Details

analyze453.0ms (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify127.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1059×	`div-sub_binary64`
943×	`cancel-sign-sub-inv_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`
411×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	19	18
2	29	18
3	41	18
4	59	18
5	81	18
6	116	18
7	158	18
8	212	18
9	228	18
10	288	18
11	458	18
12	765	18
13	1263	18
14	1205	18
15	1347	18
16	1253	18
17	1281	18
18	1473	18
19	2174	18
20	2259	18
21	3190	18
22	4245	18
23	5305	18

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

2.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
0.8b	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
6.9b	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))

rewrite95.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 71

Calls

4 calls:

7.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
5.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))
3.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
3.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))

Compiler

Compiled 1494 to 718 computations (51.9% saved)

series126.0ms (2.7%)

Error

0.0b

Counts

4 → 59

Calls

4 calls:

37.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
35.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))
21.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
5.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))

Compiler

Compiled 2444 to 1638 computations (33% saved)

simplify130.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

701×	`times-frac_binary64`
543×	`associate-/l*_binary64`
355×	`associate-/r*_binary64`
167×	`associate-/r/_binary64`
161×	`cancel-sign-sub-inv_binary64`

Counts

130 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	2764
1	534	2702
2	1610	2616
3	4896	2604
4	4955	2604

prune98.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Error

1.7b

Counts

103 → 8

Alt Table

Status	Error	Program
	36.7b	(+.f64 x (.f64 (/.f64 y (-.f64 (.f64 (pow.f64 (exp.f64 z) 2) 25824365969885543609319430368361/20282409603651670423947251286016) (.f64 (.f64 y y) (.f64 x x)))) (+.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (*.f64 x y))))
	25.1b	(+.f64 x (+.f64 (/.f64 y (-.f64 5081767996463981/4503599627370496 (.f64 y x))) (+.f64 (.f64 (.f64 (/.f64 (.f64 y z) (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2)) z) (-.f64 (/.f64 25824365969885543609319430368361/20282409603651670423947251286016 (-.f64 5081767996463981/4503599627370496 (.f64 y x))) 5081767996463981/9007199254740992)) (.f64 (/.f64 (.f64 y z) (pow.f64 (-.f64 5081767996463981/4503599627370496 (*.f64 y x)) 2)) -5081767996463981/4503599627370496))))
	21.8b	(+.f64 x (-.f64 (/.f64 y (-.f64 5081767996463981/4503599627370496 (.f64 y x))) (.f64 5081767996463981/4503599627370496 (/.f64 (.f64 y z) (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2)))))
	12.8b	(+.f64 x (/.f64 y (+.f64 (.f64 z 5081767996463981/4503599627370496) (-.f64 5081767996463981/4503599627370496 (.f64 y x)))))
	32.5b	(+.f64 x (-.f64 (+.f64 (/.f64 y (-.f64 5081767996463981/4503599627370496 (.f64 y x))) (.f64 25824365969885543609319430368361/20282409603651670423947251286016 (.f64 (/.f64 y (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 3)) (+.f64 (.f64 z z) (pow.f64 z 3))))) (+.f64 (+.f64 (.f64 5081767996463981/4503599627370496 (/.f64 (.f64 y z) (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2))) (.f64 5081767996463981/9007199254740992 (.f64 (/.f64 (.f64 y z) (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2)) z))) (.f64 (/.f64 (.f64 y (pow.f64 z 3)) (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2)) (+.f64 5081767996463981/27021597764222976 (/.f64 131233436514737870443975272996283059396298505141/91343852333181432387730302044767688728495783936 (pow.f64 (-.f64 5081767996463981/4503599627370496 (.f64 y x)) 2)))))))
	40.6b	(+.f64 x (.f64 (/.f64 y (-.f64 (.f64 (pow.f64 (exp.f64 z) 3) 131233436514737870443975272996283059396298505141/91343852333181432387730302044767688728495783936) (pow.f64 (.f64 y x) 3))) (+.f64 (.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 5081767996463981/4503599627370496 (exp.f64 z))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))))
▶	2.8b	(+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)))
	3.1b	(+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)))))

Compiler

Compiled 2243 to 1213 computations (45.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)))
0.1b	(/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y))
0.8b	(-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x))
6.8b	(/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)

rewrite203.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

84×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 131

Calls

4 calls:

14.0ms	(+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)))
6.0ms	(/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y))
5.0ms	(/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)
4.0ms	(-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x))

Compiler

Compiled 3454 to 1870 computations (45.9% saved)

series168.0ms (3.7%)

Error

Counts

4 → 71

Calls

4 calls:

40.0ms	(+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)))
36.0ms	(/.f64 1 (/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y))
29.0ms	(/.f64 (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x)) y)
23.0ms	(-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x))

Compiler

Compiled 2831 to 1945 computations (31.3% saved)

simplify227.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

765×	`associate-/l*_binary64`
382×	`associate-/r/_binary64`
246×	`associate-/l/_binary64`
226×	`cancel-sign-sub-inv_binary64`
169×	`distribute-rgt-in_binary64`

Counts

202 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	5121
1	652	4830
2	2153	4569
3	4990	4569

prune207.0ms (4.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	167	5	172

Error

Counts

172 → 5

Alt Table

Status	Error	Program
	12.8b	(+.f64 x (/.f64 y (+.f64 (.f64 z 5081767996463981/4503599627370496) (-.f64 5081767996463981/4503599627370496 (.f64 y x)))))
	36.7b	(+.f64 x (.f64 (/.f64 y (-.f64 (.f64 (pow.f64 (exp.f64 z) 2) 25824365969885543609319430368361/20282409603651670423947251286016) (.f64 (.f64 y y) (.f64 x x)))) (+.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (*.f64 x y))))
▶	0.0b	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
	10.3b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)))
	13.7b	(+.f64 x (/.f64 1 (-.f64 (/.f64 5081767996463981/4503599627370496 y) x)))

Compiler

Compiled 2520 to 1336 computations (47% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)
0.0b	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
0.1b	(/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x))
0.1b	(*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))

rewrite101.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))
7.0ms	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
4.0ms	(/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x))
3.0ms	(+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)

Compiler

Compiled 1946 to 1111 computations (42.9% saved)

series181.0ms (3.9%)

Error

Counts

4 → 62

Calls

4 calls:

67.0ms	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
43.0ms	(/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x))
26.0ms	(+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)
17.0ms	(*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))

Compiler

Compiled 2758 to 2032 computations (26.3% saved)

simplify138.0ms (3%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-/l*_binary64`
243×	`distribute-rgt-in_binary64`
189×	`distribute-lft-in_binary64`
180×	`cancel-sign-sub-inv_binary64`
169×	`associate-/l/_binary64`

Counts

153 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3255
1	638	3114
2	1986	3096
3	4977	3096
4	4943	3096

prune61.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

Counts

102 → 5

Alt Table

Status	Error	Program
	32.2b	(+.f64 x (/.f64 -1 (.f64 (sqrt.f64 (-.f64 x (.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y)))) (sqrt.f64 (-.f64 x (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y)))))))
✓	0.0b	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
	12.8b	(+.f64 x (/.f64 y (+.f64 (.f64 z 5081767996463981/4503599627370496) (-.f64 5081767996463981/4503599627370496 (.f64 y x)))))
▶	10.3b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)))
	13.7b	(+.f64 x (/.f64 1 (-.f64 (/.f64 5081767996463981/4503599627370496 y) x)))

Compiler

Compiled 1894 to 1127 computations (40.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)
0.8b	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))
6.9b	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
28.4b	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3))

rewrite157.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3))
6.0ms	(pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)
5.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
4.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))

Compiler

Compiled 2862 to 1562 computations (45.4% saved)

series198.0ms (4.3%)

Error

Counts

4 → 63

Calls

4 calls:

64.0ms	(pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)
42.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3))
42.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
25.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))

Compiler

Compiled 3306 to 2354 computations (28.8% saved)

simplify217.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

442×	`unswap-sqr_binary64`
257×	`log-prod_binary64`
183×	`distribute-rgt-in_binary64`
165×	`sqr-pow_binary64`
149×	`associate-/l*_binary64`

Counts

200 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	5422
1	700	5089
2	2491	4933
3	4622	4933
4	4941	4933

prune78.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	163	5	168

Error

Counts

168 → 5

Alt Table

Status	Error	Program
	32.2b	(+.f64 x (/.f64 -1 (.f64 (sqrt.f64 (-.f64 x (.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y)))) (sqrt.f64 (-.f64 x (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y)))))))
	0.0b	(+.f64 x (/.f64 -1 (+.f64 (neg.f64 (*.f64 5081767996463981/4503599627370496 (/.f64 (exp.f64 z) y))) x)))
	10.3b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))) 3)))
	13.7b	(+.f64 x (/.f64 1 (-.f64 (/.f64 5081767996463981/4503599627370496 y) x)))
	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 (exp.f64 z) 5081767996463981/4503599627370496) (.f64 y x))))

Compiler

Compiled 2300 to 1279 computations (44.4% saved)

regimes807.0ms (17.5%)

Accuracy

Total 0.4b remaining (98.9%)

Threshold costs 0.4b (98.9%)

Compiler

Compiled 17755 to 11579 computations (34.8% saved)

bsearch20.0ms (0.4%)

Steps

Iters	Range		Point
0	1.1283791670955126	1.128379167095518	1.1283791670955152
11	0.0	1.1283791670955126	4.251535463079424e-306

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	31	50
2	40	50
3	46	50
4	50	50
5	51	50
6	51	50

end1.0ms (0%)

Compiler: Compiled 36 to 24 computations (33.3% saved)

sample752.0ms (16.3%)

Algorithm

1×

intervals

Results

427.0ms

8000×

body

128

valid

Compiler

Compiled 142 to 99 computations (30.3% saved)

Details

analyze453.0ms (9.8%)

sample22.0ms (0.5%)

simplify127.0ms (2.8%)

prune1.0ms (0%)

localize8.0ms (0.2%)

rewrite95.0ms (2.1%)

series126.0ms (2.7%)

simplify130.0ms (2.8%)

prune98.0ms (2.1%)

localize10.0ms (0.2%)

rewrite203.0ms (4.4%)

series168.0ms (3.7%)

simplify227.0ms (4.9%)

prune207.0ms (4.5%)

localize9.0ms (0.2%)

rewrite101.0ms (2.2%)

series181.0ms (3.9%)

simplify138.0ms (3%)

prune61.0ms (1.3%)

localize12.0ms (0.3%)

rewrite157.0ms (3.4%)

series198.0ms (4.3%)

simplify217.0ms (4.7%)

prune78.0ms (1.7%)

regimes807.0ms (17.5%)

bsearch20.0ms (0.4%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample752.0ms (16.3%)

Profiling