Details

analyze1.7s (19.9%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
4.0ms	99×	body	128	invalid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify709.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

1728×	`associate-/l*_binary64`
1269×	`div-sub_binary64`
1211×	`distribute-rgt-in_binary64`
791×	`sub-neg_binary64`
779×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	30	19
2	101	19
3	305	19
4	751	19
5	1395	19
6	1737	19
7	1915	19
8	2338	19
9	2903	19
10	3317	19
11	3521	19
12	3460	19
13	3471	19
14	3481	19
15	3825	19
16	3894	19
17	3899	19
18	3899	19
19	4026	19
20	3914	19
21	4337	19
22	4484	19
23	4514	19
24	4450	19
25	4430	19
26	4175	19
27	4267	19
28	4285	19
29	4351	19
30	4471	19
31	4395	19
32	4395	19
33	4398	19
34	4398	19
35	3981	19
36	4073	19
37	4512	19
38	4679	19
39	4535	19
40	4721	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

5.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 36 to 26 computations (27.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.2b	(.f64 (.f64 z 9) t)
4.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

rewrite102.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

3 → 54

Calls

3 calls:

11.0ms	(.f64 (.f64 z 9) t)
7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

Compiler

Compiled 1166 to 671 computations (42.5% saved)

series171.0ms (2%)

Error

4.7b

Counts

3 → 57

Calls

3 calls:

95.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
49.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
17.0ms	(.f64 (.f64 z 9) t)

Compiler

Compiled 1644 to 1166 computations (29.1% saved)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

390×	`*-commutative_binary64`
364×	`cancel-sign-sub-inv_binary64`
305×	`div-sub_binary64`
289×	`associate-/l*_binary64`
241×	`times-frac_binary64`

Counts

111 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	1784
1	381	1636
2	1313	1631
3	3445	1631
4	5092	1631

prune68.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	73	11	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Error

4.6b

Counts

85 → 12

Alt Table

Status	Error	Program
	41.5b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 t (.f64 (.f64 z 9) (+.f64 (.f64 x y) (.f64 (.f64 t z) 9)))))))
	5.0b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
✓	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	28.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 (.f64 t z) 9)) (sqrt.f64 (.f64 (.f64 t z) 9)))) (*.f64 a 2))
	29.1b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (+.f64 (.f64 x y) (.f64 (*.f64 t z) 9))))
▶	5.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) a) 9/2))
	34.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9))) a) (/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))) 2))
	31.3b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (*.f64 a 2))))
	5.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
	5.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (.f64 a 2))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (.f64 a 2)))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (.f64 a 2))))
	32.9b	(/.f64 (.f64 (.f64 t z) -9) (*.f64 a 2))

Compiler

Compiled 1414 to 817 computations (42.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) a) 9/2))
0.2b	(.f64 (/.f64 (.f64 t z) a) 9/2)
4.4b	(/.f64 (.f64 x y) (.f64 a 2))
5.7b	(/.f64 (*.f64 t z) a)

rewrite147.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `*-un-lft-identity_binary64`
8×	`div-exp_binary64` `cbrt-undiv_binary64`
7×	`times-frac_binary64` `associate-l_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) a) 9/2))
7.0ms	(.f64 (/.f64 (.f64 t z) a) 9/2)
5.0ms	(/.f64 (.f64 x y) (.f64 a 2))
5.0ms	(/.f64 (*.f64 t z) a)

Compiler

Compiled 1827 to 819 computations (55.2% saved)

series203.0ms (2.3%)

Error

4.6b

Counts

4 → 54

Calls

4 calls:

101.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) a) 9/2))
33.0ms	(.f64 (/.f64 (.f64 t z) a) 9/2)
30.0ms	(/.f64 (.f64 x y) (.f64 a 2))
29.0ms	(/.f64 (*.f64 t z) a)

Compiler

Compiled 1923 to 1331 computations (30.8% saved)

simplify122.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-/r*_binary64`
486×	`*-commutative_binary64`
374×	`associate-/l/_binary64`
263×	`associate-/r/_binary64`
205×	`times-frac_binary64`

Counts

136 → 79

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	172	1921
1	452	1815
2	1857	1815
3	4343	1815
4	4942	1815
5	4964	1815

prune61.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	6	4	10
Picked	1	0	1
Done	1	0	1
Total	82	9	91

Error

0.0b

Counts

91 → 9

Alt Table

Status	Error	Program
	5.0b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
	29.1b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (+.f64 (.f64 x y) (.f64 (*.f64 t z) 9))))
▶	5.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
	7.3b	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 (/.f64 (.f64 t z) a) 9/2))
	5.9b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t (/.f64 z a)) 9/2))
	5.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
	6.2b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 t 1) (.f64 9/2 (/.f64 z a))))
	30.8b	(/.f64 (.f64 a (+.f64 (.f64 x y) (.f64 -9 (.f64 t z)))) (.f64 a (.f64 a 2)))

Compiler

Compiled 1090 to 588 computations (46.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
4.4b	(/.f64 (.f64 x y) (.f64 a 2))
5.8b	(.f64 (.f64 t z) (/.f64 9/2 a))

rewrite109.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64`
10×	`prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `times-frac_binary64`
8×	`pow1_binary64`
6×	`div-exp_binary64` `cbrt-undiv_binary64`

Counts

3 → 67

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
8.0ms	(.f64 (.f64 t z) (/.f64 9/2 a))
5.0ms	(/.f64 (.f64 x y) (.f64 a 2))

Compiler

Compiled 1550 to 807 computations (47.9% saved)

series169.0ms (1.9%)

Error

0.0b

Counts

3 → 45

Calls

3 calls:

99.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
32.0ms	(/.f64 (.f64 x y) (.f64 a 2))
32.0ms	(.f64 (.f64 t z) (/.f64 9/2 a))

Compiler

Compiled 1548 to 1074 computations (30.6% saved)

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-/r*_binary64`
267×	`associate-/l/_binary64`
246×	`associate-l_binary64`
204×	`cancel-sign-sub-inv_binary64`
203×	`distribute-rgt-neg-in_binary64`

Counts

112 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	169	1702
1	478	1638
2	2072	1638
3	4387	1638
4	4988	1638
5	4968	1638

prune50.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	66	10	76

Error

0.0b

Counts

76 → 10

Alt Table

Status	Error	Program
	5.0b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
▶	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
	5.4b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 9/2 (cbrt.f64 a))))
	29.1b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (+.f64 (.f64 x y) (.f64 (*.f64 t z) 9))))
✓	5.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
	7.3b	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 (/.f64 (.f64 t z) a) 9/2))
	5.9b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t (/.f64 z a)) 9/2))
	5.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
	6.2b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 t 1) (.f64 9/2 (/.f64 z a))))
	30.8b	(/.f64 (.f64 a (+.f64 (.f64 x y) (.f64 -9 (.f64 t z)))) (.f64 a (.f64 a 2)))

Compiler

Compiled 1097 to 619 computations (43.6% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x y) (.f64 z (*.f64 t 9)))
0.3b	(.f64 z (.f64 t 9))
4.7b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))

rewrite82.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

3 → 54

Calls

3 calls:

7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
5.0ms	(.f64 z (.f64 t 9))
4.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 t 9)))

Compiler

Compiled 1151 to 662 computations (42.5% saved)

series168.0ms (1.9%)

Error

0.0b

Counts

3 → 57

Calls

3 calls:

98.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
49.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 t 9)))
14.0ms	(.f64 z (.f64 t 9))

Compiler

Compiled 1644 to 1166 computations (29.1% saved)

simplify112.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

390×	`*-commutative_binary64`
341×	`cancel-sign-sub-inv_binary64`
317×	`div-sub_binary64`
284×	`associate-/l*_binary64`
217×	`times-frac_binary64`

Counts

111 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1782
1	364	1631
2	1258	1629
3	3297	1629
4	4934	1629
5	4934	1629

prune44.0ms (0.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	86	10	96

Error

0.0b

Counts

96 → 10

Alt Table

Status	Error	Program
	5.0b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 t 9))) (.f64 a 2))
	5.4b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 (.f64 t z) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 9/2 (cbrt.f64 a))))
	29.1b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (+.f64 (.f64 x y) (.f64 (*.f64 t z) 9))))
	5.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t z) (/.f64 9/2 a)))
	7.3b	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 (/.f64 (.f64 t z) a) 9/2))
	5.9b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (.f64 t (/.f64 z a)) 9/2))
	5.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
	6.2b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 (/.f64 t 1) (.f64 9/2 (/.f64 z a))))
	30.8b	(/.f64 (.f64 a (+.f64 (.f64 x y) (.f64 -9 (.f64 t z)))) (.f64 a (.f64 a 2)))

Compiler

Compiled 1032 to 565 computations (45.3% saved)

regimes2.6s (30.3%)

Accuracy

Total 4.4b remaining (92%)

Threshold costs 0b (0%)

Compiler

Compiled 35336 to 24340 computations (31.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`sub-neg_binary64` `+-commutative_binary64`
12×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64`
9×	`distribute-lft-neg-in_binary64`
6×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	158
1	72	158
2	111	158
3	143	158
4	160	158
5	166	158
6	167	158
7	166	158

end42.0ms (0.5%)

Compiler: Compiled 560 to 340 computations (39.3% saved)

sample1.7s (19.2%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
138.0ms	3230×	body	128	invalid

Compiler

Compiled 363 to 243 computations (33.1% saved)

Details

analyze1.7s (19.9%)

sample45.0ms (0.5%)

simplify709.0ms (8.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite102.0ms (1.2%)

series171.0ms (2%)

simplify88.0ms (1%)

prune68.0ms (0.8%)

localize11.0ms (0.1%)

rewrite147.0ms (1.7%)

series203.0ms (2.3%)

simplify122.0ms (1.4%)

prune61.0ms (0.7%)

localize11.0ms (0.1%)

rewrite109.0ms (1.3%)

series169.0ms (1.9%)

simplify117.0ms (1.3%)

prune50.0ms (0.6%)

localize12.0ms (0.1%)

rewrite82.0ms (0.9%)

series168.0ms (1.9%)

simplify112.0ms (1.3%)

prune44.0ms (0.5%)

regimes2.6s (30.3%)

bsearch4.0ms (0%)

simplify11.0ms (0.1%)

end42.0ms (0.5%)

sample1.7s (19.2%)

Profiling