Counts

3 → 54

Calls

3 calls:

24.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
5.0ms	(-.f64 y (/.f64 t y))
2.0ms	(/.f64 -1/3 z)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

3 → 110

Calls

3 calls:

6.0ms	(-.f64 y (/.f64 t y))
3.0ms	(/.f64 -1/3 z)
0.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-/l*_binary64`
411×	`associate-*l/_binary64`
388×	`associate-*r/_binary64`
368×	`times-frac_binary64`
350×	`fma-def_binary64`

Counts

164 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	2830
1	566	1960
2	1256	1654
3	4414	1654
4	4841	1654

prune139.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Status	Error	Program
	3.2b	(fma.f64 (/.f64 -1/3 z) (+.f64 y (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (/.f64 (cbrt.f64 t) (cbrt.f64 y)))) x)
▶	3.0b	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)
	3.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	3.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)
	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x) 3))
	27.4b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)

Compiler

Compiled 3587 to 1291 computations (64% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (/.f64 t y))
✓	0.4b	(*.f64 -1/3 (/.f64 1 z))
✓	2.7b	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)

series24.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

22.0ms	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)
2.0ms	(*.f64 -1/3 (/.f64 1 z))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(*.f64 -1/3 (/.f64 1 z))
0.0ms	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-neg_binary64`
310×	`associate-l_binary64`
310×	`exp-prod_binary64`
297×	`distribute-lft-neg-out_binary64`
293×	`distribute-rgt-neg-out_binary64`

Counts

108 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1331
1	185	1125
2	362	1119
3	766	1053
4	2278	1053
5	4506	1053
6	4969	1053

prune144.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Error

0.0b

Counts

174 → 8

Alt Table

Status	Error	Program
	32.7b	(fma.f64 (.f64 (.f64 -1/3 (sqrt.f64 (/.f64 1 z))) (sqrt.f64 (/.f64 1 z))) (-.f64 y (/.f64 t y)) x)
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x) 3))
▶	3.2b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
	3.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)
	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
	27.4b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)

Compiler

Compiled 4346 to 1783 computations (59% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 -1/3 (/.f64 1 z))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	2.7b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)

series142.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

72.0ms	(cbrt.f64 t)
38.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
32.0ms	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

4.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)
0.0ms	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-def_binary64`
525×	`unswap-sqr_binary64`
381×	`associate-l_binary64`
345×	`log-prod_binary64`
304×	`associate-r_binary64`

Counts

137 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1836
1	195	1411
2	586	1289
3	2251	1274
4	4362	1274
5	5188	1274

prune183.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	200	8	208

Error

0.0b

Counts

208 → 8

Alt Table

Status	Error	Program
✓	3.2b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
▶	3.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)
	13.3b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (cbrt.f64 (*.f64 t t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x) 3))
	27.4b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)

Compiler

Compiled 5410 to 2726 computations (49.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 -1/3 z)
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z)))
✓	0.6b	(cbrt.f64 (/.f64 -1/3 z))
✓	2.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)

series217.0ms (3.2%)

Counts

3 → 72

Calls

3 calls:

121.0ms

(fma.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)

56.0ms

(*.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z)))

40.0ms

(cbrt.f64 (/.f64 -1/3 z))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary64`
66×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`

Counts

3 → 114

Calls

3 calls:

13.0ms

(*.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z)))

2.0ms

(cbrt.f64 (/.f64 -1/3 z))

0.0ms

(fma.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/l*_binary64`
376×	`associate-l_binary64`
362×	`fma-def_binary64`
322×	`associate-r_binary64`
265×	`distribute-rgt-in_binary64`

Counts

186 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	3308
1	288	3055
2	759	2978
3	2018	2892
4	5111	2892

prune333.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	347	8	355

Error

0.0b

Counts

355 → 8

Alt Table

Status	Error	Program
✓	3.2b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
✓	3.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 z)) (cbrt.f64 (/.f64 -1/3 z))) (cbrt.f64 (/.f64 -1/3 z))) (-.f64 y (/.f64 t y)) x)
	13.3b	(fma.f64 (.f64 -1/3 (/.f64 1 z)) (+.f64 y (.f64 (neg.f64 (/.f64 (cbrt.f64 (*.f64 t t)) 1)) (/.f64 (cbrt.f64 t) y))) x)
	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	32.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (sqrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x) 3))
	27.4b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)

Compiler

Compiled 9534 to 5867 computations (38.5% saved)

regimes1.5s (22.2%)

Accuracy

Total 0.8b remaining (95.8%)

Threshold costs 0.8b (95.8%)

Counts

134 → 3

Compiler

Compiled 17650 to 10857 computations (38.5% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	56
1	34	56
2	43	56
3	47	56
4	49	56
5	49	56

end134.0ms (2%)

Compiler: Compiled 257 to 175 computations (31.9% saved)

Details

analyze1.3s (18.9%)

sample2.0s (29.9%)

simplify92.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series31.0ms (0.5%)

rewrite18.0ms (0.3%)

simplify100.0ms (1.5%)

prune139.0ms (2.1%)

localize10.0ms (0.1%)

series24.0ms (0.4%)

rewrite8.0ms (0.1%)

simplify91.0ms (1.4%)

prune144.0ms (2.1%)

localize17.0ms (0.3%)

series142.0ms (2.1%)

rewrite8.0ms (0.1%)

simplify90.0ms (1.3%)

prune183.0ms (2.7%)

localize13.0ms (0.2%)

series217.0ms (3.2%)

rewrite27.0ms (0.4%)

simplify115.0ms (1.7%)

prune333.0ms (4.9%)

regimes1.5s (22.2%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end134.0ms (2%)

Profiling