Details

analyze327.0ms (3.8%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.0s (12.3%)

Infinites

28.1% of outputs are infinite.

Symmetry

(sort x y)

(sort z t)

Results

950.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify209.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2966×	`fma-def_binary64`
757×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
473×	`associate-/l/_binary64`
472×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	31	17
2	103	17
3	318	17
4	794	17
5	1526	17
6	2054	17
7	2281	17
8	2975	17
9	3540	17
10	3954	17
11	4158	17
12	4097	17
13	4108	17
14	4118	17
15	4462	17
16	4531	17
17	4536	17
18	4536	17
19	6474	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

7.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.3b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	7.3b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

Compiler

Compiled 100 to 69 computations (31% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z 9) t)
✓	1.4b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	6.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series55.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

39.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
11.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
5.0ms	(.f64 (.f64 z 9) t)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

3 → 62

Calls

3 calls:

5.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
4.0ms	(.f64 (.f64 z 9) t)
3.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

470×	`fma-def_binary64`
445×	`*-commutative_binary64`
325×	`div-sub_binary64`
307×	`associate-/l*_binary64`
287×	`fma-neg_binary64`

Counts

194 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2790
1	396	2561
2	1506	2551
3	4128	2551
4	5247	2551

prune120.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	8	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

5.8b

Counts

117 → 8

Alt Table

Status	Error	Program
	32.7b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (fma.f64 t (.f64 z 9) (.f64 y x))))
	46.0b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	7.0b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
▶	6.5b	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))
	6.8b	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
	31.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	35.7b	(.f64 (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2))
	7.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2))

Compiler

Compiled 2713 to 1545 computations (43.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 t z) -9)
✓	0.5b	(fma.f64 x y (.f64 (.f64 t z) -9))
✓	6.0b	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))

series90.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

74.0ms	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))
11.0ms	(fma.f64 x y (.f64 (.f64 t z) -9))
5.0ms	(.f64 (.f64 t z) -9)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(.f64 (.f64 t z) -9)
3.0ms	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))
0.0ms	(fma.f64 x y (.f64 (.f64 t z) -9))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

377×	`distribute-rgt-in_binary64`
327×	`div-sub_binary64`
307×	`fma-def_binary64`
261×	`associate-/l*_binary64`
248×	`*-commutative_binary64`

Counts

185 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	123	2617
1	279	2353
2	907	2353
3	2487	2353
4	4983	2353

prune103.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Error

5.8b

Counts

94 → 8

Alt Table

Status	Error	Program
	32.7b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (fma.f64 t (.f64 z 9) (.f64 y x))))
	46.0b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	7.0b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
✓	6.5b	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))
▶	6.8b	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
	31.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	35.7b	(.f64 (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2))
	7.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2))

Compiler

Compiled 1996 to 1138 computations (43% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 t (.f64 z -9) (.f64 y x))
✓	6.0b	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))

series52.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

40.0ms	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
12.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

8.0ms	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
0.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-def_binary64`
395×	`associate-l_binary64`
340×	`associate-r_binary64`
325×	`associate-*l/_binary64`
317×	`associate-/l*_binary64`

Counts

176 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	136	3242
1	334	2813
2	993	2813
3	3071	2813
4	4714	2813
5	4976	2813

prune129.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	125	8	133

Error

5.8b

Counts

133 → 8

Alt Table

Status	Error	Program
	7.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (.f64 (/.f64 1 (cbrt.f64 a)) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2)))
	46.0b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	32.7b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (fma.f64 t (.f64 z 9) (.f64 y x))))
	35.7b	(.f64 (.f64 (/.f64 1 a) (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 1)) (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2))
▶	7.0b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
✓	6.8b	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
	31.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	7.4b	(.f64 (.f64 (/.f64 1 a) (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2)))

Compiler

Compiled 3272 to 1976 computations (39.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	1.1b	(fma.f64 t (.f64 z -9) (.f64 y x))
✓	6.4b	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))

series130.0ms (1.5%)

Counts

2 → 120

Calls

2 calls:

89.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))
41.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))

rewrite96.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 278

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
4.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))

simplify321.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-def_binary64`
404×	`fma-neg_binary64`
296×	`associate-/r/_binary64`
234×	`times-frac_binary64`
220×	`*-commutative_binary64`

Counts

398 → 456

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	371	13696
1	931	12823
2	3305	12672
3	4701	12660
4	5000	12660

prune804.0ms (9.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	476	3	479
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	480	7	487

Error

5.8b

Counts

487 → 7

Alt Table

Status	Error	Program
	7.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (.f64 (/.f64 1 (cbrt.f64 a)) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2)))
	46.0b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	6.8b	(/.f64 1 (.f64 a (/.f64 2 (fma.f64 y x (.f64 t (*.f64 z -9))))))
✓	6.8b	(.f64 (/.f64 1 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))
	6.5b	(.f64 (/.f64 (fma.f64 y x (.f64 t (*.f64 z -9))) a) 1/2)
	31.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	7.8b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 1 (.f64 (cbrt.f64 2) (cbrt.f64 2))))) (/.f64 1 (/.f64 (cbrt.f64 a) (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) (cbrt.f64 2)))))

Compiler

Compiled 14610 to 8880 computations (39.2% saved)

regimes4.4s (51.2%)

Accuracy

Total 0.4b remaining (7.6%)

Threshold costs 0.4b (7.6%)

Counts

293 → 1

Compiler

Compiled 104635 to 73411 computations (29.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	16	17
2	16	17

end292.0ms (3.4%)

Remove: (sort x y)
Compiler: Compiled 320 to 224 computations (30% saved)

Details

analyze327.0ms (3.8%)

sample1.0s (12.3%)

simplify209.0ms (2.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series55.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify94.0ms (1.1%)

prune120.0ms (1.4%)

localize8.0ms (0.1%)

series90.0ms (1.1%)

rewrite9.0ms (0.1%)

simplify83.0ms (1%)

prune103.0ms (1.2%)

localize11.0ms (0.1%)

series52.0ms (0.6%)

rewrite14.0ms (0.2%)

simplify121.0ms (1.4%)

prune129.0ms (1.5%)

localize10.0ms (0.1%)

series130.0ms (1.5%)

rewrite96.0ms (1.1%)

simplify321.0ms (3.8%)

prune804.0ms (9.4%)

regimes4.4s (51.2%)

simplify2.0ms (0%)

end292.0ms (3.4%)

Profiling