Details

analyze856.0ms (12.3%)

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
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
2.0ms	58×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify262.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1174×	`div-sub_binary64`
414×	`associate-/l*_binary64`
410×	`distribute-rgt-in_binary64`
404×	`sub-neg_binary64`
371×	`associate-/r/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	61	16
4	103	16
5	179	16
6	357	16
7	714	16
8	1261	16
9	1454	16
10	1447	16
11	1374	16
12	1377	16
13	1410	16
14	1499	16
15	1921	16
16	1599	16
17	1627	16
18	1645	16
19	1661	16
20	1653	16
21	1653	16
22	1653	16
23	1711	16
24	1669	16
25	1663	16
26	1665	16
27	1667	16
28	1669	16
29	1669	16
30	1484	16

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

3.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	3.8b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
3.6b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite251.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

111×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
72×	`cancel-sign-sub-inv_binary64`
46×	`add-cube-cbrt_binary64`

Counts

3 → 162

Calls

3 calls:

33.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
23.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
5.0ms	(/.f64 t (-.f64 1 z))

Compiler

Compiled 3152 to 1630 computations (48.3% saved)

series154.0ms (2.2%)

Error

0.1b

Counts

3 → 66

Calls

3 calls:

67.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
42.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
21.0ms	(/.f64 t (-.f64 1 z))

Compiler

Compiled 1862 to 1106 computations (40.6% saved)

simplify166.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

504×	`neg-mul-1_binary64`
398×	`times-frac_binary64`
237×	`distribute-lft-neg-out_binary64`
231×	`distribute-rgt-neg-out_binary64`
224×	`associate-l_binary64`

Counts

228 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	4826
1	762	4716
2	2714	4122
3	4202	4104
4	5035	4104

prune82.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	149	12	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	12	162

Error

3.1b

Counts

162 → 12

Alt Table

Status	Error	Program
	11.8b	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 t (-.f64 1 (*.f64 z z))) (+.f64 1 z))))
▶	4.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
	18.0b	(*.f64 x (/.f64 (+.f64 y t) z))
	22.5b	(+.f64 (.f64 x (/.f64 y z)) (.f64 x (/.f64 (/.f64 (neg.f64 t) (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z)))))
	35.4b	(cbrt.f64 (pow.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) 3))
	31.6b	(neg.f64 (*.f64 x (/.f64 t (-.f64 1 z))))
	33.0b	(.f64 x (-.f64 (/.f64 y z) (.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 1 z)))))
	30.8b	(*.f64 x (cbrt.f64 (pow.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) 3)))
	54.9b	(.f64 (.f64 x (+.f64 (sqrt.f64 (/.f64 t (-.f64 1 z))) (/.f64 (sqrt.f64 y) (sqrt.f64 z)))) (-.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (/.f64 t (-.f64 1 z)))))
	35.8b	(.f64 x (/.f64 (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3)) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))))
	43.4b	(.f64 (.f64 x (+.f64 (sqrt.f64 (/.f64 t (-.f64 1 z))) (sqrt.f64 (/.f64 y z)))) (-.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 t (-.f64 1 z)))))
	33.5b	(.f64 (sqrt.f64 x) (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (sqrt.f64 x)))

Compiler

Compiled 1645 to 840 computations (48.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
2.1b	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))

rewrite143.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-l_binary64`
10×	`cbrt-prod_binary64`

Counts

4 → 79

Calls

4 calls:

29.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
26.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 2004 to 792 computations (60.5% saved)

series255.0ms (3.7%)

Error

0.1b

Counts

4 → 60

Calls

4 calls:

121.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
76.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
16.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

Compiler

Compiled 2568 to 1573 computations (38.7% saved)

simplify119.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

382×	`distribute-rgt-in_binary64`
368×	`distribute-lft-in_binary64`
265×	`times-frac_binary64`
212×	`associate-l_binary64`
200×	`associate-r_binary64`

Counts

139 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3124
1	478	2434
2	1690	2338
3	4871	2338
4	5016	2338

prune68.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	8	3	11
Picked	0	1	1
Done	0	0	0
Total	113	8	121

Error

0.0b

Counts

121 → 8

Alt Table

Status	Error	Program
	11.8b	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 t (-.f64 1 (*.f64 z z))) (+.f64 1 z))))
✓	4.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
	33.0b	(.f64 x (-.f64 (/.f64 y z) (.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 1 z)))))
	21.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (cbrt.f64 x) (-.f64 (.f64 (-.f64 1 z) y) (.f64 t z))) (.f64 z (-.f64 1 z))))
	22.9b	(/.f64 (*.f64 x (+.f64 t y)) z)
	33.5b	(.f64 (sqrt.f64 x) (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (sqrt.f64 x)))
	23.3b	(+.f64 (.f64 x (+.f64 (/.f64 t z) (/.f64 t (pow.f64 z 3)))) (.f64 (/.f64 x z) (+.f64 (/.f64 t z) y)))
▶	6.3b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))

Compiler

Compiled 1701 to 790 computations (53.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))
2.8b	(*.f64 (/.f64 t (-.f64 1 z)) x)
6.8b	(/.f64 (*.f64 x y) z)

rewrite189.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
24×	`associate-l_binary64`

Counts

4 → 118

Calls

4 calls:

10.0ms	(*.f64 (/.f64 t (-.f64 1 z)) x)
6.0ms	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))
6.0ms	(/.f64 t (-.f64 1 z))
4.0ms	(/.f64 (*.f64 x y) z)

Compiler

Compiled 2331 to 1097 computations (52.9% saved)

series170.0ms (2.4%)

Error

0.0b

Counts

4 → 69

Calls

4 calls:

65.0ms	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))
37.0ms	(*.f64 (/.f64 t (-.f64 1 z)) x)
25.0ms	(/.f64 (*.f64 x y) z)
22.0ms	(/.f64 t (-.f64 1 z))

Compiler

Compiled 2335 to 1346 computations (42.4% saved)

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-/r*_binary64`
354×	`associate-/l/_binary64`
191×	`associate-/r/_binary64`
177×	`associate-+l+_binary64`
159×	`cancel-sign-sub-inv_binary64`

Counts

187 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	2930
1	625	2799
2	2027	2676
3	4645	2676
4	5028	2676

prune100.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	6	6
Picked	0	1	1
Done	1	0	1
Total	126	9	135

Error

0.0b

Counts

135 → 9

Alt Table

Status	Error	Program
	11.8b	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 t (-.f64 1 (*.f64 z z))) (+.f64 1 z))))
	33.0b	(.f64 x (-.f64 (/.f64 y z) (.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 1 z)))))
	21.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (cbrt.f64 x) (-.f64 (.f64 (-.f64 1 z) y) (.f64 t z))) (.f64 z (-.f64 1 z))))
	22.9b	(/.f64 (*.f64 x (+.f64 t y)) z)
▶	3.4b	(-.f64 (/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z)) (*.f64 (/.f64 t (-.f64 1 z)) x))
	33.5b	(.f64 (sqrt.f64 x) (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (sqrt.f64 x)))
	23.3b	(+.f64 (.f64 x (+.f64 (/.f64 t z) (/.f64 t (pow.f64 z 3)))) (.f64 (/.f64 x z) (+.f64 (/.f64 t z) y)))
✓	6.3b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))
	8.0b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 x (/.f64 (cbrt.f64 t) (-.f64 1 z)))))

Compiler

Compiled 1986 to 902 computations (54.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
1.6b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
2.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
2.8b	(*.f64 (/.f64 t (-.f64 1 z)) x)

rewrite165.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

41×	`add-sqr-sqrt_binary64`
32×	`add-exp-log_binary64` `*-un-lft-identity_binary64`
31×	`associate-l_binary64`
29×	`times-frac_binary64`
24×	`add-cbrt-cube_binary64`

Counts

4 → 114

Calls

4 calls:

10.0ms	(*.f64 (/.f64 t (-.f64 1 z)) x)
10.0ms	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
8.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 2974 to 985 computations (66.9% saved)

series181.0ms (2.6%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

80.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
39.0ms	(*.f64 (/.f64 t (-.f64 1 z)) x)
33.0ms	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
16.0ms	(cbrt.f64 z)

Compiler

Compiled 2034 to 1204 computations (40.8% saved)

simplify136.0ms (2%)

Algorithm

1×	egg-herbie

Rules

471×	`*-commutative_binary64`
394×	`associate-/r/_binary64`
296×	`log-prod_binary64`
186×	`log-div_binary64`
171×	`times-frac_binary64`

Counts

153 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	2676
1	566	1920
2	2200	1870
3	4146	1862
4	4826	1862
5	4959	1862

prune90.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Error

0.0b

Counts

125 → 10

Alt Table

Status	Error	Program
	11.8b	(.f64 x (-.f64 (/.f64 y z) (.f64 (/.f64 t (-.f64 1 (*.f64 z z))) (+.f64 1 z))))
	4.1b	(-.f64 (/.f64 1 (/.f64 (/.f64 z x) y)) (*.f64 (/.f64 t (-.f64 1 z)) x))
	33.0b	(.f64 x (-.f64 (/.f64 y z) (.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 1 z)))))
	21.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (cbrt.f64 x) (-.f64 (.f64 (-.f64 1 z) y) (.f64 t z))) (.f64 z (-.f64 1 z))))
	22.9b	(/.f64 (*.f64 x (+.f64 t y)) z)
	3.4b	(-.f64 (/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z)) (*.f64 (/.f64 t (-.f64 1 z)) x))
	33.5b	(.f64 (sqrt.f64 x) (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (sqrt.f64 x)))
	23.3b	(+.f64 (.f64 x (+.f64 (/.f64 t z) (/.f64 t (pow.f64 z 3)))) (.f64 (/.f64 x z) (+.f64 (/.f64 t z) y)))
	6.3b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 t (-.f64 1 z)) x))
	8.0b	(-.f64 (/.f64 (.f64 x y) z) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 x (/.f64 (cbrt.f64 t) (-.f64 1 z)))))

Compiler

Compiled 2189 to 948 computations (56.7% saved)

regimes2.4s (34.7%)

Accuracy

Total 1.1b remaining (97.3%)

Threshold costs 0b (0%)

Compiler

Compiled 26837 to 16686 computations (37.8% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`sub-neg_binary64` `+-commutative_binary64`
7×	`cancel-sign-sub-inv_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	102
1	48	102
2	67	102
3	76	102
4	83	102
5	85	102
6	83	102

end2.0ms (0%)

Compiler: Compiled 73 to 42 computations (42.5% saved)

sample931.0ms (13.4%)

Algorithm

1×

intervals

Results

302.0ms	8000×	body	128	valid
71.0ms	1785×	body	128	invalid

Compiler

Compiled 302 to 187 computations (38.1% saved)

Details

analyze856.0ms (12.3%)

sample23.0ms (0.3%)

simplify262.0ms (3.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite251.0ms (3.6%)

series154.0ms (2.2%)

simplify166.0ms (2.4%)

prune82.0ms (1.2%)

localize14.0ms (0.2%)

rewrite143.0ms (2.1%)

series255.0ms (3.7%)

simplify119.0ms (1.7%)

prune68.0ms (1%)

localize12.0ms (0.2%)

rewrite189.0ms (2.7%)

series170.0ms (2.4%)

simplify126.0ms (1.8%)

prune100.0ms (1.4%)

localize19.0ms (0.3%)

rewrite165.0ms (2.4%)

series181.0ms (2.6%)

simplify136.0ms (2%)

prune90.0ms (1.3%)

regimes2.4s (34.7%)

bsearch9.0ms (0.1%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample931.0ms (13.4%)

Profiling