Details

analyze91.0ms (1.8%)

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)

sample45.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 36 to 27 computations (25% saved)

simplify16.0ms (0.3%)

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

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

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)

localize17.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-log-exp_binary32`
4×	`associate-+l+_binary32`
3×	`cancel-sign-sub-inv_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`

Counts

1 → 17

Calls

1 calls:

5.0ms

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

Compiler

Compiled 244 to 129 computations (47.1% saved)

series20.0ms (0.4%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

16.0ms

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

Compiler

Compiled 189 to 133 computations (29.6% saved)

simplify124.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

550×	`unsub-neg_binary32`
455×	`*-commutative_binary32`
418×	`sub-neg_binary32`
347×	`cancel-sign-sub-inv_binary32`
269×	`exp-prod_binary32`

Counts

29 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	342
1	156	321
2	395	321
3	1624	321
4	3207	321
5	4504	321
6	4933	321

prune18.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	3	17

Error

0.0b

Counts

17 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
	0.1b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (.f32 (-.f32 1 ux) (-.f32 1 ux)) (.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))))
	0.6b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)))

Compiler

Compiled 259 to 157 computations (39.4% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite93.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-log-exp_binary32`
8×	`*-un-lft-identity_binary32`
6×	`cancel-sign-sub-inv_binary32`
6×	`add-sqr-sqrt_binary32`
4×	`diff-log_binary32`

Counts

2 → 35

Calls

2 calls:

5.0ms	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
2.0ms	(-.f32 ux (*.f32 maxCos ux))

Compiler

Compiled 483 to 188 computations (61.1% saved)

series37.0ms (0.8%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

16.0ms	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
14.0ms	(-.f32 ux (*.f32 maxCos ux))

Compiler

Compiled 369 to 267 computations (27.6% saved)

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

415×	`neg-sub0_binary32`
401×	`neg-mul-1_binary32`
342×	`associate-+l+_binary32`
285×	`associate-l_binary32`
283×	`cancel-sign-sub-inv_binary32`

Counts

56 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	610
1	178	586
2	478	583
3	1824	579
4	4165	579
5	5216	579

prune23.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Error

0.0b

Counts

35 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
▶	0.1b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (.f32 (-.f32 1 ux) (-.f32 1 ux)) (.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))))
	0.6b	(log.f32 (exp.f32 (-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)))

Compiler

Compiled 344 to 192 computations (44.2% saved)

localize67.0ms (1.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
0.2b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (.f32 (-.f32 1 ux) (-.f32 1 ux)) (.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))))
0.4b	(*.f32 (-.f32 1 ux) (-.f32 1 ux))
0.6b	(pow.f32 (-.f32 1 ux) 3)

rewrite520.0ms (10.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

56×	`*-un-lft-identity_binary32`
44×	`add-sqr-sqrt_binary32`
42×	`associate-*r/_binary32`
24×	`add-cube-cbrt_binary32`
19×	`flip--_binary32`

Counts

4 → 162

Calls

4 calls:

23.0ms	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (.f32 (-.f32 1 ux) (-.f32 1 ux)) (.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))))
9.0ms	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
8.0ms	(*.f32 (-.f32 1 ux) (-.f32 1 ux))
4.0ms	(pow.f32 (-.f32 1 ux) 3)

Compiler

Compiled 7076 to 4387 computations (38% saved)

series398.0ms (8.1%)

Error

Counts

4 → 37

Calls

4 calls:

142.0ms	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (.f32 (-.f32 1 ux) (-.f32 1 ux)) (.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))))
111.0ms	(pow.f32 (-.f32 1 ux) 3)
48.0ms	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
14.0ms	(*.f32 (-.f32 1 ux) (-.f32 1 ux))

Compiler

Compiled 3428 to 2508 computations (26.8% saved)

simplify190.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-l_binary32`
499×	`associate-r_binary32`
352×	`times-frac_binary32`
286×	`distribute-rgt-in_binary32`
267×	`distribute-lft-in_binary32`

Counts

199 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	6717
1	1014	6181
2	4310	6130
3	4964	6130

prune291.0ms (5.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	176	3	179

Error

Counts

179 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
▶	0.1b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 6)) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))
	0.7b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (log.f32 (exp.f32 (pow.f32 (-.f32 1 ux) 2))) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))

Compiler

Compiled 5219 to 3181 computations (39% saved)

localize70.0ms (1.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
0.2b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 6)) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))
0.6b	(pow.f32 (-.f32 1 ux) 3)
1.0b	(pow.f32 (-.f32 1 ux) 6)

rewrite258.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`*-un-lft-identity_binary32`
29×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
15×	`times-frac_binary32`
13×	`add-exp-log_binary32`

Counts

4 → 114

Calls

4 calls:

20.0ms	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 6)) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))
11.0ms	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
4.0ms	(pow.f32 (-.f32 1 ux) 3)
4.0ms	(pow.f32 (-.f32 1 ux) 6)

Compiler

Compiled 4297 to 2781 computations (35.3% saved)

series324.0ms (6.6%)

Error

Counts

4 → 38

Calls

4 calls:

195.0ms	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 6)) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))
49.0ms	(.f32 maxCos (.f32 ux (+.f32 (*.f32 maxCos ux) (+.f32 ux -1))))
20.0ms	(pow.f32 (-.f32 1 ux) 3)
15.0ms	(pow.f32 (-.f32 1 ux) 6)

Compiler

Compiled 3459 to 2564 computations (25.9% saved)

simplify158.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

593×	`unswap-sqr_binary32`
324×	`times-frac_binary32`
284×	`associate-r_binary32`
280×	`associate-l_binary32`
273×	`log-prod_binary32`

Counts

152 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	4751
1	820	4466
2	3076	4445
3	4806	4445
4	5050	4445

prune181.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	126	3	129

Error

Counts

129 → 3

Alt Table

Status	Error	Program
	1.0b	(/.f32 (+.f32 (+.f32 1 (.f32 (.f32 ux ux) (-.f32 3 ux))) (.f32 ux -3)) (-.f32 (+.f32 1 (.f32 ux ux)) (*.f32 ux 2)))
	0.0b	(-.f32 1 (-.f32 ux (*.f32 maxCos ux)))
	0.1b	(/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos ux) 3)) (+.f32 (cbrt.f32 (pow.f32 (-.f32 1 ux) 6)) (.f32 maxCos (.f32 ux (+.f32 (.f32 maxCos ux) (+.f32 ux -1))))))

Compiler

Compiled 3501 to 2224 computations (36.5% saved)

regimes492.0ms (10%)

Accuracy

Total 0.0b remaining (48.7%)

Threshold costs 0.0b (48.7%)

Compiler

Compiled 6043 to 4213 computations (30.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`cancel-sign-sub-inv_binary32`
18×	`distribute-rgt-neg-in_binary32`
11×	`distribute-lft-neg-in_binary32`
10×	`sub-neg_binary32`
8×	`neg-sub0_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	21	10
2	33	10
3	52	10
4	67	10
5	81	10
6	90	10
7	92	10
8	88	10

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.4s (27.6%)

Algorithm

1×

intervals

Results

344.0ms	7999×	body	128	valid
293.0ms	8000×	pre	128	true
0.0ms	1×	body	256	valid

Compiler

Compiled 105 to 76 computations (27.6% saved)

Details

analyze91.0ms (1.8%)

sample45.0ms (0.9%)

simplify16.0ms (0.3%)

prune2.0ms (0%)

localize17.0ms (0.3%)

rewrite27.0ms (0.5%)

series20.0ms (0.4%)

simplify124.0ms (2.5%)

prune18.0ms (0.4%)

localize16.0ms (0.3%)

rewrite93.0ms (1.9%)

series37.0ms (0.8%)

simplify69.0ms (1.4%)

prune23.0ms (0.5%)

localize67.0ms (1.4%)

rewrite520.0ms (10.6%)

series398.0ms (8.1%)

simplify190.0ms (3.9%)

prune291.0ms (5.9%)

localize70.0ms (1.4%)

rewrite258.0ms (5.2%)

series324.0ms (6.6%)

simplify158.0ms (3.2%)

prune181.0ms (3.7%)

regimes492.0ms (10%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.4s (27.6%)

Profiling