Details

analyze1.1s (16.5%)

Algorithm

1×

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
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	73×	body	128	nan
1.0ms	27×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify179.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	175	21
1	175	21

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

Merged error: 27.0b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 z z) (.f64 t a))
4.9b	(.f64 (.f64 x y) z)
10.5b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
11×	`add-sqr-sqrt_binary64_12904`
10×	`pow1_binary64_12941` `*-un-lft-identity_binary64_12883` `add-cube-cbrt_binary64_12915`
9×	`sqrt-prod_binary64_12898`
6×	`associate-/r*_binary64_12829` `prod-exp_binary64_12929` `cbrt-unprod_binary64_12913` `add-log-exp_binary64_12919` `times-frac_binary64_12889`
4×	`sqrt-div_binary64_12899`
3×	`pow-prod-down_binary64_12951` `associate-r_binary64_12825` `div-exp_binary64_12931` `flip3--_binary64_12887` `cbrt-undiv_binary64_12914` `flip--_binary64_12858`
2×	`associate-/r/_binary64_12831`
1×	`associate-l_binary64_12826` `-commutative_binary64_12816` `pow1/2_binary64_12960` `sub-neg_binary64_12876` `frac-2neg_binary64_12894` `diff-log_binary64_12972` `sqrt-pow1_binary64_12900` `associate-/l_binary64_12830` `rem-sqrt-square_binary64_12896` `clear-num_binary64_12882` `div-inv_binary64_12880`

Counts

4 → 75

Calls

4 calls:

12.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series481.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

261.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
109.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
58.0ms	(.f64 (.f64 x y) z)
53.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5153	1466

prune98.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 3.3b

Counts

88 → 10

Compiler

Compiled 1815 to 389 computations (78.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.2b	(-.f64 (.f64 z z) (.f64 t a))
3.5b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_12889`
34×	`add-sqr-sqrt_binary64_12904`
33×	`*-un-lft-identity_binary64_12883` `add-cube-cbrt_binary64_12915`
24×	`associate-r_binary64_12825` `sqrt-prod_binary64_12898`
18×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
10×	`pow1_binary64_12941`
6×	`sqrt-div_binary64_12899` `associate-/r*_binary64_12829` `prod-exp_binary64_12929` `cbrt-unprod_binary64_12913` `add-log-exp_binary64_12919`
4×	`flip3--_binary64_12887` `associate-/r/_binary64_12831` `flip--_binary64_12858`
3×	`pow-prod-down_binary64_12951` `associate-/l*_binary64_12830` `div-exp_binary64_12931` `cbrt-undiv_binary64_12914`
2×	`div-inv_binary64_12880`
1×	`associate-l_binary64_12826` `-commutative_binary64_12816` `pow1/2_binary64_12960` `sub-neg_binary64_12876` `associate-r/_binary64_12827` `frac-2neg_binary64_12894` `diff-log_binary64_12972` `sqrt-pow1_binary64_12900` `rem-sqrt-square_binary64_12896` `clear-num_binary64_12882`

Counts

4 → 111

Calls

4 calls:

15.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
8.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series498.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
112.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
80.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
56.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5237	2515

prune106.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 3.3b

Counts

133 → 12

Compiler

Compiled 2854 to 536 computations (81.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.9b	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
6.2b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite73.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`sqrt-prod_binary64_12898`
48×	`add-sqr-sqrt_binary64_12904` `times-frac_binary64_12889`
35×	`*-un-lft-identity_binary64_12883` `add-cube-cbrt_binary64_12915`
33×	`associate-r_binary64_12825`
30×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
16×	`sqrt-div_binary64_12899`
15×	`associate-l_binary64_12826`
9×	`associate-/r*_binary64_12829` `prod-exp_binary64_12929` `div-exp_binary64_12931` `cbrt-unprod_binary64_12913` `cbrt-undiv_binary64_12914`
8×	`pow1_binary64_12941`
6×	`associate-/r/_binary64_12831`
5×	`flip3--_binary64_12887` `flip--_binary64_12858`
4×	`add-log-exp_binary64_12919` `unswap-sqr_binary64_12851`
3×	`div-inv_binary64_12880`
2×	`pow1/2_binary64_12960` `sqrt-pow1_binary64_12900` `rem-sqrt-square_binary64_12896`
1×	`associate-l/_binary64_12828` `-commutative_binary64_12816` `frac-times_binary64_12893` `pow-prod-down_binary64_12951` `associate-r/_binary64_12827` `frac-2neg_binary64_12894` `associate-/l_binary64_12830` `clear-num_binary64_12882`

Counts

4 → 141

Calls

4 calls:

33.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
11.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series713.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
250.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
107.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
101.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4958	4161
1	4958	4161

prune153.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	154	11	165

Merged error: 3.3b

Counts

165 → 11

Compiler

Compiled 4979 to 635 computations (87.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
7.1b	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
27.3b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
27.3b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_12904`
36×	`times-frac_binary64_12889`
33×	`associate-r_binary64_12825`
30×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
29×	`*-un-lft-identity_binary64_12883` `add-cube-cbrt_binary64_12915`
20×	`sqrt-prod_binary64_12898`
16×	`cbrt-prod_binary64_12911`
9×	`prod-exp_binary64_12929` `div-exp_binary64_12931` `cbrt-unprod_binary64_12913` `cbrt-undiv_binary64_12914`
7×	`associate-l_binary64_12826`
6×	`pow1_binary64_12941` `cbrt-div_binary64_12912`
4×	`add-log-exp_binary64_12919` `unswap-sqr_binary64_12851`
3×	`associate-/r*_binary64_12829` `flip3--_binary64_12887` `flip--_binary64_12858` `div-inv_binary64_12880`
2×	`sqrt-div_binary64_12899` `pow1/3_binary64_12962` `associate-/r/_binary64_12831`
1×	`associate-l/_binary64_12828` `-commutative_binary64_12816` `frac-times_binary64_12893` `pow-prod-down_binary64_12951` `associate-r/_binary64_12827` `frac-2neg_binary64_12894` `associate-/l_binary64_12830` `clear-num_binary64_12882`

Counts

4 → 115

Calls

4 calls:

24.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
5.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series1.2s (17.3%)

Counts

4 → 12

Calls

4 calls:

680.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
160.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
157.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
155.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	4193
1	4983	4193

prune114.0ms (1.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	127	11	138

Merged error: 3.3b

Counts

138 → 11

Compiler

Compiled 4322 to 505 computations (88.3% saved)

regimes230.0ms (3.5%)

Compiler: Compiled 1582 to 1236 computations (21.9% saved)

bsearch46.0ms (0.7%)

Steps

Iters	Range		Point
7	4.178456659974218e+82	7.178330194273272e+83	1.2109648883880498e+83
7	-3.029000170814189e+154	-2.0109586073156365e+152	-9.59233644954521e+152

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	43
1	71	43

end0.0ms (0%)

sample1.2s (17.6%)

Algorithm

1×

intervals

Results

403.0ms	8000×	body	128	valid
105.0ms	2263×	body	128	nan
52.0ms	847×	body	128	invalid

Compiler

Compiled 271 to 204 computations (24.7% saved)

Details

analyze1.1s (16.5%)

sample31.0ms (0.5%)

simplify179.0ms (2.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite33.0ms (0.5%)

series481.0ms (7.2%)

simplify54.0ms (0.8%)

prune98.0ms (1.5%)

localize10.0ms (0.2%)

rewrite43.0ms (0.7%)

series498.0ms (7.5%)

simplify79.0ms (1.2%)

prune106.0ms (1.6%)

localize17.0ms (0.2%)

rewrite73.0ms (1.1%)

series713.0ms (10.7%)

simplify109.0ms (1.6%)

prune153.0ms (2.3%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series1.2s (17.3%)

simplify85.0ms (1.3%)

prune114.0ms (1.7%)

regimes230.0ms (3.5%)

bsearch46.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (17.6%)

Profiling