Details

analyze2.6s (25.5%)

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
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample3.0s (29.2%)

Results

1.8s	8256×	body	128	valid
1.1s	5179×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

prune5.0ms (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

3.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.3b	(/.f64 2/3 t)
✓	2.1b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	5.3b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series151.0ms (1.5%)

Counts

4 → 88

Calls

4 calls:

69.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
47.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
33.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify125.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
430×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
272×	`sub-neg_binary64`
270×	`fma-def_binary64`

Counts

179 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	4150
1	864	3932
2	2992	3925
3	4865	3924
4	4956	3924

prune217.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	3	190

Error

0.2b

Counts

190 → 3

Alt Table

Status	Error	Program
▶	2.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
	26.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
	17.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 6987 to 3532 computations (49.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x)
	0.3b	(/.f64 2/3 t)
✓	2.1b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
✓	7.7b	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

series667.0ms (6.5%)

Counts

3 → 134

Calls

3 calls:

555.0ms

(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x)

66.0ms

(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))

45.0ms

(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms

(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

1.0ms

(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x)

0.0ms

(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))

simplify175.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
713×	`associate-l_binary64`
297×	`*-commutative_binary64`
222×	`times-frac_binary64`
219×	`associate-/l*_binary64`

Counts

198 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	690	12757
1	2247	12415
2	5614	12415

prune312.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Error

0.2b

Counts

222 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
	26.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
▶	17.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 16043 to 8342 computations (48% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
✓	0.2b	(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x)
	0.3b	(/.f64 2/3 t)
✓	0.6b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

series510.0ms (4.9%)

Counts

3 → 129

Calls

3 calls:

440.0ms

(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x)

53.0ms

(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

15.0ms

(*.f64 (sqrt.f64 (/.f64 1 t)) z)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms

(*.f64 (sqrt.f64 (/.f64 1 t)) z)

0.0ms

(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

0.0ms

(fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x)

simplify183.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-r_binary64`
454×	`fma-def_binary64`
410×	`associate-l_binary64`
309×	`fma-neg_binary64`
228×	`associate-+l+_binary64`

Counts

186 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	9965
1	1359	9633
2	4972	9633
3	5240	9633

prune260.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	183	3	186

Error

0.2b

Counts

186 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
▶	26.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
✓	17.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 11427 to 7142 computations (37.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (-.f64 c b))
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b)))
✓	0.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
✓	0.0b	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x)

series299.0ms (2.9%)

Counts

4 → 180

Calls

4 calls:

159.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
120.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x)
13.0ms	(pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b)))
6.0ms	(*.f64 a (-.f64 c b))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 136

Calls

4 calls:

5.0ms	(*.f64 a (-.f64 c b))
4.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
4.0ms	(pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b)))
0.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x)

simplify182.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
528×	`times-frac_binary64`
330×	`associate-/l*_binary64`
288×	`associate-/r*_binary64`
284×	`*-commutative_binary64`

Counts

316 → 286

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	695	8982
1	1846	8593
2	4786	8533
3	5258	8533

prune246.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	286	3	289

Error

0.2b

Counts

289 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))) x))
✓	26.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 a (-.f64 c b))) x))
✓	17.4b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 10036 to 4828 computations (51.9% saved)

regimes1.1s (10.3%)

Accuracy

Total 1.6b remaining (86%)

Threshold costs 0b (0%)

Counts

74 → 1

Compiler

Compiled 25450 to 18348 computations (27.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	40
1	31	40
2	42	40
3	46	40
4	48	40
5	47	40

end85.0ms (0.8%)

Compiler: Compiled 154 to 106 computations (31.2% saved)

Details

analyze2.6s (25.5%)

sample3.0s (29.2%)

simplify54.0ms (0.5%)

prune5.0ms (0%)

localize22.0ms (0.2%)

series151.0ms (1.5%)

rewrite18.0ms (0.2%)

simplify125.0ms (1.2%)

prune217.0ms (2.1%)

localize21.0ms (0.2%)

series667.0ms (6.5%)

rewrite13.0ms (0.1%)

simplify175.0ms (1.7%)

prune312.0ms (3%)

localize20.0ms (0.2%)

series510.0ms (4.9%)

rewrite9.0ms (0.1%)

simplify183.0ms (1.8%)

prune260.0ms (2.5%)

localize10.0ms (0.1%)

series299.0ms (2.9%)

rewrite27.0ms (0.3%)

simplify182.0ms (1.8%)

prune246.0ms (2.4%)

regimes1.1s (10.3%)

simplify3.0ms (0%)

end85.0ms (0.8%)

Profiling