Details

analyze1.2s (19.7%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	83×	body	128	invalid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify49.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`
127×	`associate-r_binary64`
113×	`unsub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	70	19
3	211	19
4	402	19
5	715	19
6	827	19
7	784	19
8	782	19
9	785	19
10	785	19
11	704	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

6.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	6.1b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 z z) t)
0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
5.7b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite94.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

16×	`cancel-sign-sub-inv_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate--r+_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

9.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
5.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
4.0ms	(-.f64 (*.f64 z z) t)

Compiler

Compiled 1383 to 520 computations (62.4% saved)

series171.0ms (2.8%)

Error

5.1b

Counts

3 → 51

Calls

3 calls:

83.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
46.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
21.0ms	(-.f64 (*.f64 z z) t)

Compiler

Compiled 1571 to 1139 computations (27.5% saved)

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

431×	`*-commutative_binary64`
414×	`exp-prod_binary64`
391×	`cancel-sign-sub-inv_binary64`
346×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`

Counts

115 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	136	1772
1	380	1628
2	1218	1628
3	3268	1628
4	4651	1628
5	4918	1628

prune59.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Error

5.1b

Counts

99 → 7

Alt Table

Status	Error	Program
▶	6.1b	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
	34.0b	(.f64 y (.f64 4 t))
	33.1b	(-.f64 (.f64 x x) (.f64 (sqrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (sqrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))))
	27.3b	(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (*.f64 x x))))
	7.1b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))))
	45.1b	(*.f64 x x)
	29.6b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))

Compiler

Compiled 1122 to 509 computations (54.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (*.f64 y t)))
0.0b	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
0.0b	(.f64 4 (.f64 z z))
11.0b	(.f64 y (.f64 4 (*.f64 z z)))

rewrite122.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

18×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
9.0ms	(+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (*.f64 y t)))
8.0ms	(.f64 y (.f64 4 (*.f64 z z)))
6.0ms	(.f64 4 (.f64 z z))

Compiler

Compiled 1696 to 802 computations (52.7% saved)

series179.0ms (3%)

Error

5.1b

Counts

4 → 48

Calls

4 calls:

86.0ms	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
50.0ms	(+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (*.f64 y t)))
19.0ms	(.f64 y (.f64 4 (*.f64 z z)))
9.0ms	(.f64 4 (.f64 z z))

Compiler

Compiled 1670 to 1215 computations (27.2% saved)

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

560×	`*-commutative_binary64`
337×	`cancel-sign-sub-inv_binary64`
293×	`exp-prod_binary64`
260×	`unsub-neg_binary64`
216×	`distribute-rgt-neg-in_binary64`

Counts

116 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1926
1	389	1671
2	1354	1647
3	3613	1640
4	4808	1640
5	4923	1640

prune69.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Error

5.1b

Counts

104 → 8

Alt Table

Status	Error	Program
✓	6.1b	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
	34.0b	(.f64 y (.f64 4 t))
	27.3b	(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (*.f64 x x))))
	7.1b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))))
	45.1b	(*.f64 x x)
	33.1b	(.f64 (+.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (.f64 z z) t))))) (-.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (*.f64 z z) t))))))
	29.6b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
▶	6.3b	(-.f64 (.f64 x x) (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (.f64 z z)) (cbrt.f64 y))) (.f64 -4 (.f64 y t))))

Compiler

Compiled 1240 to 574 computations (53.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
3.7b	(.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y))
7.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y)))

rewrite143.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

45×	`pow1_binary64` `add-exp-log_binary64`
30×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
28×	`add-cbrt-cube_binary64`
9×	`cbrt-prod_binary64`
8×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 80

Calls

4 calls:

15.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y)))
9.0ms	(.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

Compiler

Compiled 2170 to 792 computations (63.5% saved)

series117.0ms (1.9%)

Error

5.1b

Counts

4 → 18

Calls

4 calls:

45.0ms	(.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y))
26.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (*.f64 z z)) (cbrt.f64 y)))
18.0ms	(cbrt.f64 y)
16.0ms	(cbrt.f64 y)

Compiler

Compiled 1196 to 801 computations (33% saved)

simplify120.0ms (2%)

Algorithm

1×	egg-herbie

Rules

560×	`*-commutative_binary64`
483×	`log-prod_binary64`
475×	`unswap-sqr_binary64`
395×	`exp-prod_binary64`
331×	`associate-+l+_binary64`

Counts

98 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1693
1	248	1019
2	1045	1002
3	1961	1002
4	4453	1002
5	4914	1002
6	4912	1002

prune51.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	74	9	83

Error

5.1b

Counts

83 → 9

Alt Table

Status	Error	Program
✓	6.1b	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
	34.0b	(.f64 y (.f64 4 t))
	27.3b	(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (*.f64 x x))))
▶	7.1b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))))
	34.8b	(-.f64 (.f64 x x) (+.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (pow.f64 y 2/3)) (cbrt.f64 (cbrt.f64 y)))) (.f64 (.f64 4 (.f64 z z)) (cbrt.f64 y))) (.f64 -4 (*.f64 y t))))
	45.1b	(*.f64 x x)
	33.1b	(.f64 (+.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (.f64 z z) t))))) (-.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (*.f64 z z) t))))))
	29.6b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
✓	6.3b	(-.f64 (.f64 x x) (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (.f64 z z)) (cbrt.f64 y))) (.f64 -4 (.f64 y t))))

Compiler

Compiled 1151 to 552 computations (52% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))
5.9b	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
5.9b	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
5.9b	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))

rewrite207.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

48×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
19×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
16×	`associate-*r/_binary64`
12×	`sub-neg_binary64`

Counts

4 → 119

Calls

4 calls:

11.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
10.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
10.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
7.0ms	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))

Compiler

Compiled 4882 to 2109 computations (56.8% saved)

series303.0ms (5%)

Error

5.1b

Counts

4 → 60

Calls

4 calls:

99.0ms	(cbrt.f64 (.f64 y (.f64 4 (-.f64 (*.f64 z z) t))))
54.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
53.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))
53.0ms	(.f64 y (.f64 4 (-.f64 (*.f64 z z) t)))

Compiler

Compiled 5695 to 3622 computations (36.4% saved)

simplify138.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

351×	`distribute-rgt-in_binary64`
341×	`distribute-lft-in_binary64`
247×	`times-frac_binary64`
183×	`associate-r_binary64`
179×	`exp-prod_binary64`

Counts

179 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	3134
1	513	2894
2	1437	2865
3	4889	2835
4	5076	2835

prune74.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	141	9	150

Error

5.1b

Counts

150 → 9

Alt Table

Status	Error	Program
	6.1b	(-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 4 (.f64 z z))) (.f64 -4 (.f64 y t))))
	34.0b	(.f64 y (.f64 4 t))
	27.3b	(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 (.f64 y (-.f64 (.f64 z z) t)) -4) (*.f64 x x))))
	7.1b	(-.f64 (.f64 x x) (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t)))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))) (cbrt.f64 (.f64 y (.f64 4 (-.f64 (.f64 z z) t))))))
	34.8b	(-.f64 (.f64 x x) (+.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (pow.f64 y 2/3)) (cbrt.f64 (cbrt.f64 y)))) (.f64 (.f64 4 (.f64 z z)) (cbrt.f64 y))) (.f64 -4 (*.f64 y t))))
	45.1b	(*.f64 x x)
	33.1b	(.f64 (+.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (.f64 z z) t))))) (-.f64 x (sqrt.f64 (.f64 4 (.f64 y (-.f64 (*.f64 z z) t))))))
	29.6b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
	6.3b	(-.f64 (.f64 x x) (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 4 (.f64 z z)) (cbrt.f64 y))) (.f64 -4 (.f64 y t))))

Compiler

Compiled 2202 to 1039 computations (52.8% saved)

regimes1.6s (26.4%)

Accuracy

Total -2.1b remaining (-66.5%)

Threshold costs -2.1b (-66.5%)

Compiler

Compiled 25053 to 15779 computations (37% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
20×	`+-commutative_binary64`
18×	`sub-neg_binary64` `distribute-rgt-neg-in_binary64`
16×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-lft-neg-in_binary64`
10×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	60
1	44	60
2	70	60
3	113	60
4	158	60
5	183	60
6	191	60
7	193	60
8	187	60

end1.0ms (0%)

Compiler: Compiled 44 to 25 computations (43.2% saved)

sample1.0s (16.8%)

Algorithm

1×

intervals

Results

312.0ms	8000×	body	128	valid
106.0ms	3024×	body	128	invalid

Compiler

Compiled 292 to 177 computations (39.4% saved)

Iter	Nodes	Cost
0	12	19
1	23	19
2	70	19
3	211	19
4	402	19
5	715	19
6	827	19
7	784	19
8	782	19
9	785	19
10	785	19
11	704	19

Iter	Nodes	Cost
0	12	19
1	23	19
2	70	19
3	211	19
4	402	19
5	715	19
6	827	19
7	784	19
8	782	19
9	785	19
10	785	19
11	704	19

Details

analyze1.2s (19.7%)

sample25.0ms (0.4%)

simplify49.0ms (0.8%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite94.0ms (1.5%)

series171.0ms (2.8%)

simplify124.0ms (2%)

prune59.0ms (1%)

localize14.0ms (0.2%)

rewrite122.0ms (2%)

series179.0ms (3%)

simplify130.0ms (2.2%)

prune69.0ms (1.1%)

localize17.0ms (0.3%)

rewrite143.0ms (2.4%)

series117.0ms (1.9%)

simplify120.0ms (2%)

prune51.0ms (0.8%)

localize15.0ms (0.2%)

rewrite207.0ms (3.4%)

series303.0ms (5%)

simplify138.0ms (2.3%)

prune74.0ms (1.2%)

regimes1.6s (26.4%)

bsearch6.0ms (0.1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample1.0s (16.8%)

Profiling

Iter	Nodes	Cost
0	12	19
1	23	19
2	70	19
3	211	19
4	402	19
5	715	19
6	827	19
7	784	19
8	782	19
9	785	19
10	785	19
11	704	19