Details

analyze1.2s (7.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4999	209
1	4999	209
0	5	5
1	5	5

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
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 14 to 14 computations (0% saved)

sample33.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
4.0ms	96×	body	128	invalid

Compiler

Compiled 27 to 32 computations (-18.5% saved)

simplify480.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (475.0ms)

Iter	Nodes	Cost
0	4162	19
1	4162	19

prune3.0ms (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

10.4b

Counts

2 → 1

Compiler

Compiled 26 to 26 computations (0% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.2b	(.f64 (.f64 z 9) t)
9.8b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_19210` `add-exp-log_binary64_19212`
8×	`pow1_binary64_19235`
6×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209` `add-sqr-sqrt_binary64_19196`
5×	`add-log-exp_binary64_19213`
4×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207`
3×	`associate-/l_binary64_19119` `associate-r*_binary64_19114` `pow-prod-down_binary64_19245` `times-frac_binary64_19180`
2×	`associate-/l/_binary64_19121` `flip--_binary64_19149` `flip3--_binary64_19178` `div-exp_binary64_19225` `cbrt-undiv_binary64_19208`
1×	`frac-2neg_binary64_19185` `div-inv_binary64_19171` `-commutative_binary64_19105` `diff-log_binary64_19266` `associate-/r_binary64_19118` `clear-num_binary64_19173` `associate-l_binary64_19115` `sub-neg_binary64_19167` `div-sub_binary64_19179` `cancel-sign-sub-inv_binary64_19140`

Counts

3 → 54

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
5.0ms	(.f64 (.f64 z 9) t)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

series135.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

73.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
46.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
16.0ms	(.f64 (.f64 z 9) t)

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4929	1034
1	4929	1034

prune82.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Error

4.4b

Counts

64 → 10

Compiler

Compiled 1358 to 837 computations (38.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 t (.f64 9/2 (/.f64 z a))))
0.3b	(*.f64 9/2 (/.f64 z a))
5.1b	(.f64 t (.f64 9/2 (/.f64 z a)))
6.3b	(/.f64 (.f64 x y) (.f64 a 2))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_19210` `add-exp-log_binary64_19212`
18×	`add-sqr-sqrt_binary64_19196`
14×	`associate-r_binary64_19114`
13×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
11×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207` `pow1_binary64_19235` `times-frac_binary64_19180`
6×	`add-log-exp_binary64_19213` `div-exp_binary64_19225` `associate-l_binary64_19115` `cbrt-undiv_binary64_19208`
5×	`associate-*r/_binary64_19116`
4×	`pow-prod-down_binary64_19245`
2×	`div-inv_binary64_19171` `*-commutative_binary64_19105` `unswap-sqr_binary64_19142`
1×	`frac-2neg_binary64_19185` `associate-/l_binary64_19119` `flip--_binary64_19149` `flip3--_binary64_19178` `diff-log_binary64_19266` `associate-/r_binary64_19118` `clear-num_binary64_19173` `frac-sub_binary64_19183` `sub-neg_binary64_19167` `cancel-sign-sub-inv_binary64_19140`

Counts

4 → 87

Calls

4 calls:

8.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 t (.f64 9/2 (/.f64 z a))))
7.0ms	(*.f64 9/2 (/.f64 z a))
7.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))
6.0ms	(/.f64 (.f64 x y) (.f64 a 2))

series159.0ms (1%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(-.f64 (/.f64 (.f64 x y) (.f64 a 2)) (.f64 t (.f64 9/2 (/.f64 z a))))
29.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))
24.0ms	(/.f64 (.f64 x y) (.f64 a 2))
13.0ms	(*.f64 9/2 (/.f64 z a))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4970	1367
1	4970	1367

prune103.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Error

0.0b

Counts

109 → 9

Compiler

Compiled 2093 to 1111 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 t (.f64 9/2 (/.f64 z a))))
0.3b	(*.f64 9/2 (/.f64 z a))
5.1b	(.f64 t (.f64 9/2 (/.f64 z a)))
6.6b	(/.f64 x (/.f64 a (/.f64 y 2)))

rewrite108.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

406×	`times-frac_binary64_19180`
203×	`add-sqr-sqrt_binary64_19196`
198×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
44×	`associate-/r*_binary64_19118`
27×	`add-cbrt-cube_binary64_19210` `add-exp-log_binary64_19212`
18×	`div-inv_binary64_19171`
14×	`associate-r_binary64_19114`
11×	`pow1_binary64_19235`
8×	`div-exp_binary64_19225` `cbrt-undiv_binary64_19208`
7×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207`
6×	`add-log-exp_binary64_19213` `associate-l_binary64_19115`
5×	`associate-*r/_binary64_19116` `associate-/r/_binary64_19120`
4×	`pow-prod-down_binary64_19245`
3×	`associate-/l*_binary64_19119`
2×	`*-commutative_binary64_19105` `unswap-sqr_binary64_19142`
1×	`frac-2neg_binary64_19185` `flip--_binary64_19149` `flip3--_binary64_19178` `diff-log_binary64_19266` `clear-num_binary64_19173` `frac-sub_binary64_19183` `sub-neg_binary64_19167` `cancel-sign-sub-inv_binary64_19140`

Counts

4 → 262

Calls

4 calls:

42.0ms	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 t (.f64 9/2 (/.f64 z a))))
15.0ms	(/.f64 x (/.f64 a (/.f64 y 2)))
8.0ms	(*.f64 9/2 (/.f64 z a))
7.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))

series142.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(-.f64 (/.f64 x (/.f64 a (/.f64 y 2))) (.f64 t (.f64 9/2 (/.f64 z a))))
26.0ms	(/.f64 x (/.f64 a (/.f64 y 2)))
23.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))
12.0ms	(*.f64 9/2 (/.f64 z a))

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4974	6048
1	4974	6048

prune331.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	272	11	283

Error

Counts

283 → 11

Compiler

Compiled 6949 to 3552 computations (48.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 a)
0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (sqrt.f64 2))) (/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2)))))
1.5b	(/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2))))
5.1b	(.f64 t (.f64 9/2 (/.f64 z a)))

rewrite804.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

4799×	`times-frac_binary64_19180`
2221×	`add-sqr-sqrt_binary64_19196`
2157×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
1699×	`cbrt-prod_binary64_19205`
828×	`associate-r_binary64_19114`
706×	`sqrt-prod_binary64_19190`
180×	`add-exp-log_binary64_19212`
137×	`associate-/r*_binary64_19118`
100×	`add-cbrt-cube_binary64_19210`
94×	`div-inv_binary64_19171`
73×	`div-exp_binary64_19225` `cbrt-undiv_binary64_19208`
69×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207`
15×	`associate-/r/_binary64_19120` `unswap-sqr_binary64_19142`
11×	`pow1_binary64_19235`
8×	`associate-l_binary64_19115`
6×	`associate-/l*_binary64_19119`
4×	`add-log-exp_binary64_19213` `pow-prod-down_binary64_19245`
3×	`associate-*r/_binary64_19116`
2×	`*-commutative_binary64_19105`
1×	`frac-2neg_binary64_19185` `frac-times_binary64_19184` `pow1/3_binary64_19256` `associate-*l/_binary64_19117` `clear-num_binary64_19173`

Counts

4 → 1929

Calls

4 calls:

253.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (sqrt.f64 2))) (/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2)))))
47.0ms	(/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2))))
7.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))
1.0ms	(cbrt.f64 a)

series363.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2))))
98.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (sqrt.f64 2))) (/.f64 (cbrt.f64 x) (/.f64 (cbrt.f64 a) (/.f64 y (sqrt.f64 2)))))
90.0ms	(cbrt.f64 a)
24.0ms	(.f64 t (.f64 9/2 (/.f64 z a)))

simplify709.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1941 → 1941

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5022	84929

prune7.0s (45.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	1941	0	1941
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	1941	11	1952

Error

Counts

1952 → 11

Compiler

Compiled 95268 to 40007 computations (58% saved)

regimes1.5s (9.9%)

Accuracy

Total 0.8b remaining (99.2%)

Threshold costs 0.8b (99.2%)

Compiler

Compiled 13957 to 11658 computations (16.5% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 10 computations (-11.1% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	146	99
1	146	99

Compiler

Compiled 402 to 270 computations (32.8% saved)

end0.0ms (0%)

sample1.9s (12.3%)

Algorithm

1×

intervals

Results

344.0ms	8000×	body	128	valid
143.0ms	3138×	body	128	invalid

Compiler

Compiled 1225 to 999 computations (18.4% saved)

Details

analyze1.2s (7.9%)

sample33.0ms (0.2%)

simplify480.0ms (3.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite21.0ms (0.1%)

series135.0ms (0.9%)

simplify68.0ms (0.4%)

prune82.0ms (0.5%)

localize11.0ms (0.1%)

rewrite34.0ms (0.2%)

series159.0ms (1%)

simplify87.0ms (0.6%)

prune103.0ms (0.7%)

localize11.0ms (0.1%)

rewrite108.0ms (0.7%)

series142.0ms (0.9%)

simplify129.0ms (0.8%)

prune331.0ms (2.1%)

localize24.0ms (0.2%)

rewrite804.0ms (5.2%)

series363.0ms (2.3%)

simplify709.0ms (4.5%)

prune7.0s (45.1%)

regimes1.5s (9.9%)

bsearch3.0ms (0%)

simplify24.0ms (0.2%)

end0.0ms (0%)

sample1.9s (12.3%)

Profiling