Details

analyze667.0ms (7.6%)

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
24.9%	74.8%	0.2%	6
24.9%	74.8%	0.2%	7
24.9%	74.8%	0.2%	8
37.4%	62.3%	0.2%	9
40.5%	59.2%	0.2%	10
48.3%	45.2%	6.5%	11
48.3%	45.2%	6.5%	12
48.3%	45.2%	6.5%	13
58.5%	35.1%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.3s (14.8%)

Infinites

9.6% of outputs are infinite.

Symmetry

(sort x y)

(sort t a)

Results

974.0ms	8256×	body	128	valid
206.0ms	1958×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-def_binary64`
336×	`fma-neg_binary64`
138×	`distribute-rgt-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
128×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	26	21
2	52	21
3	87	21
4	128	21
5	161	21
6	203	21
7	247	21
8	464	21
9	822	21
10	1234	21
11	1169	21
12	1237	21
13	1311	21
14	1375	21
15	1375	21
16	1282	21

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

24.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 z z) (.f64 t a))
✓	3.9b	(.f64 (.f64 x y) z)
✓	8.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	25.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series274.0ms (3.1%)

Counts

4 → 136

Calls

4 calls:

208.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
49.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
9.0ms	(.f64 (.f64 x y) z)
8.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
3.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify132.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
379×	`times-frac_binary64`
318×	`associate-r_binary64`
293×	`associate-l_binary64`
277×	`associate-/l*_binary64`

Counts

222 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4463
1	842	4196
2	3899	4138
3	4961	4138
4	4976	4138

prune155.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	11	191

Error

2.4b

Counts

191 → 11

Alt Table

Status	Error	Program
	37.3b	(*.f64 y x)
	23.9b	(.f64 (/.f64 (.f64 y x) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (/.f64 z (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
	26.4b	(/.f64 (.f64 (.f64 x y) z) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	35.8b	(neg.f64 (*.f64 y x))
	24.2b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	27.1b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	24.8b	(/.f64 (/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	43.5b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	27.8b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	24.7b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
▶	21.9b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))

Compiler

Compiled 5194 to 1595 computations (69.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)
✓	0.1b	(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
✓	2.1b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
✓	16.0b	(sqrt.f64 (neg.f64 (*.f64 a t)))

series931.0ms (10.6%)

Counts

4 → 66

Calls

4 calls:

558.0ms	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
233.0ms	(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
118.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)
21.0ms	(sqrt.f64 (neg.f64 (*.f64 a t)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 92

Calls

4 calls:

5.0ms	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
2.0ms	(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
1.0ms	(sqrt.f64 (neg.f64 (*.f64 a t)))
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
308×	`cancel-sign-sub-inv_binary64`
265×	`fma-neg_binary64`
215×	`associate-r_binary64`
215×	`associate-l_binary64`

Counts

158 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	4135
1	700	3611
2	2618	3561
3	4568	3561
4	4941	3561

prune128.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	174	8	182

Error

1.0b

Counts

182 → 8

Alt Table

Status	Error	Program
▶	21.9b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	24.2b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	37.3b	(*.f64 y x)
	35.8b	(neg.f64 (*.f64 y x))
	23.6b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
	43.5b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	22.3b	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	24.7b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 4634 to 1481 computations (68% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))))
✓	2.1b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	16.0b	(sqrt.f64 (neg.f64 (*.f64 a t)))

series690.0ms (7.8%)

Counts

3 → 46

Calls

3 calls:

523.0ms

(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))

148.0ms

(sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))

19.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`sqrt-prod_binary64`
72×	`add-sqr-sqrt_binary64`
36×	`sqrt-pow1_binary64`
33×	`pow1_binary64`
25×	`associate-r_binary64`

Counts

3 → 153

Calls

3 calls:

10.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))))

6.0ms

(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))

2.0ms

(sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

458×	`associate-*l/_binary64`
291×	`associate-l_binary64`
276×	`associate-r_binary64`
233×	`fma-def_binary64`
220×	`associate-/r/_binary64`

Counts

199 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	3973
1	606	3439
2	2382	3394
3	4997	3394

prune190.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	265	8	273

Error

1.0b

Counts

273 → 8

Alt Table

Status	Error	Program
✓	21.9b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 a t)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	24.2b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	37.3b	(*.f64 y x)
	35.8b	(neg.f64 (*.f64 y x))
	23.6b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
	43.5b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
▶	22.3b	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	24.7b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 7788 to 1922 computations (75.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
✓	0.8b	(.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))
✓	2.1b	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	16.0b	(sqrt.f64 (neg.f64 (*.f64 a t)))

series857.0ms (9.7%)

Counts

2 → 64

Calls

2 calls:

516.0ms	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
341.0ms	(.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
14×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
5.0ms	(.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

830×	`associate-/r*_binary64`
362×	`associate-/r/_binary64`
354×	`fma-def_binary64`
261×	`cancel-sign-sub-inv_binary64`
230×	`associate-r_binary64`

Counts

121 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	3901
1	624	3028
2	2396	2984
3	5705	2984

prune140.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	186	8	194

Error

0.5b

Counts

194 → 8

Alt Table

Status	Error	Program
	37.3b	(*.f64 y x)
	24.2b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	35.8b	(neg.f64 (*.f64 y x))
	23.8b	(.f64 y (.f64 x (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))))
	23.6b	(.f64 (.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
	24.3b	(.f64 y (.f64 (/.f64 x (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (/.f64 z (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))))
✓	22.3b	(.f64 y (.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	24.7b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 4959 to 1619 computations (67.4% saved)

regimes2.3s (26.6%)

Accuracy

Total 4.8b remaining (87.8%)

Threshold costs 0b (0%)

Counts

105 → 6

Compiler

Compiled 20775 to 12564 computations (39.5% saved)

bsearch174.0ms (2%)

Steps

Iters	Range		Point
8	7.599318026220604e+29	8.666361100031005e+33	7.766070028302245e+29
9	1.5302915913122459e+22	8.512827817797835e+27	8.420471240038822e+27
7	1.9825546506447513e-205	5.5273848400196326e-204	2.008610550034131e-205
9	-3.975809683411728e-151	-1.6874738847113578e-157	-1.717551219244167e-157
2	-1.134458572469338e+169	-1.0492668286827014e+148	-1.8547055447344963e+153

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	144
1	67	144
2	84	144
3	94	144
4	99	144
5	100	144
6	98	144

end285.0ms (3.2%)

Remove: (sort x y)
Compiler: Compiled 942 to 412 computations (56.3% saved)

Details

analyze667.0ms (7.6%)

sample1.3s (14.8%)

simplify60.0ms (0.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series274.0ms (3.1%)

rewrite22.0ms (0.3%)

simplify132.0ms (1.5%)

prune155.0ms (1.8%)

localize10.0ms (0.1%)

series931.0ms (10.6%)

rewrite16.0ms (0.2%)

simplify119.0ms (1.4%)

prune128.0ms (1.5%)

localize11.0ms (0.1%)

series690.0ms (7.8%)

rewrite34.0ms (0.4%)

simplify101.0ms (1.2%)

prune190.0ms (2.2%)

localize9.0ms (0.1%)

series857.0ms (9.7%)

rewrite13.0ms (0.2%)

simplify121.0ms (1.4%)

prune140.0ms (1.6%)

regimes2.3s (26.6%)

bsearch174.0ms (2%)

simplify7.0ms (0.1%)

end285.0ms (3.2%)

Profiling