Details

analyze657.0ms (9.2%)

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 (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify129.0ms (1.8%)

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

prune2.0ms (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

26.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	26.5b	(/.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 (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(-.f64 (.f64 b c) (.f64 a d))
26.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite84.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

26.4b

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/l/_binary64` `flip--_binary64` `associate-/r/_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))

Compiler

Compiled 1230 to 166 computations (86.5% saved)

series155.0ms (2.2%)

Error

6.1b

Counts

2 → 57

Calls

2 calls:

93.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
41.0ms	(-.f64 (.f64 b c) (.f64 a d))

Compiler

Compiled 1793 to 1139 computations (36.5% saved)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-l_binary64`
389×	`associate-r_binary64`
269×	`associate-/l*_binary64`
252×	`times-frac_binary64`
246×	`div-sub_binary64`

Counts

101 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2231
1	346	2111
2	1144	2109
3	4453	2109
4	5006	2109

prune56.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Error

7.2b

Counts

94 → 10

Alt Table

Status	Error	Program
	26.9b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
▶	26.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
	27.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a)))) (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
	54.2b	(.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (+.f64 (pow.f64 c 6) (pow.f64 d 6))) (+.f64 (.f64 (.f64 c c) (.f64 c c)) (-.f64 (.f64 (.f64 d d) (.f64 d d)) (.f64 (.f64 c c) (.f64 d d)))))
	27.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (+.f64 (.f64 c c) (.f64 d d))))
	36.0b	(-.f64 (/.f64 b c) (+.f64 (/.f64 (.f64 d a) (.f64 c c)) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.0b	(/.f64 (.f64 c b) (+.f64 (.f64 c c) (*.f64 d d)))
✓	26.5b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	33.1b	(-.f64 (/.f64 b c) (/.f64 (.f64 d a) (.f64 c c)))
	39.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 1631 to 422 computations (74.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 c b) (.f64 d a))
14.5b	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite110.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

23×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
18×	`sqrt-prod_binary64` `times-frac_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `associate-/r*_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `associate-/l*_binary64`

Counts

4 → 86

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
3.0ms	(-.f64 (.f64 c b) (.f64 d a))

Compiler

Compiled 3160 to 504 computations (84.1% saved)

series306.0ms (4.3%)

Error

7.2b

Counts

4 → 95

Calls

4 calls:

112.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
47.0ms	(-.f64 (.f64 c b) (.f64 d a))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 5620 to 3284 computations (41.6% saved)

simplify150.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
430×	`associate-/l*_binary64`
290×	`associate-/r*_binary64`
270×	`associate-*l/_binary64`
233×	`cancel-sign-sub-inv_binary64`

Counts

181 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	4059
1	501	3794
2	1599	3776
3	4868	3776
4	5224	3776

prune81.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	116	10	126

Error

7.2b

Counts

126 → 10

Alt Table

Status	Error	Program
	26.9b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
✓	26.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
	48.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 a (/.f64 (.f64 c b) d)))
	46.8b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))) (neg.f64 a))
	54.2b	(.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (+.f64 (pow.f64 c 6) (pow.f64 d 6))) (+.f64 (.f64 (.f64 c c) (.f64 c c)) (-.f64 (.f64 (.f64 d d) (.f64 d d)) (.f64 (.f64 c c) (.f64 d d)))))
	27.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (+.f64 (.f64 c c) (.f64 d d))))
	36.0b	(-.f64 (/.f64 b c) (+.f64 (/.f64 (.f64 d a) (.f64 c c)) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
▶	26.7b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (.f64 d a))))
	33.1b	(-.f64 (/.f64 b c) (/.f64 (.f64 d a) (.f64 c c)))
	39.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 2586 to 807 computations (68.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
14.6b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (*.f64 d a)))
30.2b	(sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite183.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`sqrt-prod_binary64`
31×	`*-un-lft-identity_binary64` `times-frac_binary64`
29×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`

Counts

4 → 123

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (*.f64 d a)))
5.0ms	(sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 4667 to 1312 computations (71.9% saved)

series286.0ms (4%)

Error

7.2b

Counts

4 → 81

Calls

4 calls:

112.0ms	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (*.f64 d a)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
42.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
39.0ms	(sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d))))

Compiler

Compiled 5225 to 3328 computations (36.3% saved)

simplify198.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
262×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-in_binary64`
224×	`distribute-lft-in_binary64`
179×	`distribute-rgt-neg-in_binary64`

Counts

204 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4794
1	592	4413
2	1982	4395
3	4936	4395
4	4994	4395
5	4998	4395

prune99.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	134	10	144

Error

7.2b

Counts

144 → 10

Alt Table

Status	Error	Program
▶	26.9b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
✓	26.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
	48.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 a (/.f64 (.f64 c b) d)))
	46.8b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))) (neg.f64 a))
	54.2b	(.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (+.f64 (pow.f64 c 6) (pow.f64 d 6))) (+.f64 (.f64 (.f64 c c) (.f64 c c)) (-.f64 (.f64 (.f64 d d) (.f64 d d)) (.f64 (.f64 c c) (.f64 d d)))))
	27.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (+.f64 (.f64 c c) (.f64 d d))))
	36.0b	(-.f64 (/.f64 b c) (+.f64 (/.f64 (.f64 d a) (.f64 c c)) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
✓	26.7b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (.f64 d a))))
	33.1b	(-.f64 (/.f64 b c) (/.f64 (.f64 d a) (.f64 c c)))
	39.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 3260 to 1151 computations (64.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.4b	(-.f64 (.f64 c b) (.f64 d a))
0.8b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
25.8b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))

rewrite156.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

90×	`times-frac_binary64`
55×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
18×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
11×	`associate-/r/_binary64`

Counts

3 → 127

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
10.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
3.0ms	(-.f64 (.f64 c b) (.f64 d a))

Compiler

Compiled 4237 to 808 computations (80.9% saved)

series299.0ms (4.2%)

Error

6.0b

Counts

3 → 96

Calls

3 calls:

125.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
91.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
41.0ms	(-.f64 (.f64 c b) (.f64 d a))

Compiler

Compiled 4401 to 2974 computations (32.4% saved)

simplify216.0ms (3%)

Algorithm

1×	egg-herbie

Rules

285×	`distribute-rgt-in_binary64`
283×	`associate-/l/_binary64`
249×	`distribute-lft-in_binary64`
219×	`times-frac_binary64`
185×	`associate-/l*_binary64`

Counts

223 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	7500
1	683	7120
2	2727	6871
3	4972	6871
4	4987	6871

prune98.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	4	3	7
Picked	0	1	1
Done	1	1	2
Total	189	10	199

Error

2.4b

Counts

199 → 10

Alt Table

Status	Error	Program
	26.9b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
	37.9b	(/.f64 1 (+.f64 (/.f64 c b) (+.f64 (/.f64 (.f64 d a) (.f64 b b)) (.f64 (/.f64 d c) (+.f64 (/.f64 d b) (/.f64 (.f64 a (*.f64 d a)) (pow.f64 b 3)))))))
	40.1b	(/.f64 1 (neg.f64 (/.f64 d a)))
	38.1b	(/.f64 1 (+.f64 (/.f64 c b) (/.f64 (.f64 d a) (.f64 b b))))
	34.7b	(/.f64 1 (-.f64 (neg.f64 (/.f64 (.f64 b c) (.f64 a a))) (+.f64 (/.f64 d a) (.f64 (/.f64 c d) (+.f64 (/.f64 (.f64 b (*.f64 b c)) (pow.f64 a 3)) (/.f64 c a))))))
	27.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 d a))) (+.f64 (.f64 c c) (.f64 d d))))
	26.7b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))) (-.f64 (.f64 c b) (.f64 d a))))
	33.1b	(-.f64 (/.f64 b c) (/.f64 (.f64 d a) (.f64 c c)))
	39.7b	(neg.f64 (/.f64 a d))
	26.7b	(.f64 (/.f64 1 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 b c) (*.f64 d a)))

Compiler

Compiled 3070 to 680 computations (77.9% saved)

regimes2.8s (39.1%)

Accuracy

Total 12.9b remaining (88.5%)

Threshold costs 0b (0%)

Compiler

Compiled 21913 to 12033 computations (45.1% saved)

bsearch51.0ms (0.7%)

Steps

Iters	Range		Point
4	1.596243778168057e+133	2.7560615812002747e+133	2.469351418967785e+133
3	5.8882925335118124e-67	8.559616377665741e-67	7.370595873778618e-67
10	-1.0684712423939782e-127	-5.705259124329251e-138	-3.8832875515775854e-129
7	-2.0654385085249887e+73	-2.831537667729279e+71	-1.7583795913022137e+73

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	148
1	47	148
2	66	148
3	76	148
4	82	148
5	83	148
6	82	148

end1.0ms (0%)

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

sample850.0ms (11.9%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
22.0ms	469×	body	128	invalid

Compiler

Compiled 361 to 182 computations (49.6% saved)

Details

analyze657.0ms (9.2%)

sample26.0ms (0.4%)

simplify129.0ms (1.8%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite84.0ms (1.2%)

series155.0ms (2.2%)

simplify92.0ms (1.3%)

prune56.0ms (0.8%)

localize13.0ms (0.2%)

rewrite110.0ms (1.5%)

series306.0ms (4.3%)

simplify150.0ms (2.1%)

prune81.0ms (1.1%)

localize18.0ms (0.3%)

rewrite183.0ms (2.6%)

series286.0ms (4%)

simplify198.0ms (2.8%)

prune99.0ms (1.4%)

localize11.0ms (0.2%)

rewrite156.0ms (2.2%)

series299.0ms (4.2%)

simplify216.0ms (3%)

prune98.0ms (1.4%)

regimes2.8s (39.1%)

bsearch51.0ms (0.7%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample850.0ms (11.9%)

Profiling