Details

analyze1.2s (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.4s (40.7%)

Results

3.3s	16317×	body	128	invalid
1.5s	7599×	body	128	valid
146.0ms	269×	body	512	valid
117.0ms	129×	body	1024	valid
88.0ms	259×	body	256	valid
68.0ms	130×	body	512	invalid
43.0ms	125×	body	256	invalid
37.0ms	39×	body	1024	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
557×	`associate-/l*_binary64`
456×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	158	25
4	405	25
5	1252	25
6	2771	25
7	4527	25
8	5117	25

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 84 to 54 computations (35.7% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.4b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.2s (9%)

Counts

3 → 136

Calls

3 calls:

556.0ms

(*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

345.0ms

(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

304.0ms

(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 81

Calls

3 calls:

7.0ms

(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))

3.0ms

(*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

0.0ms

(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

827×	`associate-r_binary64`
632×	`associate-l_binary64`
543×	`fma-def_binary64`
190×	`*-commutative_binary64`
126×	`sub-neg_binary64`

Counts

217 → 221

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	523	7684
1	1594	6955
2	5563	6955

prune217.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	219	3	222

Error

Counts

222 → 3

Alt Table

Status	Error	Program
	14.7b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
▶	2.5b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
	10.5b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

Compiler

Compiled 8943 to 3320 computations (62.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	0.0b	(fma.f64 a b (*.f64 y t))
✓	0.3b	(*.f64 (log.f64 z) y)
✓	0.5b	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))

series695.0ms (5.2%)

Counts

4 → 156

Calls

4 calls:

291.0ms	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
213.0ms	(*.f64 (log.f64 z) y)
182.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))
9.0ms	(fma.f64 a b (*.f64 y t))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

16.0ms	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
3.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t)))
3.0ms	(*.f64 (log.f64 z) y)
0.0ms	(fma.f64 a b (*.f64 y t))

simplify165.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
595×	`cancel-sign-sub-inv_binary64`
425×	`associate-r_binary64`
350×	`associate-l_binary64`
263×	`distribute-rgt-neg-in_binary64`

Counts

236 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4310
1	704	3999
2	2715	3888
3	4583	3888
4	4988	3888
5	4961	3888

prune131.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
✓	2.5b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
▶	2.2b	(.f64 x (exp.f64 (log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a b))))))
	10.5b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

Compiler

Compiled 4502 to 1040 computations (76.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b)))
✓	0.2b	(*.f64 y (-.f64 (log.f64 z) t))
✓	0.3b	(log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))))
✓	0.3b	(-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))

series722.0ms (5.4%)

Counts

4 → 216

Calls

4 calls:

250.0ms	(*.f64 y (-.f64 (log.f64 z) t))
195.0ms	(-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))
189.0ms	(log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))))
87.0ms	(expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b)))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`associate--l+_binary64`
49×	`prod-diff_binary64`
46×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 139

Calls

4 calls:

8.0ms	(*.f64 y (-.f64 (log.f64 z) t))
8.0ms	(-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))
0.0ms	(expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b)))
0.0ms	(log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a b))))

simplify168.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
487×	`cancel-sign-sub-inv_binary64`
367×	`associate-r_binary64`
309×	`associate-l_binary64`
235×	`exp-prod_binary64`

Counts

355 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	352	6127
1	779	5629
2	2748	5345
3	4682	5345
4	5003	5345

prune182.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	213	3	216

Error

Counts

216 → 3

Alt Table

Status	Error	Program
✓	2.5b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	2.2b	(.f64 x (exp.f64 (log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a b))))))
▶	10.5b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

Compiler

Compiled 6019 to 1946 computations (67.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3)
	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
	0.4b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
✓	9.9b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

series1.4s (10.5%)

Counts

2 → 144

Calls

2 calls:

842.0ms

(pow.f64 (*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3)

560.0ms

(cbrt.f64 (pow.f64 (*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64`
5×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 43

Calls

2 calls:

3.0ms

(pow.f64 (*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3)

1.0ms

(cbrt.f64 (pow.f64 (*.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

simplify223.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
440×	`fma-neg_binary64`
265×	`*-commutative_binary64`
202×	`times-frac_binary64`
196×	`associate-r_binary64`

Counts

187 → 174

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	548	11565
1	1939	10703
2	4943	10703
3	5277	10703

prune338.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	311	3	314

Error

Counts

314 → 3

Alt Table

Status	Error	Program
✓	2.5b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
✓	2.2b	(.f64 x (exp.f64 (log1p.f64 (expm1.f64 (-.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a b))))))
✓	10.5b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) 3))

Compiler

Compiled 16075 to 6869 computations (57.3% saved)

regimes931.0ms (7%)

Accuracy

Total 0.2b remaining (65.3%)

Threshold costs 0.2b (65.3%)

Counts

99 → 1

Compiler

Compiled 18011 to 13110 computations (27.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	26	25
2	34	25
3	39	25
4	41	25
5	41	25

end70.0ms (0.5%)

Compiler: Compiled 110 to 76 computations (30.9% saved)

Details

analyze1.2s (8.7%)

sample5.4s (40.7%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series1.2s (9%)

rewrite16.0ms (0.1%)

simplify123.0ms (0.9%)

prune217.0ms (1.6%)

localize11.0ms (0.1%)

series695.0ms (5.2%)

rewrite27.0ms (0.2%)

simplify165.0ms (1.2%)

prune131.0ms (1%)

localize12.0ms (0.1%)

series722.0ms (5.4%)

rewrite29.0ms (0.2%)

simplify168.0ms (1.3%)

prune182.0ms (1.4%)

localize16.0ms (0.1%)

series1.4s (10.5%)

rewrite7.0ms (0.1%)

simplify223.0ms (1.7%)

prune338.0ms (2.5%)

regimes931.0ms (7%)

simplify4.0ms (0%)

end70.0ms (0.5%)

Profiling