Details

analyze401.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	118×	body	256	valid
8.0ms	283×	pre	128	true
6.0ms	48×	body	512	valid
4.0ms	90×	body	128	valid
1.0ms	27×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify339.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1261×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
772×	`distribute-rgt-in_binary64`
702×	`distribute-lft-in_binary64`
619×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	32	24
2	65	24
3	128	24
4	178	24
5	287	24
6	460	24
7	754	24
8	1120	24
9	1142	24
10	1799	24
11	2162	24
12	1953	24
13	2041	24
14	2105	24
15	2131	24
16	2843	24
17	2603	24
18	2841	24
19	2951	24
20	3071	24
21	3113	24
22	3183	24
23	3171	24
24	3171	24
25	2191	24
26	2141	24
27	2105	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

53.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	53.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
28.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite140.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

50.1b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `sqrt-prod_binary64` `times-frac_binary64` `associate-/l*_binary64`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1903 to 1105 computations (41.9% saved)

series207.0ms (3.5%)

Error

0.2b

Counts

4 → 72

Calls

4 calls:

58.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
48.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
36.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2658 to 1932 computations (27.3% saved)

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64`
230×	`distribute-rgt-in_binary64`
199×	`distribute-lft-in_binary64`
182×	`cancel-sign-sub-inv_binary64`
181×	`div-sub_binary64`

Counts

146 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3603
1	550	3323
2	1858	3272
3	4753	3272
4	5209	3272

prune64.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Error

0.2b

Counts

123 → 4

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	1.2b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.0b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	53.5b	(/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 b)) (/.f64 a (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) 2)))

Compiler

Compiled 1964 to 1085 computations (44.8% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
0.4b	(.f64 (.f64 a a) (pow.f64 c 3))
0.4b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite330.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

112×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`pow-to-exp_binary64` `div-exp_binary64` `pow-exp_binary64`
29×	`unpow-prod-down_binary64`

Counts

4 → 186

Calls

4 calls:

10.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
8.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
8.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
8.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

Compiler

Compiled 6688 to 4032 computations (39.7% saved)

series188.0ms (3.2%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

69.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
53.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
31.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
28.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

Compiler

Compiled 2766 to 1974 computations (28.6% saved)

simplify146.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

610×	`log-prod_binary64`
399×	`associate-l_binary64`
323×	`associate-r_binary64`
302×	`times-frac_binary64`
301×	`associate-/l*_binary64`

Counts

216 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	3547
1	558	3204
2	3245	3125
3	4512	3125
4	5297	3125

prune97.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	155	4	159

Error

0.2b

Counts

159 → 4

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
▶	1.2b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
	53.0b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	53.5b	(/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 b)) (/.f64 a (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) 2)))

Compiler

Compiled 2430 to 1434 computations (41% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
0.4b	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
0.5b	(.f64 (.f64 a c) (*.f64 a c))
0.7b	(pow.f64 (*.f64 a c) 3)

rewrite276.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

80×	`add-exp-log_binary64`
46×	`pow1_binary64`
42×	`prod-exp_binary64`
39×	`add-cbrt-cube_binary64`
27×	`add-sqr-sqrt_binary64`

Counts

4 → 153

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
7.0ms	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
7.0ms	(.f64 (.f64 a c) (*.f64 a c))
4.0ms	(pow.f64 (*.f64 a c) 3)

Compiler

Compiled 6755 to 3860 computations (42.9% saved)

series153.0ms (2.6%)

Error

0.2b

Counts

4 → 27

Calls

4 calls:

59.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
31.0ms	(*.f64 (pow.f64 a 4) (pow.f64 c 4))
30.0ms	(pow.f64 (*.f64 a c) 3)
28.0ms	(.f64 (.f64 a c) (*.f64 a c))

Compiler

Compiled 2984 to 2090 computations (30% saved)

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-/r/_binary64`
574×	`unswap-sqr_binary64`
271×	`times-frac_binary64`
222×	`associate-l_binary64`
217×	`log-div_binary64`

Counts

180 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2392
1	375	1880
2	2258	1842
3	4944	1842
4	5138	1842

prune97.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	154	4	158

Error

0.2b

Counts

158 → 4

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
✓	1.2b	(/.f64 (+.f64 (+.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 (/.f64 (pow.f64 (.f64 a c) 3) (pow.f64 b 5)) -4)) (.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (.f64 a 2))
▶	53.0b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	53.5b	(/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 b)) (/.f64 a (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 b)) 2)))

Compiler

Compiled 2800 to 1674 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.2b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
28.3b	(-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b))

rewrite177.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

70×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
26×	`associate-/l*_binary64`

Counts

4 → 135

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
13.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 6256 to 2868 computations (54.2% saved)

series225.0ms (3.8%)

Error

0.0b

Counts

4 → 63

Calls

4 calls:

74.0ms	(/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
66.0ms	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
46.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.0ms	(-.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))) (.f64 b b))

Compiler

Compiled 3241 to 2156 computations (33.5% saved)

simplify234.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1132×	`div-sub_binary64`
393×	`distribute-rgt-in_binary64`
175×	`associate-/l*_binary64`
171×	`sub-neg_binary64`
155×	`cancel-sign-sub-inv_binary64`

Counts

198 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	8966
1	752	8210
2	2617	6703
3	4488	6703
4	6123	6703

prune126.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	171	5	176

Error

Counts

176 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 -4 (.f64 a c)) (+.f64 b (sqrt.f64 (+.f64 (.f64 -4 (.f64 a c)) (.f64 b b))))) 3)) (.f64 a 2))
	0.9b	(+.f64 (-.f64 (-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
	0.6b	(.f64 (/.f64 (/.f64 (.f64 -4 (.f64 a c)) a) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (+.f64 (.f64 -4 (.f64 a c)) (.f64 b b))) 3))) (/.f64 (+.f64 (+.f64 (.f64 -4 (.f64 a c)) (.f64 b b)) (.f64 b (-.f64 b (sqrt.f64 (+.f64 (.f64 -4 (.f64 a c)) (*.f64 b b)))))) 2))
	0.4b	(.f64 (/.f64 (.f64 -4 (.f64 a c)) a) (/.f64 1/2 (+.f64 b (sqrt.f64 (+.f64 (.f64 -4 (.f64 a c)) (.f64 b b))))))
	0.8b	(/.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 -4 (.f64 a c)) 3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))

Compiler

Compiled 4688 to 2368 computations (49.5% saved)

regimes742.0ms (12.5%)

Accuracy

Total 0.4b remaining (95%)

Threshold costs 0.4b (95%)

Compiler

Compiled 16904 to 10498 computations (37.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	20	33
2	20	33

end1.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

sample1.6s (26.8%)

Algorithm

1×

intervals

Results

371.0ms	3793×	body	256	valid
265.0ms	8877×	pre	128	true
205.0ms	1469×	body	512	valid
140.0ms	2738×	body	128	valid
40.0ms	877×	body	128	nan

Compiler

Compiled 240 to 159 computations (33.8% saved)

Details

analyze401.0ms (6.8%)

sample44.0ms (0.8%)

simplify339.0ms (5.7%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

rewrite140.0ms (2.4%)

series207.0ms (3.5%)

simplify130.0ms (2.2%)

prune64.0ms (1.1%)

localize25.0ms (0.4%)

rewrite330.0ms (5.6%)

series188.0ms (3.2%)

simplify146.0ms (2.5%)

prune97.0ms (1.6%)

localize33.0ms (0.6%)

rewrite276.0ms (4.7%)

series153.0ms (2.6%)

simplify118.0ms (2%)

prune97.0ms (1.6%)

localize14.0ms (0.2%)

rewrite177.0ms (3%)

series225.0ms (3.8%)

simplify234.0ms (4%)

prune126.0ms (2.1%)

regimes742.0ms (12.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.6s (26.8%)

Profiling