Details

analyze94.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	67×	body	1024	valid
6.0ms	7×	body	2048	valid
4.0ms	132×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

335×	`div-sub_binary64`
178×	`associate-/l*_binary64`
162×	`sub-neg_binary64`
146×	`times-frac_binary64`
139×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	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

29.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	29.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
1.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite261.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

29.5b

Rules

148×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
85×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
34×	`cancel-sign-sub-inv_binary64`

Counts

3 → 147

Calls

3 calls:

45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 2467 to 1786 computations (27.6% saved)

series64.0ms (1.2%)

Error

0.1b

Counts

3 → 36

Calls

3 calls:

16.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
14.0ms	(/.f64 x (+.f64 x 1))
12.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 930 to 740 computations (20.4% saved)

simplify142.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

566×	`times-frac_binary64`
534×	`associate-/l*_binary64`
331×	`distribute-rgt-in_binary64`
237×	`distribute-lft-in_binary64`
170×	`associate-/l/_binary64`

Counts

183 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3709
1	635	3606
2	1963	3158
3	4525	3142
4	4949	3142

prune115.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	5	167

Error

0.1b

Counts

167 → 5

Alt Table

Status	Error	Program
▶	29.9b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
	29.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
	31.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
	30.4b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 x -1))))

Compiler

Compiled 2139 to 1514 computations (29.2% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
0.0b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
1.8b	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))

rewrite987.0ms (17.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1159×	`*-un-lft-identity_binary64`
775×	`times-frac_binary64`
581×	`add-sqr-sqrt_binary64`
370×	`unpow-prod-down_binary64` `cube-prod_binary64`
282×	`distribute-lft-out_binary64`

Counts

4 → 604

Calls

4 calls:

157.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
125.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
11.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
7.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

Compiler

Compiled 17607 to 13050 computations (25.9% saved)

series145.0ms (2.6%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

33.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
28.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
22.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
21.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

Compiler

Compiled 3173 to 2401 computations (24.3% saved)

simplify666.0ms (12.1%)

Algorithm

1×	egg-herbie

Rules

312×	`associate-l_binary64`
258×	`associate-/l*_binary64`
199×	`associate-*l/_binary64`
195×	`associate-*r/_binary64`
153×	`sqr-pow_binary64`

Counts

652 → 551

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	570	47801
1	1593	43569
2	5141	43569

prune347.0ms (6.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	549	2	551
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	552	4	556

Error

0.0b

Counts

556 → 4

Alt Table

Status	Error	Program
▶	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
	31.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
	31.3b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (.f64 (pow.f64 (+.f64 1 x) 3) (/.f64 1 (pow.f64 (+.f64 x -1) 3)))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (*.f64 x (+.f64 3 x)) 1)

Compiler

Compiled 13016 to 9694 computations (25.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 x -1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1)))
6.5b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))

rewrite188.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

58×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

4 → 141

Calls

4 calls:

16.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1)))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
6.0ms	(/.f64 1 (+.f64 x -1))
5.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 3019 to 2280 computations (24.5% saved)

series86.0ms (1.6%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

18.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
15.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1)))
13.0ms	(/.f64 1 (+.f64 x -1))
13.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 1376 to 1084 computations (21.2% saved)

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

775×	`distribute-rgt-in_binary64`
644×	`distribute-lft-in_binary64`
477×	`times-frac_binary64`
208×	`div-sub_binary64`
166×	`distribute-neg-in_binary64`

Counts

189 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	2917
1	610	2789
2	1942	2630
3	4571	2630
4	5202	2630

prune107.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	156	4	160

Error

0.0b

Counts

160 → 4

Alt Table

Status	Error	Program
✓	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
▶	31.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
	31.3b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (.f64 (pow.f64 (+.f64 1 x) 3) (/.f64 1 (pow.f64 (+.f64 x -1) 3)))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (*.f64 x (+.f64 3 x)) 1)

Compiler

Compiled 2391 to 1706 computations (28.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
0.3b	(/.f64 3 (pow.f64 x 3))
0.3b	(/.f64 1 (*.f64 x x))
5.8b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

rewrite243.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

95×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`
54×	`cancel-sign-sub-inv_binary64`

Counts

4 → 198

Calls

4 calls:

42.0ms	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
11.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
5.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 3962 to 2795 computations (29.5% saved)

series52.0ms (0.9%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

16.0ms	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
12.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
9.0ms	(/.f64 3 (pow.f64 x 3))
7.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 586 to 478 computations (18.4% saved)

simplify179.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
300×	`log-prod_binary64`
266×	`cancel-sign-sub-inv_binary64`
250×	`associate-/r*_binary64`
246×	`distribute-neg-frac_binary64`

Counts

217 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	3198
1	656	3040
2	2553	3019
3	4542	2947
4	4650	2947
5	4942	2947

prune66.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	177	5	182

Error

0.0b

Counts

182 → 5

Alt Table

Status	Error	Program
	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 x -1))))
	31.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
	46.4b	(.f64 (sqrt.f64 (+.f64 (/.f64 -3 (pow.f64 x 3)) (-.f64 (/.f64 -3 x) (/.f64 1 (.f64 x x))))) (sqrt.f64 (+.f64 (/.f64 -3 (pow.f64 x 3)) (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))))))
	31.3b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (.f64 (pow.f64 (+.f64 1 x) 3) (/.f64 1 (pow.f64 (+.f64 x -1) 3)))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (*.f64 x (+.f64 3 x)) 1)

Compiler

Compiled 1538 to 1094 computations (28.9% saved)

regimes549.0ms (10%)

Accuracy

Total 0.1b remaining (77%)

Threshold costs 0.1b (77%)

Compiler

Compiled 7616 to 5682 computations (25.4% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
13×	`sub-neg_binary64`
10×	`*-commutative_binary64`
8×	`neg-mul-1_binary64` `neg-sub0_binary64`
3×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	119
1	59	119
2	80	119
3	98	119
4	110	119
5	114	119
6	115	119
7	109	119

end2.0ms (0%)

Compiler: Compiled 81 to 61 computations (24.7% saved)

sample913.0ms (16.6%)

Algorithm

1×

intervals

Results

252.0ms	2034×	body	1024	valid
145.0ms	4320×	body	128	valid
81.0ms	903×	body	512	valid
37.0ms	219×	body	2048	valid
34.0ms	524×	body	256	valid

Compiler

Compiled 223 to 167 computations (25.1% saved)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Details

analyze94.0ms (1.7%)

sample30.0ms (0.5%)

simplify81.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite261.0ms (4.7%)

series64.0ms (1.2%)

simplify142.0ms (2.6%)

prune115.0ms (2.1%)

localize20.0ms (0.4%)

rewrite987.0ms (17.9%)

series145.0ms (2.6%)

simplify666.0ms (12.1%)

prune347.0ms (6.3%)

localize8.0ms (0.1%)

rewrite188.0ms (3.4%)

series86.0ms (1.6%)

simplify134.0ms (2.4%)

prune107.0ms (1.9%)

localize11.0ms (0.2%)

rewrite243.0ms (4.4%)

series52.0ms (0.9%)

simplify179.0ms (3.2%)

prune66.0ms (1.2%)

regimes549.0ms (10%)

bsearch5.0ms (0.1%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample913.0ms (16.6%)

Profiling

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19