Details

analyze826.0ms (18.8%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (26.9%)

Results

989.0ms	8256×	body	128	valid
76.0ms	634×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.2b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	11.6b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series41.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
7.0ms	(*.f64 x (-.f64 y z))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 81

Calls

2 calls:

9.0ms	(*.f64 x (-.f64 y z))
8.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

simplify102.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
513×	`fma-neg_binary64`
365×	`div-sub_binary64`
202×	`associate-/l*_binary64`
196×	`sub-neg_binary64`

Counts

165 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	2954
1	576	2753
2	2576	2555
3	4147	2552
4	5042	2552

prune104.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Error

0.0b

Counts

146 → 8

Alt Table

Status	Error	Program
▶	2.2b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	35.3b	(+.f64 x (*.f64 (/.f64 x z) (-.f64 t y)))
	2.7b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	39.7b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 (-.f64 t z) (+.f64 y z)))
	12.2b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) x) 3)) (-.f64 t z))
	8.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (-.f64 y z) (cbrt.f64 (-.f64 t z))))
	35.7b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))

Compiler

Compiled 3315 to 1006 computations (69.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	2.1b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

series61.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
27.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

14.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
7.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

simplify111.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
511×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
220×	`fma-neg_binary64`
164×	`associate-/l*_binary64`

Counts

190 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4489
1	786	4288
2	2972	4076
3	5031	4076

prune107.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Error

Counts

189 → 9

Alt Table

Status	Error	Program
	2.7b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	40.6b	(/.f64 (fma.f64 -1 y z) (/.f64 z x))
▶	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	39.7b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 (-.f64 t z) (+.f64 y z)))
	22.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))))
	12.2b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	32.4b	(.f64 (.f64 x (/.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))))) (/.f64 (sqrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) x) 3)) (-.f64 t z))
✓	2.2b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 4361 to 1316 computations (69.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 t z))
✓	0.2b	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
✓	2.1b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))

series64.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

34.0ms	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
21.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
9.0ms	(/.f64 1 (-.f64 t z))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 125

Calls

3 calls:

17.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
10.0ms	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
4.0ms	(/.f64 1 (-.f64 t z))

simplify114.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

753×	`times-frac_binary64`
513×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
221×	`fma-neg_binary64`
160×	`associate-l_binary64`

Counts

233 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4914
1	792	4536
2	2901	4482
3	5046	4482

prune160.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	244	9	253

Error

Counts

253 → 9

Alt Table

Status	Error	Program
▶	2.7b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	40.6b	(/.f64 (fma.f64 -1 y z) (/.f64 z x))
✓	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	39.7b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 (-.f64 t z) (+.f64 y z)))
	12.2b	(/.f64 (.f64 x (.f64 (-.f64 y z) 1)) (-.f64 t z))
	32.4b	(.f64 (.f64 x (/.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))))) (/.f64 (sqrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))
	22.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))))
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) x) 3)) (-.f64 t z))
✓	2.2b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 5594 to 2171 computations (61.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series54.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
20.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 198

Calls

2 calls:

12.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
7.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

simplify174.0ms (4%)

Algorithm

1×	egg-herbie

Rules

562×	`cancel-sign-sub-inv_binary64`
374×	`sub-neg_binary64`
271×	`associate-/r/_binary64`
224×	`fma-neg_binary64`
198×	`associate-/l/_binary64`

Counts

282 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	7629
1	1057	7410
2	3983	7368
3	5298	7368

prune162.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	298	2	300
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	301	8	309

Error

Counts

309 → 8

Alt Table

Status	Error	Program
✓	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	39.7b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 (-.f64 t z) (+.f64 y z)))
	12.2b	(/.f64 (.f64 x (.f64 (-.f64 y z) 1)) (-.f64 t z))
	16.7b	(/.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) (-.f64 y z)) 3)))
✓	2.7b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.9b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) x) 3)) (-.f64 t z))
✓	2.2b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 7176 to 1671 computations (76.7% saved)

regimes738.0ms (16.8%)

Accuracy

Total 1.3b remaining (99.1%)

Threshold costs 0b (0%)

Counts

86 → 3

Compiler

Compiled 7520 to 4484 computations (40.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	78
1	31	78
2	36	78
3	38	78
4	39	78
5	38	78

end98.0ms (2.2%)

Compiler: Compiled 236 to 118 computations (50% saved)

Details

analyze826.0ms (18.8%)

sample1.2s (26.9%)

simplify116.0ms (2.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series41.0ms (0.9%)

rewrite21.0ms (0.5%)

simplify102.0ms (2.3%)

prune104.0ms (2.4%)

localize6.0ms (0.1%)

series61.0ms (1.4%)

rewrite29.0ms (0.7%)

simplify111.0ms (2.5%)

prune107.0ms (2.4%)

localize7.0ms (0.2%)

series64.0ms (1.5%)

rewrite42.0ms (1%)

simplify114.0ms (2.6%)

prune160.0ms (3.7%)

localize6.0ms (0.1%)

series54.0ms (1.2%)

rewrite43.0ms (1%)

simplify174.0ms (4%)

prune162.0ms (3.7%)

regimes738.0ms (16.8%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end98.0ms (2.2%)

Profiling