Details

analyze100.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0.8%	0.8%	98.5%	3
0.8%	0.8%	98.5%	4
1.2%	0.4%	98.5%	5
1.2%	0.4%	98.5%	6
1.4%	0.2%	98.5%	7
1.4%	0.2%	98.5%	8
1.4%	0.1%	98.5%	9
1.4%	0.1%	98.5%	10
1.5%	0%	98.5%	11
1.5%	0%	98.5%	12
1.5%	0%	98.5%	13
1.5%	0%	98.5%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample462.0ms (6.7%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

175×	`fma-neg_binary32`
156×	`fma-def_binary32`
46×	`cancel-sign-sub-inv_binary32`
46×	`sub-neg_binary32`
29×	`distribute-rgt-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.0b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
▶	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize21.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))

series346.0ms (5%)

Counts

2 → 36

Calls

2 calls:

343.0ms	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
3.0ms	(log1p.f32 (*.f32 u -4))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-r_binary32`
8×	`add-sqr-sqrt_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`
4×	`add-cbrt-cube_binary32`

Counts

2 → 39

Calls

2 calls:

5.0ms	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
0.0ms	(log1p.f32 (*.f32 u -4))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-neg_binary32`
622×	`fma-def_binary32`
409×	`unsub-neg_binary32`
304×	`times-frac_binary32`
234×	`associate-+l+_binary32`

Counts

75 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1231
1	441	1117
2	1415	1071
3	3645	1067
4	5107	1067

prune90.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Error

0.0b

Counts

102 → 8

Alt Table

Status	Error	Program
	16.6b	(cbrt.f32 (.f32 (.f32 (.f32 s s) s) (.f32 (.f32 (neg.f32 (log1p.f32 (.f32 u -4))) (neg.f32 (log1p.f32 (.f32 u -4)))) (neg.f32 (log1p.f32 (.f32 u -4))))))
	2.4b	(+.f32 (.f32 s (.f32 u (+.f32 4 (.f32 u 8)))) (.f32 s (fma.f32 64/3 (pow.f32 u 3) (*.f32 64 (pow.f32 u 4)))))
▶	0.5b	(.f32 (.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
	2.5b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	0.5b	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	0.8b	(.f32 (.f32 (cbrt.f32 s) (cbrt.f32 s)) (.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (.f32 u -4)))))
	0.7b	(.f32 (.f32 (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))) (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4)))))) (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))))

Compiler

Compiled 1790 to 1305 computations (27.1% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))
✓	0.2b	(.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
✓	0.3b	(.f32 (.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))

series714.0ms (10.3%)

Counts

3 → 48

Calls

3 calls:

356.0ms

(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

345.0ms

(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

12.0ms

(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary32`
26×	`associate-r_binary32`
20×	`add-sqr-sqrt_binary32`
15×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

3 → 83

Calls

3 calls:

7.0ms

(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

6.0ms

(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

2.0ms

(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify118.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

435×	`times-frac_binary32`
418×	`fma-neg_binary32`
366×	`cancel-sign-sub-inv_binary32`
291×	`associate-/r*_binary32`
291×	`associate-/l*_binary32`

Counts

131 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	3444
1	737	2979
2	2359	2881
3	4701	2859
4	4946	2859

prune272.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	254	10	264

Error

Counts

264 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (fabs.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	2.4b	(+.f32 (.f32 s (.f32 u (+.f32 4 (.f32 u 8)))) (.f32 s (fma.f32 64/3 (pow.f32 u 3) (*.f32 64 (pow.f32 u 4)))))
	0.8b	(.f32 (.f32 (cbrt.f32 s) (cbrt.f32 s)) (.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (.f32 u -4)))))
	0.9b	(.f32 (.f32 s (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
	0.6b	(.f32 (.f32 (.f32 s (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
	0.5b	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
	2.5b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
▶	0.5b	(.f32 (.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	0.7b	(.f32 (.f32 (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))) (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4)))))) (cbrt.f32 (.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))))

Compiler

Compiled 7744 to 6214 computations (19.8% saved)

localize38.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3))
✓	0.2b	(.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3)))
✓	0.3b	(.f32 (.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
✓	0.7b	(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3)

series725.0ms (10.5%)

Counts

4 → 56

Calls

4 calls:

350.0ms	(.f32 (.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
334.0ms	(.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3)))
25.0ms	(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3)
16.0ms	(cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3))

rewrite50.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary32`
70×	`cbrt-prod_binary32`
50×	`add-sqr-sqrt_binary32`
48×	`associate-r_binary32`
41×	`cube-prod_binary32`

Counts

4 → 179

Calls

4 calls:

14.0ms	(.f32 (.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
14.0ms	(.f32 s (cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3)))
4.0ms	(cbrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3))
3.0ms	(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3)

simplify189.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary32`
346×	`associate-l_binary32`
342×	`fma-neg_binary32`
310×	`associate-r_binary32`
276×	`fma-def_binary32`

Counts

235 → 257

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	370	5700
1	1019	5114
2	3318	5048
3	4478	5030
4	4940	5030

prune281.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	259	8	267

Error

Counts

267 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (fabs.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	0.9b	(.f32 (.f32 s (cbrt.f32 (exp.f32 (log.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
	2.4b	(+.f32 (.f32 s (.f32 u (+.f32 4 (.f32 u 8)))) (.f32 s (fma.f32 64/3 (pow.f32 u 3) (*.f32 64 (pow.f32 u 4)))))
▶	0.5b	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
	2.5b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	0.6b	(.f32 (.f32 (.f32 s (cbrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	0.6b	(.f32 (.f32 (.f32 s (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))

Compiler

Compiled 8311 to 6810 computations (18.1% saved)

localize31.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.3b	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
✓	0.3b	(.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (.f32 u -4))))

series263.0ms (3.8%)

Counts

2 → 32

Calls

2 calls:

243.0ms	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
19.0ms	(.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (.f32 u -4))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary32`
12×	`associate-l_binary32`
11×	`associate-r_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`

Counts

2 → 56

Calls

2 calls:

9.0ms	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
5.0ms	(.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (.f32 u -4))))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-def_binary32`
715×	`times-frac_binary32`
366×	`fma-neg_binary32`
252×	`associate-+l+_binary32`
224×	`associate-r_binary32`

Counts

88 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1744
1	541	1595
2	1721	1526
3	4453	1526
4	5562	1526

prune131.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (fabs.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	0.9b	(.f32 (.f32 s (cbrt.f32 (exp.f32 (log.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))) 3))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
	2.4b	(+.f32 (.f32 s (.f32 u (+.f32 4 (.f32 u 8)))) (.f32 s (fma.f32 64/3 (pow.f32 u 3) (*.f32 64 (pow.f32 u 4)))))
✓	0.5b	(.f32 (sqrt.f32 s) (.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
	2.9b	(fma.f32 s (.f32 (.f32 u u) 8) (.f32 s (+.f32 (.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
	0.6b	(.f32 (.f32 (.f32 s (cbrt.f32 (neg.f32 (log1p.f32 (.f32 u -4))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	0.6b	(.f32 (.f32 (.f32 s (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))) (sqrt.f32 (neg.f32 (log1p.f32 (.f32 u -4)))))

Compiler

Compiled 3030 to 1883 computations (37.9% saved)

regimes1.3s (18.4%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Counts

163 → 1

Compiler

Compiled 22297 to 17846 computations (20% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	23	11
3	29	11
4	32	11
5	33	11
6	33	11

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample1.6s (22.6%)

Algorithm

1×

intervals

Results

686.0ms	8000×	body	128	valid
250.0ms	8000×	pre	128	true

Compiler

Compiled 202 to 161 computations (20.3% saved)

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

Details

analyze100.0ms (1.4%)

sample462.0ms (6.7%)

simplify25.0ms (0.4%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

series346.0ms (5%)

rewrite7.0ms (0.1%)

simplify67.0ms (1%)

prune90.0ms (1.3%)

localize29.0ms (0.4%)

series714.0ms (10.3%)

rewrite20.0ms (0.3%)

simplify118.0ms (1.7%)

prune272.0ms (3.9%)

localize38.0ms (0.5%)

series725.0ms (10.5%)

rewrite50.0ms (0.7%)

simplify189.0ms (2.7%)

prune281.0ms (4.1%)

localize31.0ms (0.4%)

series263.0ms (3.8%)

rewrite18.0ms (0.3%)

simplify84.0ms (1.2%)

prune131.0ms (1.9%)

regimes1.3s (18.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (22.6%)

Profiling

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11