Details

analyze84.0ms (3.4%)

Algorithm

1×

Search

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

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample23.0ms (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)

simplify52.0ms (2.1%)

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

8.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	8.0b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.2b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite38.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

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:

9.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
4.0ms	(/.f64 x0 (-.f64 1 x1))

Compiler

Compiled 808 to 492 computations (39.1% saved)

series34.0ms (1.4%)

Error

4.2b

Counts

2 → 18

Calls

2 calls:

16.0ms	(/.f64 x0 (-.f64 1 x1))
13.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

Compiler

Compiled 431 to 279 computations (35.3% saved)

simplify92.0ms (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

prune13.0ms (0.5%)

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

4.2b

Counts

41 → 2

Alt Table

Status	Error	Program
▶	7.1b	(.f64 1 (.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0))
	18.4b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))

Compiler

Compiled 399 to 234 computations (41.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.6b	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
6.8b	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

rewrite52.0ms (2.1%)

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:

13.0ms	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
11.0ms	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

Compiler

Compiled 932 to 790 computations (15.2% saved)

series27.0ms (1.1%)

Error

4.1b

Counts

2 → 15

Calls

2 calls:

19.0ms	(*.f64 (-.f64 (/.f64 1 (-.f64 1 x1)) 1) x0)
5.0ms	(-.f64 (/.f64 1 (-.f64 1 x1)) 1)

Compiler

Compiled 379 to 281 computations (25.9% saved)

simplify116.0ms (4.6%)

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

3.2b

Counts

64 → 2

Alt Table

Status	Error	Program
	18.4b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))
▶	6.0b	(.f64 1 (.f64 (*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))) (cbrt.f64 x0)))

Compiler

Compiled 721 to 556 computations (22.9% saved)

localize17.0ms (0.7%)

Local error

Found 2 expressions with local error:

0.4b	(*.f64 (cbrt.f64 x0) (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
5.5b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

rewrite80.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

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:

25.0ms	(*.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)

series117.0ms (4.7%)

Error

3.1b

Counts

2 → 18

Calls

2 calls:

65.0ms	(*.f64 (cbrt.f64 x0) (-.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 1093 to 829 computations (24.2% saved)

simplify135.0ms (5.4%)

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

prune24.0ms (1%)

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

2.8b

Counts

76 → 2

Alt Table

Status	Error	Program
	18.4b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))
▶	5.6b	(.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)))

Status

Error

Program

18.4b

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

▶

5.6b

(*.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)))

Compiler

Compiled 1112 to 662 computations (40.5% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.6b	(sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
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)))
5.5b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
5.5b	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

rewrite185.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

58×	`add-sqr-sqrt_binary64`
52×	`add-exp-log_binary64`
40×	`prod-exp_binary64`
21×	`cbrt-prod_binary64`
18×	`difference-of-squares_binary64`

Counts

4 → 114

Calls

4 calls:

39.0ms	(.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)))
18.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
17.0ms	(sqrt.f64 (-.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 4943 to 2860 computations (42.1% saved)

series225.0ms (9%)

Error

2.8b

Counts

4 → 33

Calls

4 calls:

63.0ms	(.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)))
49.0ms	(sqrt.f64 (-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0)))
47.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))
45.0ms	(-.f64 (/.f64 (cbrt.f64 x0) (-.f64 1 x1)) (cbrt.f64 x0))

Compiler

Compiled 2908 to 2130 computations (26.8% saved)

simplify160.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

482×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
232×	`exp-prod_binary64`
208×	`log-prod_binary64`
177×	`associate-l_binary64`

Counts

147 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	3909
1	437	3280
2	1202	3121
3	3011	3097
4	4630	3097
5	4906	3097

prune57.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	119	2	121

Error

2.8b

Counts

121 → 2

Alt Table

Status	Error	Program
	18.4b	(.f64 x0 (.f64 (+.f64 1 x1) (+.f64 x1 (pow.f64 x1 3))))
	5.6b	(.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)))

Status

Error

Program

18.4b

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

5.6b

(*.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)))

Compiler

Compiled 2942 to 1836 computations (37.6% saved)

regimes111.0ms (4.4%)

Accuracy

Total -0.3b remaining (-9.4%)

Threshold costs -0.3b (-9.4%)

Compiler

Compiled 3625 to 2509 computations (30.8% saved)

bsearch1.0ms (0.1%)

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

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
13×	`+-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	203
1	83	203
2	95	203
3	103	203
4	107	203
5	106	203

end2.0ms (0.1%)

Compiler: Compiled 131 to 79 computations (39.7% saved)

sample805.0ms (32.1%)

Algorithm

1×

intervals

Results

234.0ms	8000×	pre	128	true
231.0ms	8000×	body	128	valid

Compiler

Compiled 206 to 130 computations (36.9% 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

analyze84.0ms (3.4%)

sample23.0ms (0.9%)

simplify52.0ms (2.1%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite38.0ms (1.5%)

series34.0ms (1.4%)

simplify92.0ms (3.7%)

prune13.0ms (0.5%)

localize7.0ms (0.3%)

rewrite52.0ms (2.1%)

series27.0ms (1.1%)

simplify116.0ms (4.6%)

prune20.0ms (0.8%)

localize17.0ms (0.7%)

rewrite80.0ms (3.2%)

series117.0ms (4.7%)

simplify135.0ms (5.4%)

prune24.0ms (1%)

localize14.0ms (0.6%)

rewrite185.0ms (7.4%)

series225.0ms (9%)

simplify160.0ms (6.4%)

prune57.0ms (2.3%)

regimes111.0ms (4.4%)

bsearch1.0ms (0.1%)

simplify8.0ms (0.3%)

end2.0ms (0.1%)

sample805.0ms (32.1%)

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