Details

analyze1.6s (20.7%)

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)

sample2.0s (25.3%)

Results

1.7s	8256×	body	128	valid
126.0ms	594×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify118.0ms (1.5%)

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

prune3.0ms (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

10.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.8b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	10.2b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series66.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

54.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
12.0ms	(*.f64 x (-.f64 y z))

rewrite34.0ms (0.4%)

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:

14.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
11.0ms	(*.f64 x (-.f64 y z))

simplify169.0ms (2.1%)

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

prune207.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	136	9	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	9	146

Error

0.0b

Counts

146 → 9

Alt Table

Status	Error	Program
	10.9b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	42.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) t) (+.f64 (/.f64 (.f64 y (.f64 z x)) (pow.f64 t 2)) (/.f64 (.f64 y (.f64 (pow.f64 z 2) x)) (pow.f64 t 3)))) (+.f64 (/.f64 (.f64 z x) t) (/.f64 (*.f64 (pow.f64 z 2) x) (pow.f64 t 2))))
	34.8b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 t z))))
	31.1b	(neg.f64 (/.f64 (*.f64 z x) (-.f64 t z)))
	2.2b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
▶	2.1b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	7.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (-.f64 y z) (cbrt.f64 (-.f64 t z))))
	11.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (cbrt.f64 (.f64 x (-.f64 y z)))) (cbrt.f64 (*.f64 x (-.f64 y z)))) (-.f64 t z))

Compiler

Compiled 3421 to 1060 computations (69% saved)

localize14.0ms (0.2%)

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)))

series90.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

59.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
30.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite49.0ms (0.6%)

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:

19.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
13.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

simplify163.0ms (2.1%)

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

prune251.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	182	8	190

Error

Counts

190 → 8

Alt Table

Status	Error	Program
	3.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))) (cbrt.f64 (.f64 x (/.f64 (-.f64 y z) (-.f64 t z))))) (cbrt.f64 (*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))))
▶	2.2b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	10.9b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	3.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (-.f64 y z) (-.f64 t z))))
	7.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (-.f64 y z) (cbrt.f64 (-.f64 t z))))
	34.3b	(*.f64 x (/.f64 y (-.f64 t z)))
	23.9b	(*.f64 x (neg.f64 (/.f64 z (-.f64 t z))))

Compiler

Compiled 4352 to 1296 computations (70.2% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series84.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

54.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
30.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

rewrite75.0ms (0.9%)

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:

19.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
12.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

simplify292.0ms (3.7%)

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

prune295.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	298	2	300
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	302	6	308

Error

Counts

308 → 6

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
✓	2.2b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	34.3b	(*.f64 x (/.f64 y (-.f64 t z)))
	23.9b	(*.f64 x (neg.f64 (/.f64 z (-.f64 t z))))

Compiler

Compiled 7205 to 1691 computations (76.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series129.0ms (1.6%)

Counts

4 → 144

Calls

4 calls:

56.0ms	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
31.0ms	(/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
30.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
11.0ms	(/.f64 1 (-.f64 t z))

rewrite107.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
86×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
52×	`div-exp_binary64`

Counts

4 → 229

Calls

4 calls:

23.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
22.0ms	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
16.0ms	(/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
6.0ms	(/.f64 1 (-.f64 t z))

simplify356.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

394×	`fma-neg_binary64`
221×	`associate-/l*_binary64`
220×	`associate--r+_binary64`
220×	`associate--l+_binary64`
219×	`times-frac_binary64`

Counts

373 → 422

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	455	8101
1	1131	7399
2	4282	7261
3	4925	7258
4	5013	7258

prune473.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	422	6	428

Error

Counts

428 → 6

Alt Table

Status	Error	Program
✓	2.5b	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
✓	2.2b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	34.3b	(*.f64 x (/.f64 y (-.f64 t z)))
	23.9b	(*.f64 x (neg.f64 (/.f64 z (-.f64 t z))))

Compiler

Compiled 9742 to 4046 computations (58.5% saved)

regimes1.1s (14.4%)

Accuracy

Total 1.1b remaining (98.5%)

Threshold costs 0b (0%)

Counts

140 → 1

Compiler

Compiled 13411 to 7653 computations (42.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	15	49
1	20	49
2	26	49
3	28	49
4	29	49
5	29	49

end134.0ms (1.7%)

Compiler: Compiled 152 to 81 computations (46.7% saved)

Details

analyze1.6s (20.7%)

sample2.0s (25.3%)

simplify118.0ms (1.5%)

prune3.0ms (0%)

localize13.0ms (0.2%)

series66.0ms (0.8%)

rewrite34.0ms (0.4%)

simplify169.0ms (2.1%)

prune207.0ms (2.6%)

localize14.0ms (0.2%)

series90.0ms (1.1%)

rewrite49.0ms (0.6%)

simplify163.0ms (2.1%)

prune251.0ms (3.2%)

localize12.0ms (0.2%)

series84.0ms (1.1%)

rewrite75.0ms (0.9%)

simplify292.0ms (3.7%)

prune295.0ms (3.7%)

localize17.0ms (0.2%)

series129.0ms (1.6%)

rewrite107.0ms (1.3%)

simplify356.0ms (4.5%)

prune473.0ms (6%)

regimes1.1s (14.4%)

simplify5.0ms (0.1%)

end134.0ms (1.7%)

Profiling