Details

analyze82.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample22.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify51.0ms (2%)

Algorithm

1×	egg-herbie

Rules

243×	`div-sub_binary64`
166×	`associate-/l/_binary64`
143×	`times-frac_binary64`
130×	`associate-/l*_binary64`
86×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	31	10
4	42	10
5	66	10
6	110	10
7	184	10
8	308	10
9	462	10
10	533	10
11	599	10
12	568	10
13	564	10
14	568	10
15	572	10
16	574	10
17	498	10

prune1.0ms (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

8.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	8.7b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.9b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite49.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

2 → 58

Calls

2 calls:

10.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
4.0ms	(/.f64 x0 (-.f64 1 x1))

Compiler

Compiled 808 to 492 computations (39.1% saved)

series27.0ms (1.1%)

Error

4.1b

Counts

2 → 18

Calls

2 calls:

12.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
11.0ms	(/.f64 x0 (-.f64 1 x1))

Compiler

Compiled 431 to 279 computations (35.3% saved)

simplify96.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

477×	`distribute-rgt-in_binary64`
302×	`distribute-rgt-out_binary64`
295×	`distribute-lft-out_binary64`
194×	`associate-l_binary64`
178×	`log-prod_binary64`

Counts

76 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1052
1	272	1020
2	644	999
3	2136	987
4	4848	987
5	5001	987

prune11.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Error

4.1b

Counts

41 → 2

Alt Table

Status	Error	Program
▶	7.8b	(.f64 1 (.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0))
	15.6b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Compiler

Compiled 399 to 234 computations (41.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
7.6b	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

rewrite57.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

37×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
12×	`difference-of-squares_binary64`
12×	`times-frac_binary64`

Counts

2 → 56

Calls

2 calls:

21.0ms	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
10.0ms	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

Compiler

Compiled 932 to 790 computations (15.2% saved)

series23.0ms (0.9%)

Error

4.1b

Counts

2 → 15

Calls

2 calls:

13.0ms	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
6.0ms	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

Compiler

Compiled 379 to 281 computations (25.9% saved)

simplify106.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
577×	`distribute-lft-in_binary64`
512×	`div-sub_binary64`
319×	`times-frac_binary64`
229×	`associate-*l/_binary64`

Counts

71 → 62

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	87	1123
1	183	1042
2	470	952
3	1073	945
4	2235	944
5	3826	944
6	4939	944
7	4899	944

prune20.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Error

3.3b

Counts

64 → 2

Alt Table

Status	Error	Program
▶	6.8b	(.f64 1 (.f64 (*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (cbrt.f64 x0)))
	15.6b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Compiler

Compiled 721 to 556 computations (22.9% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
6.3b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

rewrite81.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

47×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
18×	`cancel-sign-sub-inv_binary64`
15×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`

Counts

2 → 69

Calls

2 calls:

22.0ms	(*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
17.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

Compiler

Compiled 1828 to 857 computations (53.1% saved)

series119.0ms (4.6%)

Error

3.3b

Counts

2 → 18

Calls

2 calls:

72.0ms	(*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
37.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

Compiler

Compiled 1093 to 829 computations (24.2% saved)

simplify130.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

390×	`unswap-sqr_binary64`
383×	`*-commutative_binary64`
258×	`exp-prod_binary64`
254×	`div-sub_binary64`
213×	`unsub-neg_binary64`

Counts

87 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1978
1	362	1749
2	1278	1693
3	2899	1653
4	4411	1575
5	4758	1575
6	4849	1575

prune23.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	2	76

Error

3.0b

Counts

76 → 2

Alt Table

Status	Error	Program
▶	6.5b	(.f64 1 (.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))) (cbrt.f64 x0)))
	15.6b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Status

Error

Program

▶

6.5b

(*.f64 1 (*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))) (cbrt.f64 x0)))

15.6b

(*.f64 x0 (*.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Compiler

Compiled 1112 to 662 computations (40.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))
1.0b	(.f64 (.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)))
6.3b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
6.3b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

rewrite216.0ms (8.4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

70×	`add-sqr-sqrt_binary64`
57×	`add-exp-log_binary64`
43×	`prod-exp_binary64`
21×	`cbrt-prod_binary64`
18×	`difference-of-squares_binary64`

Counts

4 → 132

Calls

4 calls:

43.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)))
23.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))
19.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
17.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

Compiler

Compiled 5580 to 3249 computations (41.8% saved)

series232.0ms (9.1%)

Error

3.0b

Counts

4 → 33

Calls

4 calls:

66.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))
61.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)))
42.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
42.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

Compiler

Compiled 2962 to 2173 computations (26.6% saved)

simplify174.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

501×	`*-commutative_binary64`
470×	`unswap-sqr_binary64`
249×	`log-prod_binary64`
219×	`associate-l_binary64`
199×	`associate-r_binary64`

Counts

165 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	4511
1	496	3867
2	1416	3623
3	3324	3595
4	4841	3595
5	4984	3595

prune85.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	2	139

Error

3.0b

Counts

139 → 2

Alt Table

Status	Error	Program
	6.5b	(.f64 1 (.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))) (cbrt.f64 x0)))
	15.6b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Status

Error

Program

6.5b

(*.f64 1 (*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6)) (*.f64 (sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (pow.f64 x0 1/6))) (cbrt.f64 x0)))

15.6b

(*.f64 x0 (*.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Compiler

Compiled 3494 to 2177 computations (37.7% saved)

regimes122.0ms (4.8%)

Accuracy

Total -0.6b remaining (-23.3%)

Threshold costs -0.6b (-23.3%)

Compiler

Compiled 3860 to 2669 computations (30.9% saved)

bsearch1.0ms (0.1%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-lft-identity_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	131
1	63	131
2	70	131
3	74	131
4	76	131
5	75	131

end2.0ms (0.1%)

Compiler: Compiled 86 to 58 computations (32.6% saved)

sample792.0ms (30.9%)

Algorithm

1×

intervals

Results

229.0ms	8000×	body	128	valid
224.0ms	8000×	pre	128	true

Compiler

Compiled 161 to 109 computations (32.3% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	31	10
4	42	10
5	66	10
6	110	10
7	184	10
8	308	10
9	462	10
10	533	10
11	599	10
12	568	10
13	564	10
14	568	10
15	572	10
16	574	10
17	498	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	31	10
4	42	10
5	66	10
6	110	10
7	184	10
8	308	10
9	462	10
10	533	10
11	599	10
12	568	10
13	564	10
14	568	10
15	572	10
16	574	10
17	498	10

Details

analyze82.0ms (3.2%)

sample22.0ms (0.9%)

simplify51.0ms (2%)

prune1.0ms (0%)

localize4.0ms (0.2%)

rewrite49.0ms (1.9%)

series27.0ms (1.1%)

simplify96.0ms (3.7%)

prune11.0ms (0.4%)

localize6.0ms (0.2%)

rewrite57.0ms (2.2%)

series23.0ms (0.9%)

simplify106.0ms (4.1%)

prune20.0ms (0.8%)

localize8.0ms (0.3%)

rewrite81.0ms (3.2%)

series119.0ms (4.6%)

simplify130.0ms (5.1%)

prune23.0ms (0.9%)

localize14.0ms (0.5%)

rewrite216.0ms (8.4%)

series232.0ms (9.1%)

simplify174.0ms (6.8%)

prune85.0ms (3.3%)

regimes122.0ms (4.8%)

bsearch1.0ms (0.1%)

simplify6.0ms (0.2%)

end2.0ms (0.1%)

sample792.0ms (30.9%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	31	10
4	42	10
5	66	10
6	110	10
7	184	10
8	308	10
9	462	10
10	533	10
11	599	10
12	568	10
13	564	10
14	568	10
15	572	10
16	574	10
17	498	10