Details

analyze700.0ms (10.9%)

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
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample34.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	16	22
2	16	22

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

24.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	24.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 38 to 22 computations (42.1% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 a c) (.f64 b d))
24.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

24.8b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
3.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1190 to 158 computations (86.7% saved)

series99.0ms (1.5%)

Error

3.9b

Counts

2 → 48

Calls

2 calls:

64.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
26.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1446 to 906 computations (37.3% saved)

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

781×	`distribute-rgt-in_binary64`
412×	`associate-l_binary64`
331×	`associate-r_binary64`
281×	`unswap-sqr_binary64`
277×	`times-frac_binary64`

Counts

90 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	1920
1	272	1791
2	813	1791
3	2475	1791
4	5120	1791

prune39.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	9	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	9	68

Error

5.6b

Counts

68 → 9

Alt Table

Status	Error	Program
	25.3b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
	33.7b	(+.f64 (/.f64 a c) (/.f64 (.f64 d b) (.f64 c c)))
	25.0b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (*.f64 c c)))))
	25.4b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 d b) (.f64 c a))) (cbrt.f64 (+.f64 (.f64 d b) (.f64 c a)))) (/.f64 (cbrt.f64 (+.f64 (.f64 d b) (.f64 c a))) (+.f64 (.f64 d d) (.f64 c c))))
	38.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (*.f64 c c)))))
▶	24.9b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
	35.3b	(+.f64 (/.f64 b d) (/.f64 (.f64 c a) (.f64 d d)))
	39.1b	(/.f64 (.f64 c a) (+.f64 (.f64 d d) (*.f64 c c)))
	39.2b	(/.f64 (.f64 d b) (+.f64 (.f64 d d) (*.f64 c c)))

Compiler

Compiled 1484 to 370 computations (75.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
15.7b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c))))
28.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.3b	(sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))

rewrite273.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64`
162×	`add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`

Counts

4 → 264

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
7.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c))))
3.0ms	(sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
3.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 10393 to 951 computations (90.8% saved)

series234.0ms (3.6%)

Error

5.6b

Counts

4 → 95

Calls

4 calls:

74.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c))))
54.0ms	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
31.0ms	(sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
30.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 4899 to 2950 computations (39.8% saved)

simplify394.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

823×	`times-frac_binary64`
582×	`associate-/l/_binary64`
253×	`cancel-sign-sub-inv_binary64`
178×	`neg-sub0_binary64`
175×	`neg-mul-1_binary64`

Counts

359 → 299

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	363	16689
1	878	16140
2	2170	15382
3	4581	15136
4	4993	15136

prune202.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	295	4	299
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	301	7	308

Error

5.3b

Counts

308 → 7

Alt Table

Status	Error	Program
	35.6b	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
	34.2b	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
	47.3b	(/.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
	38.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (*.f64 c c)))))
✓	24.9b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
▶	25.3b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
	37.4b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) 3)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

Compiler

Compiled 6009 to 984 computations (83.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

20.4b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (*.f64 c c)))))
29.2b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.2b	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
29.2b	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))

rewrite66.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

18×	`cbrt-div_binary64`
10×	`flip-+_binary64`
10×	`flip3-+_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (*.f64 c c)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
3.0ms	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
2.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3375 to 375 computations (88.9% saved)

series285.0ms (4.4%)

Error

5.3b

Counts

4 → 60

Calls

4 calls:

168.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (*.f64 c c)))))
35.0ms	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))
34.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
34.0ms	(cbrt.f64 (+.f64 (.f64 d d) (.f64 c c)))

Compiler

Compiled 4646 to 2949 computations (36.5% saved)

simplify110.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
502×	`associate-l_binary64`
465×	`associate-r_binary64`
408×	`unswap-sqr_binary64`
366×	`cancel-sign-sub-inv_binary64`

Counts

130 → 113

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	155	3416
1	397	3092
2	1030	3092
3	3094	3092
4	5044	3092

prune49.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Error

5.3b

Counts

120 → 7

Alt Table

Status	Error	Program
	35.6b	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
▶	34.2b	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
	47.3b	(/.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
	38.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (*.f64 c c)))))
✓	24.9b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
✓	25.3b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
	37.4b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) 3)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

Compiler

Compiled 3032 to 628 computations (79.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

2.3b	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
4.1b	(/.f64 (*.f64 c c) d)
5.5b	(/.f64 b (/.f64 (*.f64 c c) d))

rewrite89.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

38×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 83

Calls

3 calls:

17.0ms	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
5.0ms	(/.f64 b (/.f64 (*.f64 c c) d))
3.0ms	(/.f64 (*.f64 c c) d)

Compiler

Compiled 1542 to 351 computations (77.2% saved)

series81.0ms (1.3%)

Error

5.3b

Counts

3 → 39

Calls

3 calls:

45.0ms	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
22.0ms	(/.f64 b (/.f64 (*.f64 c c) d))
10.0ms	(/.f64 (*.f64 c c) d)

Compiler

Compiled 954 to 636 computations (33.3% saved)

simplify146.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

638×	`times-frac_binary64`
437×	`associate-/l*_binary64`
420×	`associate-/r/_binary64`
393×	`associate-/l/_binary64`
384×	`associate-*l/_binary64`

Counts

122 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1832
1	347	1742
2	1072	1730
3	4374	1730
4	4898	1730
5	4988	1730
6	4953	1730

prune40.0ms (0.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	80	11	91

Error

2.5b

Counts

91 → 11

Alt Table

Status	Error	Program
	35.6b	(+.f64 (/.f64 b d) (/.f64 a (/.f64 (*.f64 d d) c)))
	45.5b	(exp.f64 (log.f64 (+.f64 (/.f64 (.f64 d b) (.f64 c c)) (/.f64 a c))))
	34.2b	(+.f64 (/.f64 a c) (/.f64 b (/.f64 (*.f64 c c) d)))
	31.0b	(+.f64 (/.f64 a c) (.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) c) (/.f64 (cbrt.f64 b) (/.f64 c d))))
	31.4b	(+.f64 (/.f64 a c) (/.f64 (/.f64 b c) (/.f64 c d)))
	30.9b	(+.f64 (/.f64 a c) (/.f64 1 (/.f64 c (/.f64 b (/.f64 c d)))))
	38.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (+.f64 (.f64 d d) (*.f64 c c)))))
	24.9b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
	25.3b	(/.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (.f64 (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))) (cbrt.f64 (+.f64 (.f64 d d) (.f64 c c))))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
	37.4b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 d d) (.f64 c c)))) 3)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
	48.5b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 (.f64 d b) (.f64 c c)) (/.f64 a c)) 3))

Compiler

Compiled 955 to 309 computations (67.6% saved)

regimes2.4s (37.5%)

Accuracy

Total 11.0b remaining (77.6%)

Threshold costs 0b (0%)

Compiler

Compiled 21478 to 10988 computations (48.8% saved)

bsearch111.0ms (1.7%)

Steps

Iters	Range		Point
7	3.0883384137849206e+75	1.8412237375943484e+77	1.2016013962778195e+76
9	2.0679518232087616e-175	5.721434040544388e-168	8.191619328525054e-172
8	-6.6950210941454126e-164	-3.0156131024116788e-167	-2.567158710874279e-166
6	-1.1326888681918286e-87	-1.5810231256597345e-88	-6.071421943859113e-88
10	-9.197853514977536e-19	-5.753240770969358e-31	-5.831437032843926e-31
8	-7.684894851708738e+81	-2.48377969896453e+77	-4.2044927924302215e+81

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	192
1	57	192
2	56	192

end1.0ms (0%)

Compiler: Compiled 133 to 46 computations (65.4% saved)

sample861.0ms (13.4%)

Algorithm

1×

intervals

Results

402.0ms	8000×	body	128	valid
26.0ms	473×	body	128	invalid

Compiler

Compiled 412 to 197 computations (52.2% saved)

Details

analyze700.0ms (10.9%)

sample34.0ms (0.5%)

simplify9.0ms (0.1%)

prune1.0ms (0%)

localize12.0ms (0.2%)

rewrite56.0ms (0.9%)

series99.0ms (1.5%)

simplify76.0ms (1.2%)

prune39.0ms (0.6%)

localize13.0ms (0.2%)

rewrite273.0ms (4.2%)

series234.0ms (3.6%)

simplify394.0ms (6.1%)

prune202.0ms (3.1%)

localize15.0ms (0.2%)

rewrite66.0ms (1%)

series285.0ms (4.4%)

simplify110.0ms (1.7%)

prune49.0ms (0.8%)

localize8.0ms (0.1%)

rewrite89.0ms (1.4%)

series81.0ms (1.3%)

simplify146.0ms (2.3%)

prune40.0ms (0.6%)

regimes2.4s (37.5%)

bsearch111.0ms (1.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample861.0ms (13.4%)

Profiling