Details

analyze959.0ms (18.7%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	24×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

271×	`associate-/l*_binary64`
259×	`div-sub_binary64`
255×	`cancel-sign-sub-inv_binary64`
243×	`distribute-rgt-in_binary64`
173×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	51	13
3	102	13
4	171	13
5	306	13
6	456	13
7	707	13
8	1344	13
9	1323	13
10	1307	13
11	1328	13
12	1318	13
13	1319	13
14	1323	13
15	1196	13

prune3.0ms (0.1%)

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

2.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	2.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	3.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 69 to 47 computations (31.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (-.f64 y t))
0.3b	(/.f64 (/.f64 2 (-.f64 y t)) z)
2.6b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

rewrite196.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 228

Calls

3 calls:

16.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
6.0ms	(/.f64 2 (-.f64 y t))

Compiler

Compiled 4155 to 1912 computations (54% saved)

series124.0ms (2.4%)

Error

2.6b

Counts

3 → 57

Calls

3 calls:

52.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
34.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
22.0ms	(/.f64 2 (-.f64 y t))

Compiler

Compiled 2224 to 1597 computations (28.2% saved)

simplify194.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-/r/_binary64`
202×	`associate-/l*_binary64`
194×	`associate-/l/_binary64`
191×	`associate-/r*_binary64`
190×	`associate-l_binary64`

Counts

285 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	5731
1	937	5449
2	3160	5368
3	4634	5368
4	5004	5368

prune103.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	163	10	173
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	163	12	175

Error

0.0b

Counts

175 → 12

Alt Table

Status	Error	Program
	20.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
✓	2.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	33.9b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (sqrt.f64 z)))
	35.7b	(.f64 (/.f64 x z) (+.f64 (/.f64 2 y) (.f64 2 (/.f64 t (*.f64 y y)))))
	4.0b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
▶	3.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	47.4b	(.f64 (/.f64 x (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))) (/.f64 (/.f64 2 (-.f64 (sqrt.f64 y) (sqrt.f64 t))) (cbrt.f64 z)))
	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	30.2b	(.f64 x (-.f64 (/.f64 -2 (.f64 t z)) (.f64 2 (/.f64 y (.f64 t (*.f64 t z))))))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	34.1b	(.f64 (/.f64 x z) (-.f64 (/.f64 -2 t) (.f64 2 (/.f64 y (*.f64 t t)))))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 2709 to 1268 computations (53.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (.f64 y z) (.f64 t z))
2.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`*-un-lft-identity_binary64`
4×	`times-frac_binary64`

Counts

2 → 38

Calls

2 calls:

5.0ms	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
2.0ms	(-.f64 (.f64 y z) (.f64 t z))

Compiler

Compiled 762 to 238 computations (68.8% saved)

series91.0ms (1.8%)

Error

0.0b

Counts

2 → 36

Calls

2 calls:

59.0ms	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
22.0ms	(-.f64 (.f64 y z) (.f64 t z))

Compiler

Compiled 1257 to 849 computations (32.5% saved)

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

837×	`associate-/l*_binary64`
447×	`associate-/r*_binary64`
391×	`associate-*l/_binary64`
324×	`associate-/l/_binary64`
200×	`associate-/r/_binary64`

Counts

74 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1201
1	337	1090
2	1360	1049
3	4953	1049
4	4966	1049

prune37.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Error

Counts

73 → 9

Alt Table

Status	Error	Program
	20.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
✓	2.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.3b	(/.f64 1 (*.f64 1/2 (/.f64 z (/.f64 x (-.f64 y t)))))
	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	7.9b	(/.f64 (*.f64 (/.f64 x z) 2) (-.f64 y t))
▶	2.7b	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
✓	3.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 868 to 406 computations (53.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 z (-.f64 y t))
0.5b	(/.f64 1 (*.f64 z (-.f64 y t)))
2.6b	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))

rewrite94.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`add-exp-log_binary64`
31×	`add-cbrt-cube_binary64`
31×	`prod-exp_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64`

Counts

3 → 102

Calls

3 calls:

10.0ms	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))
5.0ms	(*.f64 z (-.f64 y t))
5.0ms	(/.f64 1 (*.f64 z (-.f64 y t)))

Compiler

Compiled 1710 to 831 computations (51.4% saved)

series113.0ms (2.2%)

Error

Counts

3 → 54

Calls

3 calls:

51.0ms	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))
31.0ms	(/.f64 1 (*.f64 z (-.f64 y t)))
19.0ms	(*.f64 z (-.f64 y t))

Compiler

Compiled 1969 to 1377 computations (30.1% saved)

simplify122.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

451×	`*-commutative_binary64`
389×	`cancel-sign-sub-inv_binary64`
256×	`exp-prod_binary64`
222×	`associate-l_binary64`
191×	`distribute-rgt-in_binary64`

Counts

156 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2301
1	461	1992
2	1820	1948
3	3487	1948
4	4937	1948
5	4937	1948

prune52.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	112	9	121

Error

Counts

121 → 9

Alt Table

Status	Error	Program
	6.3b	(/.f64 1 (*.f64 1/2 (/.f64 z (/.f64 x (-.f64 y t)))))
▶	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	25.6b	(.f64 (.f64 x 2) (cbrt.f64 (pow.f64 (/.f64 1 (*.f64 (-.f64 y t) z)) 3)))
✓	3.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	7.9b	(/.f64 (*.f64 (/.f64 x z) 2) (-.f64 y t))
✓	2.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
✓	2.7b	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 1051 to 555 computations (47.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 y t))
0.6b	(cbrt.f64 (-.f64 y t))
0.6b	(cbrt.f64 (-.f64 y t))
3.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

rewrite191.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

179×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
94×	`associate-r_binary64`
85×	`add-cube-cbrt_binary64`

Counts

4 → 192

Calls

4 calls:

45.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
2.0ms	(cbrt.f64 (-.f64 y t))
2.0ms	(cbrt.f64 (-.f64 y t))
2.0ms	(cbrt.f64 (-.f64 y t))

Compiler

Compiled 6004 to 1711 computations (71.5% saved)

series164.0ms (3.2%)

Error

Counts

4 → 54

Calls

4 calls:

60.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
29.0ms	(cbrt.f64 (-.f64 y t))
28.0ms	(cbrt.f64 (-.f64 y t))
28.0ms	(cbrt.f64 (-.f64 y t))

Compiler

Compiled 3460 to 2359 computations (31.8% saved)

simplify242.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-*r/_binary64`
414×	`associate-*l/_binary64`
345×	`associate-/l*_binary64`
275×	`associate-/r*_binary64`
268×	`associate-l_binary64`

Counts

246 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	387	7335
1	1202	6220
2	4917	6217
3	4975	6217

prune86.0ms (1.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	174	9	183

Error

Counts

183 → 9

Alt Table

Status	Error	Program
	6.3b	(/.f64 1 (*.f64 1/2 (/.f64 z (/.f64 x (-.f64 y t)))))
	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	25.6b	(.f64 (.f64 x 2) (cbrt.f64 (pow.f64 (/.f64 1 (*.f64 (-.f64 y t) z)) 3)))
	3.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	6.1b	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)
	2.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	2.7b	(.f64 (.f64 x 2) (/.f64 1 (*.f64 z (-.f64 y t))))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 3416 to 1151 computations (66.3% saved)

regimes1.3s (24.5%)

Accuracy

Total 1.7b remaining (98.6%)

Threshold costs 0b (0%)

Compiler

Compiled 22649 to 15104 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	24	46
2	28	46
3	30	46
4	31	46
5	30	46

end1.0ms (0%)

Compiler: Compiled 33 to 17 computations (48.5% saved)

sample831.0ms (16.2%)

Algorithm

1×

intervals

Results

380.0ms	8000×	body	128	valid
30.0ms	740×	body	128	invalid

Compiler

Compiled 221 to 143 computations (35.3% saved)

Details

analyze959.0ms (18.7%)

sample24.0ms (0.5%)

simplify78.0ms (1.5%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite196.0ms (3.8%)

series124.0ms (2.4%)

simplify194.0ms (3.8%)

prune103.0ms (2%)

localize10.0ms (0.2%)

rewrite47.0ms (0.9%)

series91.0ms (1.8%)

simplify73.0ms (1.4%)

prune37.0ms (0.7%)

localize7.0ms (0.1%)

rewrite94.0ms (1.8%)

series113.0ms (2.2%)

simplify122.0ms (2.4%)

prune52.0ms (1%)

localize11.0ms (0.2%)

rewrite191.0ms (3.7%)

series164.0ms (3.2%)

simplify242.0ms (4.7%)

prune86.0ms (1.7%)

regimes1.3s (24.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample831.0ms (16.2%)

Profiling