Details

analyze1.1s (9.1%)

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%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.8s (14.1%)

Symmetry

(sort x y)

Results

1.3s	8247×	body	128	valid
370.0ms	2355×	body	128	invalid
2.0ms	6×	body	256	valid
1.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify278.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	20

prune4.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.0b	(-.f64 1 (log.f64 t))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

series252.0ms (2%)

Counts

3 → 128

Calls

3 calls:

213.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
26.0ms	(-.f64 1 (log.f64 t))
12.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(-.f64 1 (log.f64 t))
0.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
593×	`exp-sum_binary64`
523×	`fma-def_binary64`
300×	`associate-+l+_binary64`
285×	`sub-neg_binary64`

Counts

187 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2997
1	318	2754
2	918	2521
3	3268	2521
4	4379	2521
5	5221	2521

prune119.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	32.8b	(*.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	52.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y))) (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))

Compiler

Compiled 2473 to 1216 computations (50.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))
✓	0.0b	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
✓	0.3b	(*.f64 z (log.f64 t))

series540.0ms (4.3%)

Counts

4 → 60

Calls

4 calls:

221.0ms	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
210.0ms	(*.f64 z (log.f64 t))
95.0ms	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
13.0ms	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-log-exp_binary64`
23×	`sum-log_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
9.0ms	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))
3.0ms	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
3.0ms	(*.f64 z (log.f64 t))

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
358×	`cancel-sign-sub-inv_binary64`
221×	`distribute-rgt-neg-in_binary64`
214×	`associate-l_binary64`
192×	`associate-r_binary64`

Counts

167 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	3150
1	659	2997
2	2695	2852
3	4377	2852
4	4998	2852
5	4934	2852

prune206.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	195	9	204

Error

0.0b

Counts

204 → 9

Alt Table

Status	Error	Program
	52.8b	(cbrt.f64 (pow.f64 (fma.f64 b a (-.f64 (+.f64 y (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 1/2 b)))) 3))
	32.8b	(*.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
▶	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (log.f64 t))) (*.f64 1/2 b)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t)))) (*.f64 1/2 b)))
	49.8b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (log.f64 t))) (.f64 (sqrt.f64 z) (sqrt.f64 (log.f64 t)))) (*.f64 1/2 b)))
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 z (log.f64 t))) (cbrt.f64 (.f64 z (log.f64 t)))) (cbrt.f64 (.f64 z (log.f64 t)))) (*.f64 1/2 b)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))

Compiler

Compiled 6266 to 2117 computations (66.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.4b	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
✓	0.5b	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)
✓	0.8b	(pow.f64 (log.f64 t) 3)

series1.1s (8.8%)

Counts

4 → 104

Calls

4 calls:

885.0ms	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
147.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
43.0ms	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)
27.0ms	(pow.f64 (log.f64 t) 3)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
32×	`difference-of-squares_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
2.0ms	(pow.f64 (log.f64 t) 3)
0.0ms	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)

simplify205.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

660×	`times-frac_binary64`
646×	`fma-def_binary64`
298×	`exp-prod_binary64`
235×	`unswap-sqr_binary64`
209×	`fma-neg_binary64`

Counts

219 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	9641
1	629	8856
2	2034	8650
3	4333	8650
4	4991	8650

prune267.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	197	6	203

Error

0.0b

Counts

203 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (/.f64 z (fma.f64 (log.f64 t) (+.f64 1 (log.f64 t)) 1)) (-.f64 (+.f64 (fma.f64 b (-.f64 a 1/2) y) x) (*.f64 (pow.f64 (log.f64 t) 3) (/.f64 z (fma.f64 (log.f64 t) (+.f64 1 (log.f64 t)) 1)))))
	52.8b	(cbrt.f64 (pow.f64 (fma.f64 b a (-.f64 (+.f64 y (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 1/2 b)))) 3))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t)))) (*.f64 1/2 b)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))

Compiler

Compiled 7484 to 4512 computations (39.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (log.f64 (cbrt.f64 t)))
✓	0.2b	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
✓	0.3b	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
✓	0.6b	(cbrt.f64 t)

series3.6s (29%)

Counts

4 → 84

Calls

4 calls:

1.3s	(*.f64 z (log.f64 (cbrt.f64 t)))
1.2s	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
1.1s	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
29.0ms	(cbrt.f64 t)

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`log-prod_binary64`
60×	`distribute-lft-in_binary64`
60×	`distribute-rgt-in_binary64`
39×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

4 → 142

Calls

4 calls:

9.0ms	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
5.0ms	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
4.0ms	(*.f64 z (log.f64 (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
475×	`fma-neg_binary64`
441×	`*-commutative_binary64`
440×	`cancel-sign-sub-inv_binary64`
306×	`distribute-rgt-in_binary64`

Counts

226 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3066
1	407	2725
2	1353	2500
3	3821	2492
4	4971	2492

prune352.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	249	5	254

Error

0.0b

Counts

254 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 (.f64 z 1/3) (log.f64 t))) (.f64 1/2 b)))
	52.8b	(cbrt.f64 (pow.f64 (fma.f64 b a (-.f64 (+.f64 y (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 1/2 b)))) 3))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (+.f64 (.f64 z (fma.f64 2/3 (log.f64 t) (log.f64 (cbrt.f64 (sqrt.f64 t))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 t))) z)) (.f64 1/2 b)))

Compiler

Compiled 8338 to 2918 computations (65% saved)

regimes2.0s (16.3%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

141 → 1

Compiler

Compiled 46832 to 32039 computations (31.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`+-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	23	23
2	27	23
3	29	23
4	30	23
5	30	23

end105.0ms (0.8%)

Remove: (sort x y)
Compiler: Compiled 239 to 157 computations (34.3% saved)

Details

analyze1.1s (9.1%)

sample1.8s (14.1%)

simplify278.0ms (2.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series252.0ms (2%)

rewrite7.0ms (0.1%)

simplify112.0ms (0.9%)

prune119.0ms (1%)

localize13.0ms (0.1%)

series540.0ms (4.3%)

rewrite35.0ms (0.3%)

simplify133.0ms (1.1%)

prune206.0ms (1.6%)

localize17.0ms (0.1%)

series1.1s (8.8%)

rewrite21.0ms (0.2%)

simplify205.0ms (1.6%)

prune267.0ms (2.1%)

localize18.0ms (0.1%)

series3.6s (29%)

rewrite30.0ms (0.2%)

simplify111.0ms (0.9%)

prune352.0ms (2.8%)

regimes2.0s (16.3%)

simplify3.0ms (0%)

end105.0ms (0.8%)

Profiling