Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample29.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	74×	body	2048	valid
5.0ms	129×	body	128	valid
4.0ms	32×	body	1024	valid
1.0ms	15×	body	512	valid
0.0ms	6×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify97.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

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

Merged error: 14.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
2×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `diff-atan_binary64_2281` `sub-neg_binary64_2117`

Counts

2 → 24

Calls

2 calls:

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

series30.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

21.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
9.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 108 to 96 computations (11.1% saved)

simplify68.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4886	409
1	4886	409

prune22.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	1	31

Merged error: 0.3b

Counts

31 → 1

Compiler

Compiled 363 to 243 computations (33.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-l_binary64_2065`
2×	`add-log-exp_binary64_2163` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `prod-exp_binary64_2173` `distribute-rgt-in_binary64_2074` `flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series32.0ms (1.3%)

Counts

2 → 7

Calls

2 calls:

16.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
16.0ms	(*.f64 N (+.f64 N 1))

Compiler

Compiled 137 to 127 computations (7.3% saved)

simplify72.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4937	396
1	4937	396

prune39.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Merged error: 0.3b

Counts

38 → 5

Compiler

Compiled 558 to 433 computations (22.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64_2066`
18×	`cbrt-div_binary64_2156`
11×	`pow1_binary64_2185`
10×	`add-sqr-sqrt_binary64_2146`
9×	`pow1/3_binary64_2206` `flip3-+_binary64_2127` `flip-+_binary64_2098`
8×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
7×	`cbrt-prod_binary64_2155`
6×	`add-exp-log_binary64_2162`
4×	`swap-sqr_binary64_2091` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-r_binary64_2064` `frac-times_binary64_2134` `add-cbrt-cube_binary64_2160`
2×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `associate-*l/_binary64_2067` `pow-sqr_binary64_2097`
1×	`unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

series240.0ms (9.7%)

Counts

4 → 29

Calls

4 calls:

79.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
57.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
53.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
50.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

Compiler

Compiled 1219 to 1043 computations (14.4% saved)

simplify117.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4868	1439
1	4868	1439

prune143.0ms (5.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	101	5	106

Merged error: 0.3b

Counts

106 → 5

Compiler

Compiled 2771 to 2111 computations (23.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
15.4b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.4b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
24×	`sqrt-prod_binary64_2140`
21×	`pow1_binary64_2185`
14×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204`
8×	`swap-sqr_binary64_2091`
6×	`associate-l_binary64_2065` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-up_binary64_2194`
4×	`unswap-sqr_binary64_2092` `rem-sqrt-square_binary64_2137` `add-log-exp_binary64_2163`
3×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
1×	`sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `sqr-abs_binary64_2139` `cbrt-unprod_binary64_2157`

Counts

4 → 83

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series93.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
31.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
14.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))

Compiler

Compiled 496 to 436 computations (12.1% saved)

simplify68.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4973	1533
1	4973	1533

prune108.0ms (4.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	93	7	100

Merged error: 0.3b

Counts

100 → 7

Compiler

Compiled 2024 to 1656 computations (18.2% saved)

regimes54.0ms (2.2%)

Compiler: Compiled 540 to 456 computations (15.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.2s (47.1%)

Algorithm

1×

intervals

Results

370.0ms	2103×	body	2048	valid
151.0ms	4121×	body	128	valid
128.0ms	1024×	body	1024	valid
51.0ms	520×	body	512	valid
15.0ms	232×	body	256	valid

Compiler

Compiled 289 to 246 computations (14.9% saved)

Details

analyze2.0ms (0.1%)

sample29.0ms (1.2%)

simplify97.0ms (3.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite6.0ms (0.3%)

series30.0ms (1.2%)

simplify68.0ms (2.7%)

prune22.0ms (0.9%)

localize5.0ms (0.2%)

rewrite8.0ms (0.3%)

series32.0ms (1.3%)

simplify72.0ms (2.9%)

prune39.0ms (1.6%)

localize9.0ms (0.4%)

rewrite27.0ms (1.1%)

series240.0ms (9.7%)

simplify117.0ms (4.7%)

prune143.0ms (5.8%)

localize8.0ms (0.3%)

rewrite17.0ms (0.7%)

series93.0ms (3.8%)

simplify68.0ms (2.7%)

prune108.0ms (4.4%)

regimes54.0ms (2.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (47.1%)

Profiling