Details

analyze39.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify251.0ms (11.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4853	17
1	4853	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.6b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
29.7b	(/.f64 (.f64 b b) (.f64 a a))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_1825` `add-exp-log_binary64_1827`
4×	`cbrt-undiv_binary64_1823` `cbrt-unprod_binary64_1822` `prod-exp_binary64_1838` `div-exp_binary64_1840` `add-sqr-sqrt_binary64_1811`
3×	`pow1_binary64_1850` `sqrt-prod_binary64_1805` `*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
2×	`add-log-exp_binary64_1828`
1×	`associate-/l_binary64_1734` `clear-num_binary64_1788` `div-inv_binary64_1786` `associate-/r_binary64_1733` `rem-sqrt-square_binary64_1802` `frac-2neg_binary64_1800` `sqrt-pow1_binary64_1807` `times-frac_binary64_1795` `pow1/2_binary64_1869`

Counts

2 → 34

Calls

2 calls:

7.0ms	(/.f64 (.f64 b b) (.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

series93.0ms (4.2%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
40.0ms	(/.f64 (.f64 b b) (.f64 a a))

simplify92.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5171	452

prune40.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0b

Counts

41 → 3

Compiler

Compiled 537 to 354 computations (34.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
0.0b	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
0.4b	(pow.f64 (/.f64 b a) 2)

rewrite22.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`unpow-prod-down_binary64_1868`
24×	`add-sqr-sqrt_binary64_1811`
23×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
18×	`cbrt-prod_binary64_1820`
15×	`sqrt-prod_binary64_1805`
12×	`cube-prod_binary64_1817`
9×	`times-frac_binary64_1795`
8×	`pow1_binary64_1850` `add-exp-log_binary64_1827`
6×	`pow-unpow_binary64_1866`
5×	`add-cbrt-cube_binary64_1825`
4×	`pow-pow_binary64_1861` `add-log-exp_binary64_1828`
3×	`sqr-pow_binary64_1761` `pow-exp_binary64_1857`
2×	`unpow3_binary64_1855` `cube-mult_binary64_1819` `sqrt-pow1_binary64_1807` `pow-to-exp_binary64_1858` `pow1/2_binary64_1869`
1×	`rem-cbrt-cube_binary64_1813` `pow1/3_binary64_1871` `div-inv_binary64_1786` `rem-sqrt-square_binary64_1802` `div-exp_binary64_1840` `rem-cube-cbrt_binary64_1812` `sqrt-pow2_binary64_1808` `unpow2_binary64_1854`

Counts

4 → 101

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 b a) 2)
3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

series274.0ms (12.2%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
52.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
52.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
27.0ms	(pow.f64 (/.f64 b a) 2)

simplify63.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4958	1916
1	4958	1916

prune117.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Merged error: 0b

Counts

116 → 3

Compiler

Compiled 1890 to 1387 computations (26.6% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)
5.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64_1868`
22×	`add-sqr-sqrt_binary64_1811`
21×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
19×	`log-pow_binary64_1878`
18×	`exp-prod_binary64_1841` `times-frac_binary64_1795`
6×	`pow1_binary64_1850` `add-exp-log_binary64_1827`
3×	`add-cbrt-cube_binary64_1825` `sqrt-prod_binary64_1805` `log-prod_binary64_1875` `pow-unpow_binary64_1866` `add-log-exp_binary64_1828`
2×	`sqr-pow_binary64_1761` `div-inv_binary64_1786` `pow-exp_binary64_1857` `unpow2_binary64_1854`
1×	`rem-sqrt-square_binary64_1802` `div-exp_binary64_1840` `sqrt-pow1_binary64_1807` `pow-pow_binary64_1861` `pow-to-exp_binary64_1858` `pow1/2_binary64_1869` `rem-log-exp_binary64_1830`

Counts

3 → 72

Calls

3 calls:

8.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
5.0ms	(pow.f64 (/.f64 b a) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

series133.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

54.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
53.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
26.0ms	(pow.f64 (/.f64 b a) 2)

simplify39.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5264	858

prune74.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Merged error: 0b

Counts

84 → 3

Compiler

Compiled 1183 to 786 computations (33.6% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
0.4b	(pow.f64 (/.f64 b a) 2)

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64_1868`
12×	`add-sqr-sqrt_binary64_1811`
11×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
9×	`times-frac_binary64_1795`
5×	`add-exp-log_binary64_1827`
4×	`pow1_binary64_1850`
3×	`sqrt-prod_binary64_1805` `pow-unpow_binary64_1866`
2×	`pow-exp_binary64_1857` `add-cbrt-cube_binary64_1825` `add-log-exp_binary64_1828`
1×	`sqr-pow_binary64_1761` `div-inv_binary64_1786` `rem-sqrt-square_binary64_1802` `div-exp_binary64_1840` `sqrt-pow1_binary64_1807` `pow-pow_binary64_1861` `pow-to-exp_binary64_1858` `unpow2_binary64_1854` `pow1/2_binary64_1869`

Counts

2 → 42

Calls

2 calls:

6.0ms	(pow.f64 (/.f64 b a) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

series79.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
30.0ms	(pow.f64 (/.f64 b a) 2)

simplify56.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5033	588

prune38.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	48	3	51

Merged error: 0b

Counts

51 → 3

Compiler

Compiled 630 to 411 computations (34.8% saved)

regimes21.0ms (0.9%)

Compiler: Compiled 68 to 72 computations (-5.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample714.0ms (31.8%)

Algorithm

1×

intervals

Results

277.0ms	8000×	body	128	valid
158.0ms	8000×	pre	128	true
5.0ms	132×	pre	128	false

Compiler

Compiled 62 to 57 computations (8.1% saved)

Details

analyze39.0ms (1.7%)

sample21.0ms (0.9%)

simplify251.0ms (11.2%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

rewrite11.0ms (0.5%)

series93.0ms (4.2%)

simplify92.0ms (4.1%)

prune40.0ms (1.8%)

localize9.0ms (0.4%)

rewrite22.0ms (1%)

series274.0ms (12.2%)

simplify63.0ms (2.8%)

prune117.0ms (5.2%)

localize9.0ms (0.4%)

rewrite21.0ms (0.9%)

series133.0ms (5.9%)

simplify39.0ms (1.7%)

prune74.0ms (3.3%)

localize7.0ms (0.3%)

rewrite10.0ms (0.5%)

series79.0ms (3.5%)

simplify56.0ms (2.5%)

prune38.0ms (1.7%)

regimes21.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample714.0ms (31.8%)

Profiling