Details

analyze1.4s (18.4%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99%	1%	11
0%	98.1%	1.9%	12
0.4%	96.1%	3.5%	13
0.6%	95.6%	3.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.0s (27.1%)

Symmetry

(sort y t)

Results

978.0ms	8256×	body	128	valid
794.0ms	1441×	body	8192	exit
107.0ms	877×	body	128	invalid

Compiler

Compiled 27 to 17 computations (37% saved)

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def_binary64`
304×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
90×	`associate-l_binary64`
87×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

prune3.0ms (0%)

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
▶	7.8b	(.f64 y (.f64 t (-.f64 x z)))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	7.4b	(.f64 y (.f64 t (-.f64 x z)))

series21.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

13.0ms	(.f64 y (.f64 t (-.f64 x z)))
8.0ms	(*.f64 t (-.f64 x z))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

7.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

449×	`*-commutative_binary64`
402×	`distribute-rgt-in_binary64`
400×	`distribute-rgt-neg-out_binary64`
379×	`distribute-lft-in_binary64`
309×	`fma-def_binary64`

Counts

208 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	2765
1	326	2564
2	1079	2402
3	3077	2078
4	4965	2078
5	4751	2078

prune76.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Error

0.0b

Counts

155 → 8

Alt Table

Status	Error	Program
✓	7.8b	(.f64 y (.f64 t (-.f64 x z)))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
	25.8b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	34.5b	(.f64 y (cbrt.f64 (.f64 (.f64 (.f64 t (-.f64 x z)) (.f64 t (-.f64 x z))) (.f64 t (-.f64 x z)))))
	31.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	35.8b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	6.4b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 3229 to 832 computations (74.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.3b	(.f64 (-.f64 x z) (.f64 y t))

series14.0ms (0.2%)

Counts

1 → 32

Calls

1 calls:

14.0ms

(*.f64 (-.f64 x z) (*.f64 y t))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (-.f64 x z) (*.f64 y t))

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
483×	`fma-def_binary64`
414×	`associate-r_binary64`
378×	`distribute-rgt-neg-out_binary64`
327×	`unsub-neg_binary64`

Counts

56 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	661
1	178	598
2	527	598
3	1835	598
4	3260	598
5	5376	598

prune30.0ms (0.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	41	9	50

Error

0.0b

Counts

50 → 9

Alt Table

Status	Error	Program
✓	7.8b	(.f64 y (.f64 t (-.f64 x z)))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
	53.6b	(.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 z)) (.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 z)) (*.f64 y t)))
	25.8b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	34.5b	(.f64 y (cbrt.f64 (.f64 (.f64 (.f64 t (-.f64 x z)) (.f64 t (-.f64 x z))) (.f64 t (-.f64 x z)))))
	31.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	35.8b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
▶	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	6.4b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 848 to 286 computations (66.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (.f64 x y) (.f64 z y))
✓	8.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series27.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

18.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
9.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

5.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
3.0ms	(-.f64 (.f64 x y) (.f64 z y))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
443×	`neg-mul-1_binary64`
246×	`*-commutative_binary64`
223×	`fma-neg_binary64`
217×	`distribute-lft-neg-out_binary64`

Counts

124 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1269
1	221	1209
2	783	1202
3	1981	1199
4	4246	1199
5	5104	1199

prune47.0ms (0.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	84	8	92

Error

Counts

92 → 8

Alt Table

Status	Error	Program
✓	7.8b	(.f64 y (.f64 t (-.f64 x z)))
▶	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
	22.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	6.4b	(.f64 (-.f64 x z) (.f64 y t))
	31.7b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))
	31.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	35.8b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
✓	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 1452 to 380 computations (73.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (*.f64 t (-.f64 x z)))))
✓	6.4b	(cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))
	7.4b	(.f64 y (.f64 t (-.f64 x z)))

series2.0s (26.6%)

Counts

3 → 144

Calls

3 calls:

1.3s

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

636.0ms

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

51.0ms

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

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

10.0ms

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

5.0ms

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

5.0ms

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

simplify193.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

356×	`associate-r_binary64`
319×	`associate-l_binary64`
252×	`fma-neg_binary64`
247×	`*-commutative_binary64`
185×	`fma-def_binary64`

Counts

259 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	485	8686
1	1305	8306
2	4410	7856
3	5042	7856

prune438.0ms (5.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	722	0	722
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	722	8	730

Error

Counts

730 → 8

Alt Table

Status	Error	Program
✓	7.8b	(.f64 y (.f64 t (-.f64 x z)))
✓	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
	22.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	6.4b	(.f64 (-.f64 x z) (.f64 y t))
	31.7b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))
	31.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	35.8b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
✓	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 30670 to 7955 computations (74.1% saved)

regimes734.0ms (9.8%)

Accuracy

Total 0.4b remaining (94.1%)

Threshold costs 0.4b (94.1%)

Counts

52 → 5

Compiler

Compiled 6238 to 3375 computations (45.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	110
1	42	110
2	52	110
3	58	110
4	62	110
5	63	110
6	63	110

end103.0ms (1.4%)

Compiler: Compiled 467 to 178 computations (61.9% saved)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Details

analyze1.4s (18.4%)

sample2.0s (27.1%)

simplify41.0ms (0.6%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series21.0ms (0.3%)

rewrite29.0ms (0.4%)

simplify114.0ms (1.5%)

prune76.0ms (1%)

localize5.0ms (0.1%)

series14.0ms (0.2%)

rewrite7.0ms (0.1%)

simplify54.0ms (0.7%)

prune30.0ms (0.4%)

localize6.0ms (0.1%)

series27.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify79.0ms (1.1%)

prune47.0ms (0.6%)

localize10.0ms (0.1%)

series2.0s (26.6%)

rewrite42.0ms (0.6%)

simplify193.0ms (2.6%)

prune438.0ms (5.8%)

regimes734.0ms (9.8%)

bsearch2.0ms (0%)

simplify7.0ms (0.1%)

end103.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10