Details

analyze1.0s (22.9%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (28.6%)

Symmetry

(sort y t)

Results

907.0ms	8256×	body	128	valid
203.0ms	1989×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify39.0ms (0.9%)

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

prune6.0ms (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
▶	6.1b	(.f64 y (.f64 t (-.f64 x z)))
	6.6b	(.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))
✓	5.8b	(.f64 y (.f64 t (-.f64 x z)))

series18.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

12.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

rewrite25.0ms (0.6%)

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:

10.0ms	(.f64 y (.f64 t (-.f64 x z)))
5.0ms	(*.f64 t (-.f64 x z))

simplify112.0ms (2.5%)

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

prune107.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	10	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Error

0.0b

Counts

155 → 11

Alt Table

Status	Error	Program
	6.9b	(.f64 y (.f64 (.f64 t (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z)))) (cbrt.f64 (-.f64 x z))))
	49.1b	(.f64 (sqrt.f64 y) (.f64 t (*.f64 (-.f64 x z) (sqrt.f64 y))))
	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	35.2b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	35.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	7.0b	(.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)))))
	6.1b	(.f64 (.f64 t (-.f64 x z)) y)
	23.8b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	6.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	6.0b	(.f64 (-.f64 x z) (.f64 y t))
	6.5b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))

Compiler

Compiled 3386 to 911 computations (73.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 (-.f64 x z) (.f64 y t))

series17.0ms (0.4%)

Counts

1 → 32

Calls

1 calls:

17.0ms

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

rewrite7.0ms (0.2%)

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))

simplify62.0ms (1.4%)

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

prune32.0ms (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	41	12	53

Error

0.0b

Counts

53 → 12

Alt Table

Status	Error	Program
	35.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	7.0b	(.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)))))
	6.6b	(.f64 (.f64 (-.f64 x z) y) t)
✓	6.0b	(.f64 (-.f64 x z) (.f64 y t))
	6.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	6.5b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
▶	6.1b	(.f64 (.f64 t (-.f64 x z)) y)
	49.1b	(.f64 (sqrt.f64 y) (.f64 t (*.f64 (-.f64 x z) (sqrt.f64 y))))
	23.8b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	33.3b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))
	33.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 993 to 363 computations (63.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 t (-.f64 x z))
✓	5.8b	(.f64 (.f64 t (-.f64 x z)) y)

series13.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

13.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 22

Calls

1 calls:

9.0ms

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

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
534×	`neg-mul-1_binary64`
330×	`distribute-rgt-in_binary64`
327×	`distribute-lft-in_binary64`
262×	`*-commutative_binary64`

Counts

70 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	69	799
1	184	736
2	674	736
3	2046	736
4	4482	736
5	5203	736

prune71.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	100	11	111

Error

0.0b

Counts

111 → 11

Alt Table

Status	Error	Program
	35.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	7.0b	(.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)))))
	6.6b	(.f64 (.f64 (-.f64 x z) y) t)
✓	6.0b	(.f64 (-.f64 x z) (.f64 y t))
	6.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	6.5b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
	49.1b	(.f64 (sqrt.f64 y) (.f64 t (*.f64 (-.f64 x z) (sqrt.f64 y))))
	23.8b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
▶	6.1b	(.f64 (+.f64 (.f64 t x) (*.f64 t (neg.f64 z))) y)
	33.3b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))
	33.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 1955 to 616 computations (68.5% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 t x) (.f64 t (neg.f64 z)))
✓	5.8b	(.f64 (+.f64 (.f64 t x) (*.f64 t (neg.f64 z))) y)

series21.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

15.0ms	(.f64 (+.f64 (.f64 t x) (*.f64 t (neg.f64 z))) y)
6.0ms	(+.f64 (.f64 t x) (.f64 t (neg.f64 z)))

rewrite9.0ms (0.2%)

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 → 39

Calls

2 calls:

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

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-neg_binary64`
464×	`distribute-rgt-neg-out_binary64`
437×	`fma-def_binary64`
359×	`unsub-neg_binary64`
298×	`*-commutative_binary64`

Counts

123 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	1251
1	238	1186
2	994	1177
3	2793	1175
4	4415	1174
5	4925	1174

prune53.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	81	11	92

Error

0.0b

Counts

92 → 11

Alt Table

Status	Error	Program
	41.6b	(/.f64 (.f64 y (-.f64 (pow.f64 (.f64 x t) 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 (.f64 t x) (.f64 t x)) (-.f64 (.f64 (.f64 t (neg.f64 z)) (.f64 t (neg.f64 z))) (.f64 (.f64 t x) (.f64 t (neg.f64 z))))))
	49.1b	(.f64 (sqrt.f64 y) (.f64 t (*.f64 (-.f64 x z) (sqrt.f64 y))))
	35.5b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	7.0b	(.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)))))
	6.6b	(.f64 (.f64 (-.f64 x z) y) t)
✓	6.0b	(.f64 (-.f64 x z) (.f64 y t))
	6.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	6.5b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
✓	6.1b	(.f64 (+.f64 (.f64 t x) (*.f64 t (neg.f64 z))) y)
	33.3b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))
	33.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 1459 to 365 computations (75% saved)

regimes1.1s (24.4%)

Accuracy

Total 0.5b remaining (96.1%)

Threshold costs 0.5b (96.1%)

Counts

90 → 5

Compiler

Compiled 10222 to 5666 computations (44.6% saved)

bsearch3.0ms (0.1%)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	118
1	59	118
2	71	116
3	81	116
4	88	116
5	91	116
6	92	116
7	88	116

end275.0ms (6.2%)

Compiler: Compiled 576 to 237 computations (58.9% 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

analyze1.0s (22.9%)

sample1.3s (28.6%)

simplify39.0ms (0.9%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series18.0ms (0.4%)

rewrite25.0ms (0.6%)

simplify112.0ms (2.5%)

prune107.0ms (2.4%)

localize5.0ms (0.1%)

series17.0ms (0.4%)

rewrite7.0ms (0.2%)

simplify62.0ms (1.4%)

prune32.0ms (0.7%)

localize5.0ms (0.1%)

series13.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify64.0ms (1.4%)

prune71.0ms (1.6%)

localize9.0ms (0.2%)

series21.0ms (0.5%)

rewrite9.0ms (0.2%)

simplify84.0ms (1.9%)

prune53.0ms (1.2%)

regimes1.1s (24.4%)

bsearch3.0ms (0.1%)

simplify7.0ms (0.2%)

end275.0ms (6.2%)

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