Details

analyze1.5s (19.6%)

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
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.6s (20.8%)

Symmetry

(sort x y)

(sort t a)

Results

1.2s	8256×	body	128	valid
401.0ms	3014×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	26	21
2	56	21
3	95	21
4	143	21
5	199	21
6	267	21
7	343	21
8	603	21
9	1383	21
10	2682	21
11	3425	21
12	3539	21
13	3669	21
14	3749	21
15	3749	21

Stop Event

1×

saturated

Counts

1 → 2

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

24.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
▶	26.6b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))

Compiler

Compiled 109 to 63 computations (42.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.0b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
✓	9.6b	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
✓	26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series289.0ms (3.7%)

Counts

4 → 132

Calls

4 calls:

151.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
103.0ms	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
27.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
7.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite91.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
263×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	288	61
2	4012	61

Stop Event

1×	node limit

Counts

4 → 263

Calls

4 calls:

85.0ms	(-.f64 (.f64 z z) (.f64 t a))
85.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
85.0ms	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
85.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Rules

380×	`times-frac_binary64`
257×	`associate-r_binary64`
243×	`associate-/r*_binary64`
243×	`cancel-sign-sub-inv_binary64`
221×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	233	3633
1	828	3614
2	3985	3614

Stop Event

1×	node limit

Counts

395 → 342

prune253.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	334	8	342
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	336	8	344

Error

3.7b

Counts

344 → 8

Alt Table

Status	Error	Program
	26.8b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
	28.5b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	27.0b	(.f64 x (.f64 (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z))
	29.4b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
▶	24.8b	(.f64 x (.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2))))
	36.9b	(*.f64 x y)
	35.8b	(.f64 x (/.f64 (.f64 y z) (-.f64 (.f64 1/2 (.f64 (/.f64 a z) t)) z)))
	38.3b	(*.f64 x (neg.f64 y))

Compiler

Compiled 10362 to 3606 computations (65.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.4b	(.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)))
✓	2.0b	(.f64 x (.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2))))
✓	26.4b	(pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)

series289.0ms (3.7%)

Counts

3 → 112

Calls

3 calls:

151.0ms	(.f64 x (.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2))))
102.0ms	(.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)))
35.0ms	(pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
149×	`associate-r_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	308	54
2	3989	54

Stop Event

1×	node limit

Counts

3 → 47

Calls

3 calls:

57.0ms	(.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)))
57.0ms	(.f64 x (.f64 y (.f64 z (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2))))
57.0ms	(pow.f64 (-.f64 (.f64 z z) (.f64 t a)) -1/2)

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

491×	`times-frac_binary64`
360×	`associate-/r*_binary64`
314×	`associate-r_binary64`
297×	`associate-/l*_binary64`
211×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	320	4530
1	1107	4455

Stop Event

1×	node limit

Counts

159 → 151

prune263.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	323	3	326
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	325	9	334

Error

1.5b

Counts

334 → 9

Alt Table

Status	Error	Program
▶	26.8b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
	28.5b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	27.0b	(.f64 x (.f64 (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z))
	29.4b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
	42.9b	(.f64 x (.f64 y (.f64 z (fma.f64 1/2 (.f64 (*.f64 (/.f64 z a) (/.f64 z t)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	41.8b	(.f64 x (.f64 y (.f64 z (exp.f64 (.f64 -1/2 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	43.3b	(.f64 x (.f64 y (*.f64 z (sqrt.f64 (/.f64 (/.f64 -1 a) t)))))
	38.3b	(*.f64 x (neg.f64 y))
	36.9b	(*.f64 x y)

Compiler

Compiled 11409 to 5100 computations (55.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.3b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
✓	9.6b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y))
	26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series205.0ms (2.6%)

Counts

2 → 76

Calls

2 calls:

151.0ms	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
53.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y))

rewrite62.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

901×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	294	39
2	4258	39

Stop Event

1×	node limit

Counts

2 → 86

Calls

2 calls:

61.0ms	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
60.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y))

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
244×	`times-frac_binary64`
215×	`associate-r_binary64`
169×	`associate-/l/_binary64`
164×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2607
1	608	2555
2	2929	2520

Stop Event

1×	node limit

Counts

162 → 135

prune276.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	356	2	358
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	357	10	367

Error

1.5b

Counts

367 → 10

Alt Table

Status	Error	Program
✓	26.8b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
	28.5b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
▶	25.8b	(.f64 (/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)) y)
	42.9b	(.f64 x (.f64 y (.f64 z (fma.f64 1/2 (.f64 (*.f64 (/.f64 z a) (/.f64 z t)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	27.2b	(.f64 x (/.f64 z (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) y)))
	41.8b	(.f64 x (.f64 y (.f64 z (exp.f64 (.f64 -1/2 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	43.3b	(.f64 x (.f64 y (*.f64 z (sqrt.f64 (/.f64 (/.f64 -1 a) t)))))
	29.4b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
	38.3b	(*.f64 x (neg.f64 y))
	36.9b	(*.f64 x y)

Compiler

Compiled 10590 to 3513 computations (66.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.4b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
✓	2.6b	(.f64 (/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)) y)
	26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series288.0ms (3.7%)

Counts

2 → 76

Calls

2 calls:

161.0ms	(.f64 (/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)) y)
126.0ms	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

rewrite65.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	294	39
2	4204	39

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

64.0ms	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
64.0ms	(.f64 (/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)) y)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
305×	`times-frac_binary64`
224×	`associate-r_binary64`
211×	`associate-/r*_binary64`
191×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2765
1	646	2759
2	3249	2753

Stop Event

1×	node limit

Counts

145 → 119

prune250.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	343	9	352

Error

1.5b

Counts

352 → 9

Alt Table

Status	Error	Program
	25.0b	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))
✓	26.8b	(/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (*.f64 z y)))
✓	25.8b	(.f64 (/.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)) y)
	42.9b	(.f64 x (.f64 y (.f64 z (fma.f64 1/2 (.f64 (*.f64 (/.f64 z a) (/.f64 z t)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	41.8b	(.f64 x (.f64 y (.f64 z (exp.f64 (.f64 -1/2 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 t))))))))
	43.3b	(.f64 x (.f64 y (*.f64 z (sqrt.f64 (/.f64 (/.f64 -1 a) t)))))
	29.4b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
	38.3b	(*.f64 x (neg.f64 y))
	36.9b	(*.f64 x y)

Compiler

Compiled 10254 to 3736 computations (63.6% saved)

regimes1.5s (19.8%)

Accuracy

Total 4.4b remaining (66.5%)

Threshold costs 0b (0%)

Counts

78 → 3

Compiler

Compiled 12794 to 8513 computations (33.5% saved)

bsearch74.0ms (0.9%)

Steps

Iters	Range		Point
9	2.9028680014476404e+45	3.101255513179682e+53	3.0514905924256488e+53
7	-3.074560788667349e+64	-1.8494435933669867e+63	-2.7002634376703844e+64

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-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	24	44
1	40	44
2	57	44
3	68	44
4	75	44
5	77	44

Stop Event

1×

saturated

end309.0ms (3.9%)

Remove: (sort t a)
Compiler: Compiled 454 to 297 computations (34.6% saved)

Details

analyze1.5s (19.6%)

sample1.6s (20.8%)

simplify44.0ms (0.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series289.0ms (3.7%)

rewrite91.0ms (1.2%)

simplify75.0ms (1%)

prune253.0ms (3.2%)

localize12.0ms (0.2%)

series289.0ms (3.7%)

rewrite58.0ms (0.7%)

simplify58.0ms (0.7%)

prune263.0ms (3.4%)

localize10.0ms (0.1%)

series205.0ms (2.6%)

rewrite62.0ms (0.8%)

simplify61.0ms (0.8%)

prune276.0ms (3.5%)

localize10.0ms (0.1%)

series288.0ms (3.7%)

rewrite65.0ms (0.8%)

simplify59.0ms (0.8%)

prune250.0ms (3.2%)

regimes1.5s (19.8%)

bsearch74.0ms (0.9%)

simplify3.0ms (0%)

end309.0ms (3.9%)

Profiling