Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (19%)

Symmetry

(sort y t)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify59.0ms (0.8%)

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
▶	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	4.5b	(.f64 y (.f64 t (-.f64 x z)))

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z y))
✓	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series49.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
16.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite18.0ms (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 → 40

Calls

2 calls:

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

simplify142.0ms (1.8%)

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

prune104.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	4.2b	(.f64 (-.f64 x z) (.f64 y t))
✓	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	33.1b	(.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 x z))) (sqrt.f64 (.f64 y (-.f64 x z)))) t)
	31.8b	(/.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)))
	31.1b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
▶	3.2b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	4.5b	(.f64 y (.f64 t (-.f64 x z)))

Compiler

Compiled 1440 to 370 computations (74.3% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
✓	2.6b	(.f64 t (.f64 y (-.f64 x z)))
✓	19.3b	(cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))

series3.0s (37.8%)

Counts

4 → 192

Calls

4 calls:

1.8s	(.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
1.1s	(cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))
70.0ms	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
28.0ms	(.f64 t (.f64 y (-.f64 x z)))

rewrite83.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
41×	`add-sqr-sqrt_binary64`

Counts

4 → 189

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
7.0ms	(.f64 t (.f64 y (-.f64 x z)))
5.0ms	(.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
4.0ms	(cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))

simplify195.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-r_binary64`
487×	`associate-l_binary64`
253×	`*-commutative_binary64`
244×	`times-frac_binary64`
198×	`fma-def_binary64`

Counts

381 → 359

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	643	10466
1	1462	9997
2	4992	9997

prune760.0ms (9.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	700	1	701
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	701	7	708

Error

0.0b

Counts

708 → 7

Alt Table

Status	Error	Program
	4.2b	(.f64 (-.f64 x z) (.f64 y t))
✓	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	3.2b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (.f64 (cbrt.f64 t) (cbrt.f64 (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	4.5b	(.f64 y (.f64 t (-.f64 x z)))
	33.1b	(.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 x z))) (sqrt.f64 (.f64 y (-.f64 x z)))) t)
	31.8b	(/.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)))
	31.1b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))

Compiler

Compiled 30803 to 8175 computations (73.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 t)
	2.6b	(.f64 t (.f64 y (-.f64 x z)))
✓	12.6b	(cbrt.f64 (*.f64 y (-.f64 x z)))
	19.3b	(cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))

series338.0ms (4.3%)

Counts

2 → 48

Calls

2 calls:

308.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))
29.0ms	(cbrt.f64 t)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`cbrt-div_binary64`

Counts

2 → 26

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))
1.0ms	(cbrt.f64 t)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
423×	`fma-def_binary64`
301×	`fma-neg_binary64`
274×	`cancel-sign-sub-inv_binary64`
212×	`distribute-rgt-neg-in_binary64`

Counts

74 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	1811
1	574	1765
2	1859	1671
3	4771	1669
4	4990	1669

prune340.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	434	0	434
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	434	7	441

Error

0.0b

Counts

441 → 7

Alt Table

Status	Error	Program
▶	4.2b	(.f64 (-.f64 x z) (.f64 y t))
✓	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	3.2b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (.f64 (cbrt.f64 t) (cbrt.f64 (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	4.5b	(.f64 y (.f64 t (-.f64 x z)))
	33.1b	(.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 x z))) (sqrt.f64 (.f64 y (-.f64 x z)))) t)
	31.8b	(/.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)))
	31.1b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))

Compiler

Compiled 19438 to 5204 computations (73.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.2b	(.f64 (-.f64 x z) (.f64 y t))

series16.0ms (0.2%)

Counts

1 → 32

Calls

1 calls:

16.0ms

(*.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))

simplify57.0ms (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

prune36.0ms (0.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	41	8	49

Error

0.0b

Counts

49 → 8

Alt Table

Status	Error	Program
✓	4.2b	(.f64 (-.f64 x z) (.f64 y t))
✓	2.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x z) (.f64 y t))) (cbrt.f64 (.f64 (-.f64 x z) (.f64 y t)))) (cbrt.f64 (.f64 (-.f64 x z) (.f64 y t))))
	31.8b	(/.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)))
✓	3.2b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (.f64 (cbrt.f64 t) (cbrt.f64 (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	4.5b	(.f64 y (.f64 t (-.f64 x z)))
	33.1b	(.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 x z))) (sqrt.f64 (.f64 y (-.f64 x z)))) t)
	31.1b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))

Compiler

Compiled 709 to 211 computations (70.2% saved)

regimes489.0ms (6.2%)

Accuracy

Total 1.7b remaining (98.8%)

Threshold costs 0b (0%)

Counts

60 → 2

Compiler

Compiled 9229 to 4486 computations (51.4% saved)

bsearch24.0ms (0.3%)

Steps

Iters	Range		Point
7	-6.391322642309015e-14	-6.441762334739955e-16	-4.9610827629677216e-15

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	16	29
1	27	29
2	38	29
3	44	29
4	48	29
5	49	29
6	49	29

end498.0ms (6.4%)

Compiler: Compiled 261 to 131 computations (49.8% 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

analyze5.0ms (0.1%)

sample1.5s (19%)

simplify59.0ms (0.8%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

series49.0ms (0.6%)

rewrite18.0ms (0.2%)

simplify142.0ms (1.8%)

prune104.0ms (1.3%)

localize22.0ms (0.3%)

series3.0s (37.8%)

rewrite83.0ms (1.1%)

simplify195.0ms (2.5%)

prune760.0ms (9.7%)

localize20.0ms (0.3%)

series338.0ms (4.3%)

rewrite4.0ms (0.1%)

simplify81.0ms (1%)

prune340.0ms (4.3%)

localize5.0ms (0.1%)

series16.0ms (0.2%)

rewrite7.0ms (0.1%)

simplify57.0ms (0.7%)

prune36.0ms (0.5%)

regimes489.0ms (6.2%)

bsearch24.0ms (0.3%)

simplify5.0ms (0.1%)

end498.0ms (6.4%)

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