Details

analyze808.0ms (13.8%)

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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify119.0ms (2%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
766×	`div-sub_binary64`
654×	`unswap-sqr_binary64`
570×	`unsub-neg_binary64`
551×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	23	22
2	43	22
3	69	22
4	132	22
5	186	22
6	246	22
7	385	22
8	533	22
9	650	22
10	697	22
11	2043	22
12	3598	22
13	3068	22
14	3257	22
15	3443	22
16	3848	22
17	5230	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

24.4b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 38 to 22 computations (42.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.3b	(-.f64 (.f64 b c) (.f64 a d))
23.9b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite80.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

24.2b

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 55

Calls

3 calls:

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

Compiler

Compiled 1496 to 199 computations (86.7% saved)

series115.0ms (2%)

Error

4.1b

Counts

3 → 63

Calls

3 calls:

60.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
27.0ms	(-.f64 (.f64 b c) (.f64 a d))
15.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 1957 to 1249 computations (36.2% saved)

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Rules

886×	`div-sub_binary64`
483×	`associate-l_binary64`
405×	`associate-r_binary64`
208×	`distribute-rgt-in_binary64`
199×	`associate-*l/_binary64`

Counts

118 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2295
1	346	2127
2	1090	2125
3	3890	2125
4	4683	2125
5	6085	2125

prune41.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Error

4.6b

Counts

90 → 7

Alt Table

Status	Error	Program
	43.2b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 c b) (.f64 a d)) 3)) (+.f64 (.f64 c c) (.f64 d d)))
	46.4b	(/.f64 (-.f64 (pow.f64 (.f64 b c) 3) (pow.f64 (.f64 a d) 3)) (.f64 (+.f64 (.f64 d d) (.f64 c c)) (+.f64 (.f64 (.f64 c b) (.f64 c b)) (.f64 a (.f64 d (+.f64 (.f64 a d) (.f64 c b)))))))
✓	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	36.1b	(neg.f64 (/.f64 a d))
▶	24.4b	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
	41.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (*.f64 c c)))))
	33.4b	(-.f64 (/.f64 b c) (/.f64 (.f64 a d) (.f64 c c)))

Compiler

Compiled 1599 to 363 computations (77.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 d d) (.f64 c c))
0.3b	(-.f64 (.f64 c b) (.f64 a d))
0.4b	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
23.8b	(/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d)))

rewrite137.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

90×	`times-frac_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
56×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

4 → 138

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
6.0ms	(/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d)))
4.0ms	(-.f64 (.f64 c b) (.f64 a d))
3.0ms	(+.f64 (.f64 d d) (.f64 c c))

Compiler

Compiled 4525 to 863 computations (80.9% saved)

series206.0ms (3.5%)

Error

4.0b

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d)))
61.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
28.0ms	(-.f64 (.f64 c b) (.f64 a d))
18.0ms	(+.f64 (.f64 d d) (.f64 c c))

Compiler

Compiled 3968 to 2682 computations (32.4% saved)

simplify213.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/r*_binary64`
324×	`distribute-rgt-in_binary64`
299×	`associate-/r/_binary64`
273×	`distribute-lft-in_binary64`
201×	`associate-/l/_binary64`

Counts

234 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	6880
1	591	6461
2	2190	6311
3	5447	6311

prune49.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	160	5	165
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	162	10	172

Error

2.7b

Counts

172 → 10

Alt Table

Status	Error	Program
	36.1b	(/.f64 1 (neg.f64 (/.f64 d a)))
✓	24.4b	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
	37.8b	(/.f64 1 (+.f64 (/.f64 c b) (/.f64 (.f64 a d) (.f64 b b))))
	41.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (*.f64 c c)))))
✓	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	36.1b	(neg.f64 (/.f64 a d))
	45.5b	(/.f64 1 (-.f64 (neg.f64 (.f64 (/.f64 c a) (+.f64 (/.f64 b a) (/.f64 c d)))) (+.f64 (/.f64 d a) (/.f64 (.f64 (.f64 b b) (.f64 c c)) (*.f64 d (pow.f64 a 3))))))
	38.9b	(/.f64 1 (-.f64 (neg.f64 (/.f64 d a)) (/.f64 (.f64 c b) (.f64 a a))))
	34.6b	(/.f64 1 (+.f64 (+.f64 (/.f64 c b) (/.f64 (.f64 (.f64 a d) (.f64 a d)) (.f64 c (pow.f64 b 3)))) (*.f64 (/.f64 d b) (+.f64 (/.f64 a b) (/.f64 d c)))))
▶	33.4b	(-.f64 (/.f64 b c) (/.f64 (.f64 a d) (.f64 c c)))

Compiler

Compiled 2279 to 589 computations (74.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (/.f64 b c) (/.f64 (.f64 a d) (.f64 c c)))
9.7b	(/.f64 (.f64 a d) (.f64 c c))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
5×	`cancel-sign-sub-inv_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

8.0ms	(-.f64 (/.f64 b c) (/.f64 (.f64 a d) (.f64 c c)))
4.0ms	(/.f64 (.f64 a d) (.f64 c c))

Compiler

Compiled 808 to 162 computations (80% saved)

series68.0ms (1.2%)

Error

2.7b

Counts

2 → 33

Calls

2 calls:

44.0ms	(-.f64 (/.f64 b c) (/.f64 (.f64 a d) (.f64 c c)))
22.0ms	(/.f64 (.f64 a d) (.f64 c c))

Compiler

Compiled 777 to 525 computations (32.4% saved)

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

789×	`associate-/l*_binary64`
676×	`associate-l_binary64`
487×	`associate-*l/_binary64`
372×	`associate-*r/_binary64`
358×	`associate-/r*_binary64`

Counts

74 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	1130
1	261	1088
2	954	1088
3	4704	1088
4	5008	1088

prune16.0ms (0.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	51	9	60

Error

0.7b

Counts

60 → 9

Alt Table

Status	Error	Program
	36.1b	(/.f64 1 (neg.f64 (/.f64 d a)))
✓	24.4b	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
	41.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (*.f64 c c)))))
	31.7b	(-.f64 (/.f64 b c) (/.f64 a (/.f64 c (/.f64 d c))))
✓	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	36.1b	(neg.f64 (/.f64 a d))
	38.9b	(/.f64 1 (-.f64 (neg.f64 (/.f64 d a)) (/.f64 (.f64 c b) (.f64 a a))))
	34.6b	(/.f64 1 (+.f64 (+.f64 (/.f64 c b) (/.f64 (.f64 (.f64 a d) (.f64 a d)) (.f64 c (pow.f64 b 3)))) (*.f64 (/.f64 d b) (+.f64 (/.f64 a b) (/.f64 d c)))))
▶	30.7b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a (/.f64 d c)) c))

Compiler

Compiled 570 to 241 computations (57.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.2b	(/.f64 (*.f64 a (/.f64 d c)) c)
1.4b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a (/.f64 d c)) c))
6.0b	(*.f64 a (/.f64 d c))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

25×	`add-sqr-sqrt_binary64`
17×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`

Counts

3 → 80

Calls

3 calls:

9.0ms	(-.f64 (/.f64 b c) (/.f64 (*.f64 a (/.f64 d c)) c))
5.0ms	(*.f64 a (/.f64 d c))
4.0ms	(/.f64 (*.f64 a (/.f64 d c)) c)

Compiler

Compiled 1440 to 338 computations (76.5% saved)

series86.0ms (1.5%)

Error

0.7b

Counts

3 → 42

Calls

3 calls:

43.0ms	(-.f64 (/.f64 b c) (/.f64 (*.f64 a (/.f64 d c)) c))
22.0ms	(/.f64 (*.f64 a (/.f64 d c)) c)
19.0ms	(*.f64 a (/.f64 d c))

Compiler

Compiled 1058 to 690 computations (34.8% saved)

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

391×	`associate-/r*_binary64`
365×	`distribute-neg-frac_binary64`
332×	`associate-/r/_binary64`
292×	`*-commutative_binary64`
275×	`cancel-sign-sub-inv_binary64`

Counts

122 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1661
1	396	1577
2	1391	1577
3	3175	1568
4	4770	1568
5	4999	1568
6	4918	1568

prune30.0ms (0.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	85	9	94

Error

0.7b

Counts

94 → 9

Alt Table

Status	Error	Program
	36.1b	(/.f64 1 (neg.f64 (/.f64 d a)))
	24.4b	(/.f64 1 (/.f64 (+.f64 (.f64 d d) (.f64 c c)) (-.f64 (.f64 c b) (.f64 a d))))
	41.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (.f64 c c)))) (sqrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (+.f64 (.f64 d d) (*.f64 c c)))))
	31.7b	(-.f64 (/.f64 b c) (/.f64 a (/.f64 c (/.f64 d c))))
	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	36.1b	(neg.f64 (/.f64 a d))
	38.9b	(/.f64 1 (-.f64 (neg.f64 (/.f64 d a)) (/.f64 (.f64 c b) (.f64 a a))))
	34.6b	(/.f64 1 (+.f64 (+.f64 (/.f64 c b) (/.f64 (.f64 (.f64 a d) (.f64 a d)) (.f64 c (pow.f64 b 3)))) (*.f64 (/.f64 d b) (+.f64 (/.f64 a b) (/.f64 d c)))))
	30.7b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a (/.f64 d c)) c))

Compiler

Compiled 896 to 275 computations (69.3% saved)

regimes2.5s (42.6%)

Accuracy

Total 12.3b remaining (90.2%)

Threshold costs 0b (0%)

Compiler

Compiled 18219 to 9561 computations (47.5% saved)

bsearch68.0ms (1.2%)

Steps

Iters	Range		Point
4	1.5212360037452252e+151	2.485070478084798e+151	1.5513558310683366e+151
9	1.1342283362689801e-180	2.0679518232087616e-175	2.046408208770978e-175
9	-0.006000872087764519	-1.21083364260822e-10	-1.3557623343064346e-10
9	-2.278165257455917e+140	-1.3674659228548739e+133	-1.3940742026862542e+133

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	148
1	51	148
2	74	148
3	89	148
4	98	148
5	100	148
6	100	148

end1.0ms (0%)

Compiler: Compiled 103 to 33 computations (68% saved)

sample835.0ms (14.3%)

Algorithm

1×

intervals

Results

410.0ms	8000×	body	128	valid
23.0ms	472×	body	128	invalid

Compiler

Compiled 305 to 150 computations (50.8% saved)

Details

analyze808.0ms (13.8%)

sample26.0ms (0.5%)

simplify119.0ms (2%)

prune1.0ms (0%)

localize10.0ms (0.2%)

rewrite80.0ms (1.4%)

series115.0ms (2%)

simplify115.0ms (2%)

prune41.0ms (0.7%)

localize12.0ms (0.2%)

rewrite137.0ms (2.3%)

series206.0ms (3.5%)

simplify213.0ms (3.6%)

prune49.0ms (0.8%)

localize9.0ms (0.1%)

rewrite47.0ms (0.8%)

series68.0ms (1.2%)

simplify71.0ms (1.2%)

prune16.0ms (0.3%)

localize9.0ms (0.2%)

rewrite64.0ms (1.1%)

series86.0ms (1.5%)

simplify114.0ms (1.9%)

prune30.0ms (0.5%)

regimes2.5s (42.6%)

bsearch68.0ms (1.2%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample835.0ms (14.3%)

Profiling