Details

analyze267.0ms (3.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	25%	25.1%	8
49.9%	25%	25.1%	9
49.9%	25%	25.1%	10
49.9%	25%	25.1%	11
49.9%	12.5%	37.6%	12
49.9%	12.5%	37.6%	13
49.9%	12.5%	37.6%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.3s (17.9%)

Infinites

55.2% of outputs are infinite.

Results

942.0ms	8256×	body	128	valid
242.0ms	2064×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify131.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
522×	`fma-def_binary64`
417×	`neg-sub0_binary64`
408×	`neg-mul-1_binary64`
378×	`prod-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	51	25
3	102	25
4	219	25
5	464	25
6	1225	25
7	2416	25
8	3703	25
9	4714	25
10	4874	25
11	4224	25
12	4608	25
13	4555	25
14	4942	25

prune4.0ms (0.1%)

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 77 to 57 computations (26% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
✓	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

series412.0ms (5.8%)

Counts

3 → 64

Calls

3 calls:

361.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
48.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
2.0ms	(sqrt.f64 (exp.f64 t))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`associate-r_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
10.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
1.0ms	(sqrt.f64 (exp.f64 t))

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
658×	`fma-def_binary64`
291×	`associate-l_binary64`
267×	`associate-r_binary64`
256×	`distribute-rgt-in_binary64`

Counts

136 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3480
1	495	3220
2	1783	3055
3	4590	3055
4	5133	3055

prune124.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	127	5	132

Error

0.0b

Counts

132 → 5

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3511 to 2040 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.2b	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series355.0ms (5%)

Counts

3 → 60

Calls

3 calls:

198.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

152.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

5.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
17×	`associate-r_binary64`

Counts

3 → 90

Calls

3 calls:

12.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

10.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

7.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

simplify150.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
408×	`associate-l_binary64`
371×	`associate-r_binary64`
291×	`distribute-rgt-in_binary64`

Counts

150 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	4875
1	622	3816
2	2407	3714
3	4506	3712
4	4994	3712
5	4975	3712

prune188.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	167	6	173

Error

Counts

173 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))

Compiler

Compiled 4771 to 2732 computations (42.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))
✓	0.2b	(.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))))
✓	0.2b	(sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
✓	0.5b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))

series361.0ms (5.1%)

Counts

4 → 88

Calls

4 calls:

190.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))
156.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))))
9.0ms	(sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
5.0ms	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow-prod-down_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))
16.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))))
9.0ms	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))
4.0ms	(sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

simplify152.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
427×	`associate-l_binary64`
405×	`associate-r_binary64`
251×	`exp-prod_binary64`

Counts

191 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	6174
1	621	4502
2	2577	4401
3	4301	4382
4	4967	4382

prune267.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	202	6	208

Error

Counts

208 → 6

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))

Compiler

Compiled 7207 to 4111 computations (43% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z))))
✓	0.2b	(.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))
✓	0.6b	(cbrt.f64 z)

series1.2s (17%)

Counts

4 → 144

Calls

4 calls:

711.0ms	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
447.0ms	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z))))
32.0ms	(cbrt.f64 z)
18.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64`
46×	`prod-exp_binary64`
36×	`add-cbrt-cube_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`cbrt-unprod_binary64`

Counts

4 → 114

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
12.0ms	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z))))
7.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)

simplify200.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-l_binary64`
625×	`associate-r_binary64`
598×	`cancel-sign-sub-inv_binary64`
351×	`fma-neg_binary64`
315×	`*-commutative_binary64`

Counts

258 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	8975
1	763	7387
2	3120	7277
3	4736	7277
4	4954	7277

prune271.0ms (3.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	229	6	235

Error

Counts

235 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)) (.f64 (-.f64 (*.f64 1/2 x) y) (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.8b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))))) (sqrt.f64 z))

Compiler

Compiled 7662 to 3955 computations (48.4% saved)

regimes1.3s (18.1%)

Accuracy

Total 0.1b remaining (89.5%)

Threshold costs 0.1b (89.5%)

Counts

71 → 1

Compiler

Compiled 24475 to 18039 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25
5	30	25

end129.0ms (1.8%)

Compiler: Compiled 194 to 144 computations (25.8% saved)

Details

analyze267.0ms (3.7%)

sample1.3s (17.9%)

simplify131.0ms (1.8%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series412.0ms (5.8%)

rewrite27.0ms (0.4%)

simplify114.0ms (1.6%)

prune124.0ms (1.7%)

localize12.0ms (0.2%)

series355.0ms (5%)

rewrite41.0ms (0.6%)

simplify150.0ms (2.1%)

prune188.0ms (2.6%)

localize13.0ms (0.2%)

series361.0ms (5.1%)

rewrite54.0ms (0.8%)

simplify152.0ms (2.1%)

prune267.0ms (3.8%)

localize18.0ms (0.3%)

series1.2s (17%)

rewrite47.0ms (0.7%)

simplify200.0ms (2.8%)

prune271.0ms (3.8%)

regimes1.3s (18.1%)

simplify3.0ms (0%)

end129.0ms (1.8%)

Profiling