Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample26.0ms (0.1%)

Algorithm

1×

intervals

Results

10.0ms	63×	body	2048	valid
4.0ms	134×	body	128	valid
3.0ms	28×	body	1024	valid
2.0ms	22×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify135.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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

15.7b

Counts

2 → 1

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `diff-atan_binary64_1940` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 24

Calls

4 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series26.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
8.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 84 to 72 computations (14.3% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune74.0ms (0.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	14	16	30
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	14	17	31

Error

0.1b

Counts

31 → 17

Compiler

Compiled 496 to 362 computations (27% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0b	(*.f64 N (+.f64 N 1))
0.0b	(*.f64 N (+.f64 N 1))
0.1b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723` `pow1_binary64_1844`
3×	`associate-l_binary64_1724`
2×	`associate-*r/_binary64_1725` `add-log-exp_binary64_1822`
1×	`distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

2 → 30

Calls

4 calls:

7.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series52.0ms (0.2%)

Counts

2 → 9

Calls

2 calls:

37.0ms	(*.f64 N (+.f64 N 1))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 127 to 115 computations (9.4% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

1.9b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
1.9b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
2×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `pow1_binary64_1844`
1×	`unsub-neg_binary64_1777` `+-commutative_binary64_1713` `flip-+_binary64_1757` `neg-sub0_binary64_1778` `flip3-+_binary64_1786` `neg-log_binary64_1876` `distribute-rgt-neg-in_binary64_1741` `associate-+r-_binary64_1717`

Counts

2 → 23

Calls

4 calls:

5.0ms	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
1.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))

series31.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
12.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 90 to 78 computations (13.3% saved)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4862	360
1	4862	360

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

1.9b	(-.f64 (log.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
0.5b	(log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))
0.2b	(exp.f64 (atan.f64 (+.f64 N 1)))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.2b	(exp.f64 (atan.f64 (+.f64 N 1)))
0.5b	(log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))
1.9b	(-.f64 (log.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_1783`
11×	`add-sqr-sqrt_binary64_1805`
9×	`add-cube-cbrt_binary64_1818`
6×	`log-prod_binary64_1869` `exp-prod_binary64_1835` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`log-pow_binary64_1872`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
3×	`cancel-sign-sub-inv_binary64_1749` `associate--l+_binary64_1720`
2×	`distribute-lft-out--_binary64_1735`
1×	`flip3--_binary64_1787` `rem-exp-log_binary64_1823` `difference-of-squares_binary64_1752` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776` `rem-log-exp_binary64_1824`

Counts

4 → 53

Calls

8 calls:

7.0ms	(-.f64 (log.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
2.0ms	(log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))
2.0ms	(exp.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(atan.f64 (+.f64 N 1))

series192.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(-.f64 (log.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
76.0ms	(log.f64 (exp.f64 (atan.f64 (+.f64 N 1))))
17.0ms	(exp.f64 (atan.f64 (+.f64 N 1)))
9.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 216 to 192 computations (11.1% saved)

simplify117.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4881	740
1	4881	740

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))
15.4b	(-.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1805`
24×	`sqrt-prod_binary64_1799`
21×	`pow1_binary64_1844`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
8×	`swap-sqr_binary64_1750`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
5×	`pow-prod-up_binary64_1853`
4×	`unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796`
3×	`cancel-sign-sub-inv_binary64_1749` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `diff-log_binary64_1875` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `flip--_binary64_1758` `sub-neg_binary64_1776` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

4 → 91

Calls

8 calls:

8.0ms	(-.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
7.0ms	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	(atan.f64 (+.f64 N 1))

series71.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
21.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
18.0ms	(-.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
10.0ms	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))

Compiler

Compiled 252 to 216 computations (14.3% saved)

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4894	1042
1	4894	1042

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))
0.0b	(+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N)))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.3b	(sqrt.f64 (atan.f64 N))
0.6b	(-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N)))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1805`
18×	`sqrt-prod_binary64_1799`
13×	`*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818`
7×	`pow1_binary64_1844`
6×	`cancel-sign-sub-inv_binary64_1749` `add-log-exp_binary64_1822`
4×	`add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821`
3×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`
2×	`distribute-lft-out--_binary64_1735`
1×	`flip3--_binary64_1787` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 62

Calls

8 calls:

6.0ms	(-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N)))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(sqrt.f64 (atan.f64 N))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	(atan.f64 (+.f64 N 1))

series110.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N)))
23.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
22.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
19.0ms	(sqrt.f64 (atan.f64 N))

Compiler

Compiled 456 to 336 computations (26.3% saved)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5046	930

prune2.0s (7.4%)

Pruning

98 alts after pruning (92 fresh and 6 done)

	Pruned	Kept	Total
New	229	81	310
Fresh	0	11	11
Picked	0	0	0
Done	0	6	6
Total	229	98	327

Error

0.0b

Counts

327 → 98

Compiler

Compiled 4596 to 3397 computations (26.1% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))
0.0b	(*.f64 N (+.f64 1 N))
0.0b	(*.f64 N (+.f64 1 N))
0.1b	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723` `pow1_binary64_1844`
3×	`associate-l_binary64_1724`
2×	`associate-*r/_binary64_1725` `add-log-exp_binary64_1822`
1×	`distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

2 → 30

Calls

4 calls:

7.0ms	(*.f64 N (+.f64 1 N))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))
0.0ms	(*.f64 N (+.f64 1 N))
0.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

series53.0ms (0.2%)

Counts

2 → 9

Calls

2 calls:

39.0ms	(*.f64 N (+.f64 1 N))
13.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

Compiler

Compiled 145 to 133 computations (8.3% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4909	392
1	4909	392

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(atan2.f64 1 (+.f64 1 N))
0.0b	(atan2.f64 1 (+.f64 1 N))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822` `pow1_binary64_1844`

Counts

1 → 7

Calls

2 calls:

0.0ms	(atan2.f64 1 (+.f64 1 N))
0.0ms	(atan2.f64 1 (+.f64 1 N))

series9.0ms (0%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(atan2.f64 1 (+.f64 1 N))

Compiler

Compiled 30 to 30 computations (0% saved)

simplify150.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4716	96
1	4716	96

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

1.9b	(+.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (neg.f64 (atan.f64 N)))
1.0b	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
0.5b	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.5b	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
1.0b	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
1.9b	(+.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (neg.f64 (atan.f64 N)))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_1783`
12×	`cbrt-prod_binary64_1814`
10×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
6×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
3×	`pow-unpow_binary64_1860`
2×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `distribute-lft-out_binary64_1734` `unpow3_binary64_1849` `sum-log_binary64_1874`
1×	`unsub-neg_binary64_1777` `+-commutative_binary64_1713` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `flip-+_binary64_1757` `neg-sub0_binary64_1778` `flip3-+_binary64_1786` `neg-log_binary64_1876` `pow-pow_binary64_1855` `pow1/3_binary64_1865` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `distribute-rgt-neg-in_binary64_1741` `associate-+r-_binary64_1717`

Counts

4 → 67

Calls

8 calls:

12.0ms	(+.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (neg.f64 (atan.f64 N)))
3.0ms	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
2.0ms	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
1.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(atan.f64 (+.f64 N 1))

series80.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
18.0ms	(+.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (neg.f64 (atan.f64 N)))
9.0ms	(atan.f64 (+.f64 N 1))
8.0ms	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))

Compiler

Compiled 222 to 198 computations (10.8% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4843	896
1	4843	896

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.5b	(log.f64 (exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.7b	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))
15.4b	(-.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))))) (atan.f64 N))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_1805`
24×	`sqrt-prod_binary64_1799`
22×	`pow1_binary64_1844`
19×	`*-un-lft-identity_binary64_1783`
16×	`add-cube-cbrt_binary64_1818`
10×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
8×	`swap-sqr_binary64_1750`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
5×	`pow-prod-up_binary64_1853` `add-log-exp_binary64_1822`
4×	`unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796`
3×	`log-prod_binary64_1869` `cancel-sign-sub-inv_binary64_1749` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `associate--l+_binary64_1720`
2×	`distribute-lft-out--_binary64_1735`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `log-pow_binary64_1872` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `diff-log_binary64_1875` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `flip--_binary64_1758` `sub-neg_binary64_1776` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

4 → 96

Calls

8 calls:

7.0ms	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))
6.0ms	(-.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))))) (atan.f64 N))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	(exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))))

series147.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(-.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1)))))) (atan.f64 N))
27.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
24.0ms	(sqrt.f64 (atan.f64 (+.f64 N 1)))
10.0ms	(*.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))

Compiler

Compiled 300 to 264 computations (12% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4843	1106
1	4843	1106

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.5b	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
10×	`add-log-exp_binary64_1822`
9×	`cancel-sign-sub-inv_binary64_1749`
8×	`add-cube-cbrt_binary64_1818`
5×	`cbrt-prod_binary64_1814`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821` `distribute-lft-out--_binary64_1735` `flip--_binary64_1758` `pow1_binary64_1844`
3×	`diff-log_binary64_1875` `diff-atan_binary64_1940` `sub-neg_binary64_1776`
2×	`cbrt-div_binary64_1815`
1×	`pow1/3_binary64_1865`

Counts

4 → 66

Calls

8 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	(atan.f64 (+.f64 N 1))

series201.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
21.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
20.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
19.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 630 to 462 computations (26.7% saved)

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5123	1249

prune4.3s (16.1%)

Pruning

184 alts after pruning (173 fresh and 11 done)

	Pruned	Kept	Total
New	227	87	314
Fresh	1	86	87
Picked	0	0	0
Done	0	11	11
Total	228	184	412

Error

0.0b

Counts

412 → 184

Compiler

Compiled 7334 to 5582 computations (23.9% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))
0.0b	(*.f64 N (+.f64 1 N))
0.0b	(*.f64 N (+.f64 1 N))
0.1b	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723` `pow1_binary64_1844`
3×	`associate-l_binary64_1724`
2×	`associate-*r/_binary64_1725` `add-log-exp_binary64_1822`
1×	`distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

2 → 30

Calls

4 calls:

7.0ms	(*.f64 N (+.f64 1 N))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))
0.0ms	(*.f64 N (+.f64 1 N))
0.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

series46.0ms (0.2%)

Counts

2 → 9

Calls

2 calls:

32.0ms	(*.f64 N (+.f64 1 N))
14.0ms	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 N (+.f64 1 N)))))

Compiler

Compiled 175 to 163 computations (6.9% saved)

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4909	392
1	4909	392

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(atan2.f64 1 (+.f64 1 N))
0.0b	(atan2.f64 1 (+.f64 1 N))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822` `pow1_binary64_1844`

Counts

1 → 7

Calls

2 calls:

0.0ms	(atan2.f64 1 (+.f64 1 N))
0.0ms	(atan2.f64 1 (+.f64 1 N))

series8.0ms (0%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(atan2.f64 1 (+.f64 1 N))

Compiler

Compiled 42 to 42 computations (0% saved)

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4716	96
1	4716	96

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
0.1b	(atan2.f64 1 (+.f64 1 (.f64 1 (.f64 (.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 1 N))))))
0.1b	(.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 1 N)))
0.1b	(.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N))))
0.2b	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
0.3b	(cbrt.f64 (+.f64 1 N))
0.3b	(cbrt.f64 (+.f64 1 N))
0.3b	(cbrt.f64 (+.f64 1 N))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_1814`
35×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818`
11×	`pow1_binary64_1844`
9×	`swap-sqr_binary64_1750` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1/3_binary64_1865`
7×	`associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
2×	`associate-r/_binary64_1725` `pow-prod-up_binary64_1853` `associate-l/_binary64_1726` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `pow2_binary64_1864`

Counts

4 → 95

Calls

8 calls:

12.0ms	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
3.0ms	(cbrt.f64 (+.f64 1 N))
3.0ms	(cbrt.f64 (+.f64 1 N))
3.0ms	(cbrt.f64 (+.f64 1 N))
0.0ms	(.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N))))

series225.0ms (0.8%)

Counts

4 → 39

Calls

4 calls:

69.0ms	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
53.0ms	(cbrt.f64 (+.f64 1 N))
52.0ms	(cbrt.f64 (+.f64 1 N))
50.0ms	(cbrt.f64 (+.f64 1 N))

Compiler

Compiled 1301 to 1143 computations (12.1% saved)

simplify130.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5304	1820

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1))))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
30.0b	(-.f64 (.f64 (.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_1814`
8×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
3×	`cancel-sign-sub-inv_binary64_1749` `pow1/3_binary64_1865`
1×	`flip3--_binary64_1787` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 47

Calls

8 calls:

9.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))
1.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	(atan.f64 (+.f64 N 1))

series299.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
92.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
88.0ms	(cbrt.f64 (atan.f64 (+.f64 N 1)))
22.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))) (atan.f64 N))

Compiler

Compiled 420 to 360 computations (14.3% saved)

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5021	713

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (*.f64 (cbrt.f64 1) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
0.5b	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
10×	`add-log-exp_binary64_1822`
9×	`cancel-sign-sub-inv_binary64_1749`
8×	`add-cube-cbrt_binary64_1818`
5×	`cbrt-prod_binary64_1814`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821` `distribute-lft-out--_binary64_1735` `flip--_binary64_1758` `pow1_binary64_1844`
3×	`diff-log_binary64_1875` `diff-atan_binary64_1940` `sub-neg_binary64_1776`
2×	`cbrt-div_binary64_1815`
1×	`pow1/3_binary64_1865`

Counts

4 → 66

Calls

8 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
3.0ms	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
0.0ms	(atan.f64 (+.f64 N 1))

series211.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
24.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
21.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
21.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 702 to 534 computations (23.9% saved)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5123	1249

prune7.8s (29.3%)

Pruning

293 alts after pruning (277 fresh and 16 done)

	Pruned	Kept	Total
New	207	113	320
Fresh	4	164	168
Picked	0	0	0
Done	0	16	16
Total	211	293	504

Error

0.0b

Counts

504 → 293

Compiler

Compiled 5827 to 4451 computations (23.6% saved)

simplify263.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	2177	18179
1	2177	18179

regimes652.0ms (2.4%)

Compiler: Compiled 6933 to 5582 computations (19.5% saved)

bsearch0.0ms (0%)

regimes9.0ms (0%)

Compiler: Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

regimes20.0ms (0.1%)

Compiler: Compiled 10 to 13 computations (-30% saved)

bsearch49.0ms (0.2%)

Steps

Iters	Range		Point
7	3.1898519091160693e+101	5.300336184821042e+103	4.523856998161439e+102
10	-9.275724468759783e+83	-1.3086408741605237e+69	-7.239595071046961e+76

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.1%)

Accuracy

Total 0.1b remaining (13.9%)

Threshold costs 0.1b (13.9%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch51.0ms (0.2%)

Steps

Iters	Range		Point
7	1.4001132721294372e+76	2.9569576374337423e+77	9.446085470791922e+76
10	-9.275724468759783e+83	-1.3086408741605237e+69	-9.473704474378471e+76

Compiler

Compiled 44 to 40 computations (9.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	60
1	35	60

end0.0ms (0%)

sample7.7s (28.7%)

Algorithm

1×

intervals

Results

351.0ms	2069×	body	2048	valid
139.0ms	4220×	body	128	valid
116.0ms	983×	body	1024	valid
44.0ms	490×	body	512	valid
15.0ms	238×	body	256	valid

Compiler

Compiled 7078 to 5714 computations (19.3% saved)

Pareto

0.1976249631330549