Details

analyze295.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample66.0ms (1.5%)

Algorithm

1×

intervals

Results

31.0ms	87×	body	1024	valid
14.0ms	41×	body	2048	valid
6.0ms	28×	body	512	valid
4.0ms	80×	body	128	valid
2.0ms	19×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

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

52.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.7b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.8b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite88.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

52.0b

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 42

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 704 to 424 computations (39.8% saved)

series87.0ms (2%)

Error

0.0b

Counts

3 → 36

Calls

3 calls:

21.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
13.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 1069 to 884 computations (17.3% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
410×	`sub-neg_binary64`
248×	`distribute-rgt-in_binary64`
230×	`cancel-sign-sub-inv_binary64`
210×	`associate-r_binary64`

Counts

78 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1363
1	408	1286
2	1008	1256
3	2904	1250
4	4674	1250
5	5287	1250

prune58.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Error

0.0b

Counts

63 → 6

Alt Table

Status	Error	Program
	52.4b	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x))))))) (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))
▶	30.5b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
	48.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
✓	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
	52.4b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 1031 to 705 computations (31.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.1b	(*.f64 (pow.f64 x 5) 3/40)
0.3b	(*.f64 (pow.f64 x 3) 1/6)
19.0b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))

rewrite95.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(*.f64 (pow.f64 x 5) 3/40)
3.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))

Compiler

Compiled 1554 to 1223 computations (21.3% saved)

series62.0ms (1.4%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

24.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
13.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
11.0ms	(*.f64 (pow.f64 x 5) 3/40)
8.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 496 to 390 computations (21.4% saved)

simplify133.0ms (3%)

Algorithm

1×	egg-herbie

Rules

473×	`cancel-sign-sub-inv_binary64`
467×	`log-prod_binary64`
406×	`exp-prod_binary64`
386×	`*-commutative_binary64`
332×	`unswap-sqr_binary64`

Counts

104 → 72

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	147	1388
1	322	1349
2	1104	1334
3	2704	1310
4	4457	1283
5	4941	1283
6	4941	1283

prune52.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Error

0.0b

Counts

78 → 6

Alt Table

Status	Error	Program
	52.4b	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x))))))) (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))
✓	30.5b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
	48.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
▶	47.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
✓	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
	52.4b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 1086 to 845 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
7×	`distribute-lft-out_binary64`
5×	`log-prod_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 43

Calls

3 calls:

8.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
8.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
6.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 612 to 407 computations (33.5% saved)

series36.0ms (0.8%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

11.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
10.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
9.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 356 to 283 computations (20.5% saved)

simplify102.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

325×	`associate-*l/_binary64`
299×	`div-sub_binary64`
272×	`associate-*r/_binary64`
265×	`times-frac_binary64`
256×	`associate-/l*_binary64`

Counts

60 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	859
1	208	765
2	531	738
3	1759	734
4	4321	734
5	4946	734

prune25.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	40	6	46

Error

0.0b

Counts

46 → 6

Alt Table

Status	Error	Program
	52.4b	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x))))))) (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))
✓	30.5b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
▶	48.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
✓	47.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
✓	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
	52.4b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 544 to 352 computations (35.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.6b	(/.f64 1/8 (pow.f64 x 3))
11.7b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
20.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite258.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

75×	`*-un-lft-identity_binary64`
73×	`times-frac_binary64`
73×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`

Counts

4 → 164

Calls

4 calls:

43.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
43.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

Compiler

Compiled 3877 to 3168 computations (18.3% saved)

series64.0ms (1.5%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

26.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
12.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
9.0ms	(/.f64 1/16 (pow.f64 x 5))
9.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 670 to 571 computations (14.8% saved)

simplify159.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

469×	`log-prod_binary64`
346×	`cancel-sign-sub-inv_binary64`
302×	`unswap-sqr_binary64`
254×	`distribute-rgt-in_binary64`
199×	`distribute-rgt-neg-in_binary64`

Counts

184 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	4019
1	624	3792
2	2159	3666
3	4521	3666
4	4980	3666

prune83.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	52.4b	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x))))))) (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))
	30.5b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 (pow.f64 x 5) 3/40))
	48.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
	47.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	52.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
	52.4b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 2120 to 1686 computations (20.5% saved)

regimes344.0ms (7.8%)

Accuracy

Total 0.2b remaining (92.9%)

Threshold costs 0.2b (92.9%)

Compiler

Compiled 3235 to 2313 computations (28.5% saved)

bsearch26.0ms (0.6%)

Steps

Iters	Range		Point
7	0.04409844628945373	1.421681649185019	1.0106614979101263
8	-2.2610248131128037	-0.0006189360082884834	-1.0415323700440298

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	70
1	51	70
2	65	70
3	83	70
4	91	70
5	94	70
6	90	70

end2.0ms (0%)

Compiler: Compiled 48 to 37 computations (22.9% saved)

sample2.2s (49.3%)

Algorithm

1×

intervals

Results

925.0ms	2554×	body	1024	valid
403.0ms	1226×	body	2048	valid
244.0ms	1209×	body	512	valid
110.0ms	2357×	body	128	valid
67.0ms	606×	body	256	valid
21.0ms	48×	body	4096	valid

Compiler

Compiled 147 to 111 computations (24.5% saved)

Details

analyze295.0ms (6.7%)

sample66.0ms (1.5%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite88.0ms (2%)

series87.0ms (2%)

simplify98.0ms (2.2%)

prune58.0ms (1.3%)

localize8.0ms (0.2%)

rewrite95.0ms (2.2%)

series62.0ms (1.4%)

simplify133.0ms (3%)

prune52.0ms (1.2%)

localize5.0ms (0.1%)

rewrite52.0ms (1.2%)

series36.0ms (0.8%)

simplify102.0ms (2.3%)

prune25.0ms (0.6%)

localize11.0ms (0.2%)

rewrite258.0ms (5.8%)

series64.0ms (1.5%)

simplify159.0ms (3.6%)

prune83.0ms (1.9%)

regimes344.0ms (7.8%)

bsearch26.0ms (0.6%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample2.2s (49.3%)

Profiling