Details

analyze273.0ms (5.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0.1%	0%	99.9%	1

Compiler

Compiled 23 to 17 computations (26.1% saved)

sample37.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 36 to 27 computations (25% saved)

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

47×	`cancel-sign-sub-inv_binary32`
43×	`sub-neg_binary32`
27×	`unsub-neg_binary32`
23×	`associate--r+_binary32`
20×	`distribute-rgt-neg-in_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	33	10
3	57	10
4	122	10
5	212	10
6	256	10
7	256	10
8	257	10
9	222	10

prune4.0ms (0.1%)

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

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 20 to 14 computations (30% saved)

localize24.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(*.f32 ux maxCos)
0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

rewrite68.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`add-log-exp_binary32` `add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32` `*-un-lft-identity_binary32`
4×	`pow1_binary32` `add-exp-log_binary32` `add-cbrt-cube_binary32` `associate-+l+_binary32`
3×	`cancel-sign-sub-inv_binary32` `associate-l_binary32` `associate-r_binary32`
2×	`sum-log_binary32`

Counts

2 → 35

Calls

2 calls:

8.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
3.0ms	(*.f32 ux maxCos)

Compiler

Compiled 434 to 218 computations (49.8% saved)

series55.0ms (1.2%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

33.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
15.0ms	(*.f32 ux maxCos)

Compiler

Compiled 330 to 227 computations (31.2% saved)

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-l_binary32`
326×	`exp-prod_binary32`
313×	`associate-r_binary32`
296×	`distribute-rgt-out_binary32`
193×	`distribute-rgt-in_binary32`

Counts

53 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	484
1	190	463
2	513	463
3	2007	463
4	4512	463
5	4966	463
6	4999	463
7	4932	463

prune29.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	4	31

Error

0.0b

Counts

31 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))
	0.5b	(.f32 (.f32 (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux)) (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux))) (cbrt.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	0.5b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))

Compiler

Compiled 296 to 176 computations (40.5% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f32 ux maxCos)
0.0b	(-.f32 (*.f32 ux maxCos) ux)
0.0b	(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))

rewrite85.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`add-log-exp_binary32`
9×	`add-sqr-sqrt_binary32` `*-un-lft-identity_binary32`
7×	`add-cube-cbrt_binary32`
6×	`cancel-sign-sub-inv_binary32`
5×	`pow1_binary32` `add-exp-log_binary32` `add-cbrt-cube_binary32`

Counts

3 → 50

Calls

3 calls:

6.0ms	(*.f32 ux maxCos)
6.0ms	(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))
4.0ms	(-.f32 (*.f32 ux maxCos) ux)

Compiler

Compiled 630 to 262 computations (58.4% saved)

series71.0ms (1.5%)

Error

0.0b

Counts

3 → 27

Calls

3 calls:

24.0ms	(+.f32 1 (-.f32 (*.f32 ux maxCos) ux))
19.0ms	(-.f32 (*.f32 ux maxCos) ux)
17.0ms	(*.f32 ux maxCos)

Compiler

Compiled 504 to 358 computations (29% saved)

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-l_binary32`
396×	`distribute-rgt-out_binary32`
348×	`associate-r_binary32`
314×	`exp-prod_binary32`
301×	`log-prod_binary32`

Counts

77 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	689
1	203	662
2	552	659
3	2196	659
4	4400	659
5	5060	659

prune45.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux)) (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux))) (cbrt.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	0.5b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
▶	0.4b	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))

Compiler

Compiled 411 to 232 computations (43.6% saved)

localize48.0ms (1%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1))
0.2b	(pow.f32 (-.f32 (*.f32 ux maxCos) ux) 3)
0.3b	(.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (*.f32 ux maxCos) ux) -1)))
0.4b	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))

rewrite271.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`*-un-lft-identity_binary32`
26×	`add-sqr-sqrt_binary32`
19×	`add-cube-cbrt_binary32`
14×	`add-exp-log_binary32` `add-cbrt-cube_binary32`
12×	`pow1_binary32` `times-frac_binary32` `associate-*r/_binary32`

Counts

4 → 124

Calls

4 calls:

16.0ms	(.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1))
14.0ms	(.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (*.f32 ux maxCos) ux) -1)))
13.0ms	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))
5.0ms	(pow.f32 (-.f32 (*.f32 ux maxCos) ux) 3)

Compiler

Compiled 4325 to 2314 computations (46.5% saved)

series559.0ms (11.9%)

Error

Counts

4 → 43

Calls

4 calls:

330.0ms	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))
52.0ms	(.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (*.f32 ux maxCos) ux) -1)))
44.0ms	(.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1))
37.0ms	(pow.f32 (-.f32 (*.f32 ux maxCos) ux) 3)

Compiler

Compiled 5763 to 4376 computations (24.1% saved)

simplify157.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

369×	`associate-r_binary32`
350×	`associate-l_binary32`
250×	`distribute-rgt-in_binary32`
243×	`distribute-lft-in_binary32`
210×	`associate-+r+_binary32`

Counts

167 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	6064
1	1134	5717
2	4788	5704
3	5055	5704

prune241.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux)) (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux))) (cbrt.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
✓	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
▶	0.5b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
✓	0.4b	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))

Compiler

Compiled 4591 to 2772 computations (39.6% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f32 ux maxCos)
0.1b	(-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)
0.1b	(exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux))
0.5b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))

rewrite114.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary32`
18×	`*-un-lft-identity_binary32`
15×	`add-log-exp_binary32`
12×	`add-cube-cbrt_binary32`
10×	`exp-prod_binary32` `exp-sum_binary32`

Counts

4 → 80

Calls

4 calls:

8.0ms	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
6.0ms	(exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux))
6.0ms	(-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)
4.0ms	(*.f32 ux maxCos)

Compiler

Compiled 1148 to 648 computations (43.6% saved)

series177.0ms (3.8%)

Error

Counts

4 → 37

Calls

4 calls:

80.0ms	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
32.0ms	(exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux))
26.0ms	(-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)
17.0ms	(*.f32 ux maxCos)

Compiler

Compiled 1104 to 802 computations (27.4% saved)

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

366×	`associate-+l+_binary32`
348×	`sub-neg_binary32`
282×	`times-frac_binary32`
249×	`*-commutative_binary32`
237×	`associate-+r+_binary32`

Counts

117 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	1531
1	370	1432
2	1184	1362
3	3601	1362
4	4764	1362
5	4975	1362

prune55.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	70	4	74

Error

Counts

74 → 4

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux)) (cbrt.f32 (-.f32 (+.f32 1 (.f32 ux maxCos)) ux))) (cbrt.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
	0.5b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 ux maxCos)) ux)))
	0.4b	(/.f32 (+.f32 1 (pow.f32 (-.f32 (.f32 ux maxCos) ux) 3)) (+.f32 1 (.f32 ux (.f32 (-.f32 maxCos 1) (+.f32 (-.f32 (.f32 ux maxCos) ux) -1)))))

Compiler

Compiled 622 to 361 computations (42% saved)

regimes761.0ms (16.3%)

Accuracy

Total 0.0b remaining (69.1%)

Threshold costs 0.0b (69.1%)

Compiler

Compiled 7014 to 4868 computations (30.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32` `+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`1-exp_binary32` `neg-mul-1_binary32` `neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	21	25
2	25	25
3	27	25
4	28	25
5	27	25

end2.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

sample1.2s (26.4%)

Algorithm

1×

intervals

Results

294.0ms	7999×	body	128	valid
238.0ms	8000×	pre	128	true
0.0ms	1×	body	256	valid

Compiler

Compiled 125 to 84 computations (32.8% saved)

Details

analyze273.0ms (5.8%)

sample37.0ms (0.8%)

simplify17.0ms (0.4%)

prune4.0ms (0.1%)

localize24.0ms (0.5%)

rewrite68.0ms (1.5%)

series55.0ms (1.2%)

simplify118.0ms (2.5%)

prune29.0ms (0.6%)

localize15.0ms (0.3%)

rewrite85.0ms (1.8%)

series71.0ms (1.5%)

simplify86.0ms (1.8%)

prune45.0ms (1%)

localize48.0ms (1%)

rewrite271.0ms (5.8%)

series559.0ms (11.9%)

simplify157.0ms (3.3%)

prune241.0ms (5.2%)

localize23.0ms (0.5%)

rewrite114.0ms (2.4%)

series177.0ms (3.8%)

simplify105.0ms (2.2%)

prune55.0ms (1.2%)

regimes761.0ms (16.3%)

simplify4.0ms (0.1%)

end2.0ms (0%)

sample1.2s (26.4%)

Profiling