Details

analyze1.1s (20%)

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)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	71×	body	128	nan
2.0ms	32×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	806	21
1	806	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

Error

23.6b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 z z) (.f64 t a))
3.3b	(.f64 (.f64 x y) z)
8.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
23.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
11×	`add-sqr-sqrt_binary64_10330`
10×	`pow1_binary64_10369` `add-cube-cbrt_binary64_10343` `*-un-lft-identity_binary64_10308`
9×	`sqrt-prod_binary64_10324`
6×	`cbrt-unprod_binary64_10341` `associate-/r*_binary64_10252` `prod-exp_binary64_10357` `add-log-exp_binary64_10347` `times-frac_binary64_10314`
4×	`sqrt-div_binary64_10325`
3×	`flip--_binary64_10283` `div-exp_binary64_10359` `associate-r_binary64_10248` `flip3--_binary64_10312` `pow-prod-down_binary64_10379` `cbrt-undiv_binary64_10342`
2×	`associate-/r/_binary64_10254`
1×	`rem-sqrt-square_binary64_10321` `associate-/l_binary64_10253` `sqrt-pow1_binary64_10326` `sub-neg_binary64_10301` `clear-num_binary64_10307` `associate-l_binary64_10249` `diff-log_binary64_10400` `div-inv_binary64_10305` `frac-2neg_binary64_10319` `-commutative_binary64_10239` `pow1/2_binary64_10388` `cancel-sign-sub-inv_binary64_10274`

Counts

4 → 76

Calls

4 calls:

10.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series230.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
52.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
30.0ms	(-.f64 (.f64 z z) (.f64 t a))
25.0ms	(.f64 (.f64 x y) z)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5138	1472

prune98.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	12	89

Error

4.3b

Counts

89 → 12

Compiler

Compiled 1848 to 407 computations (78% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
1.2b	(-.f64 (.f64 z z) (.f64 t a))
2.0b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
23.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_10314`
47×	`add-sqr-sqrt_binary64_10330`
46×	`add-cube-cbrt_binary64_10343` `*-un-lft-identity_binary64_10308`
33×	`sqrt-prod_binary64_10324`
25×	`associate-/r*_binary64_10252`
18×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
7×	`associate-/l*_binary64_10253` `div-exp_binary64_10359` `cbrt-undiv_binary64_10342`
6×	`add-log-exp_binary64_10347`
5×	`pow1_binary64_10369`
4×	`sqrt-div_binary64_10325` `div-inv_binary64_10305`
3×	`flip--_binary64_10283` `flip3--_binary64_10312`
2×	`cbrt-unprod_binary64_10341` `prod-exp_binary64_10357` `associate-/l/_binary64_10255` `clear-num_binary64_10307` `frac-2neg_binary64_10319`
1×	`rem-sqrt-square_binary64_10321` `sqrt-pow1_binary64_10326` `sub-neg_binary64_10301` `associate-/r/_binary64_10254` `diff-log_binary64_10400` `pow1/2_binary64_10388` `cancel-sign-sub-inv_binary64_10274`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
6.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series266.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
57.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
57.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
28.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5073	3422

prune120.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Error

4.0b

Counts

156 → 9

Compiler

Compiled 3348 to 542 computations (83.8% 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))))
1.2b	(-.f64 (.f64 z z) (.f64 t a))
2.0b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
23.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_10314`
34×	`add-sqr-sqrt_binary64_10330`
33×	`add-cube-cbrt_binary64_10343` `*-un-lft-identity_binary64_10308`
24×	`associate-r_binary64_10248` `sqrt-prod_binary64_10324`
18×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
10×	`pow1_binary64_10369`
6×	`cbrt-unprod_binary64_10341` `associate-/r*_binary64_10252` `prod-exp_binary64_10357` `add-log-exp_binary64_10347` `sqrt-div_binary64_10325`
4×	`flip--_binary64_10283` `flip3--_binary64_10312` `associate-/r/_binary64_10254`
3×	`associate-/l*_binary64_10253` `div-exp_binary64_10359` `pow-prod-down_binary64_10379` `cbrt-undiv_binary64_10342`
2×	`div-inv_binary64_10305`
1×	`rem-sqrt-square_binary64_10321` `associate-r/_binary64_10250` `sqrt-pow1_binary64_10326` `sub-neg_binary64_10301` `clear-num_binary64_10307` `associate-l_binary64_10249` `diff-log_binary64_10400` `frac-2neg_binary64_10319` `-commutative_binary64_10239` `pow1/2_binary64_10388` `cancel-sign-sub-inv_binary64_10274`

Counts

4 → 112

Calls

4 calls:

14.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series247.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
40.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
32.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5326	2521

prune92.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	124	9	133

Error

4.0b

Counts

133 → 9

Compiler

Compiled 2786 to 485 computations (82.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 z z) (.f64 t a))
2.0b	(/.f64 (.f64 x y) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z))
23.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
23.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
13×	`times-frac_binary64_10314`
12×	`add-sqr-sqrt_binary64_10330`
10×	`div-exp_binary64_10359` `add-cube-cbrt_binary64_10343` `*-un-lft-identity_binary64_10308` `cbrt-undiv_binary64_10342`
7×	`associate-/r*_binary64_10252`
6×	`add-log-exp_binary64_10347` `pow1_binary64_10369` `sqrt-prod_binary64_10324`
5×	`cbrt-unprod_binary64_10341` `prod-exp_binary64_10357`
4×	`sqrt-div_binary64_10325`
3×	`flip--_binary64_10283` `flip3--_binary64_10312` `div-inv_binary64_10305`
2×	`rem-sqrt-square_binary64_10321` `sqrt-pow1_binary64_10326` `pow1/2_binary64_10388`
1×	`associate-/l*_binary64_10253` `sub-neg_binary64_10301` `clear-num_binary64_10307` `associate-/r/_binary64_10254` `diff-log_binary64_10400` `frac-2neg_binary64_10319` `cancel-sign-sub-inv_binary64_10274`

Counts

4 → 80

Calls

4 calls:

16.0ms	(/.f64 (.f64 x y) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series254.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.f64 (.f64 x y) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z))
51.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
47.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
27.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4986	1812
1	4986	1812

prune75.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Error

4.0b

Counts

101 → 9

Compiler

Compiled 2419 to 414 computations (82.9% saved)

regimes798.0ms (14.4%)

Accuracy

Total 3.2b remaining (49.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6157 to 4252 computations (30.9% saved)

bsearch37.0ms (0.7%)

Steps

Iters	Range		Point
6	2.8982550004366603e+147	2.1315009582008775e+148	8.356197534345669e+147
5	-1.0508814674049765e+88	-3.2374887321141925e+87	-1.0298295872319982e+88

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	43
1	70	43

end0.0ms (0%)

sample1.5s (27.9%)

Algorithm

1×

intervals

Results

419.0ms	8000×	body	128	valid
103.0ms	2158×	body	128	nan
41.0ms	829×	body	128	invalid

Compiler

Compiled 831 to 571 computations (31.3% saved)

Details

analyze1.1s (20%)

sample34.0ms (0.6%)

simplify145.0ms (2.6%)

prune2.0ms (0%)

localize16.0ms (0.3%)

rewrite28.0ms (0.5%)

series230.0ms (4.2%)

simplify55.0ms (1%)

prune98.0ms (1.8%)

localize10.0ms (0.2%)

rewrite37.0ms (0.7%)

series266.0ms (4.8%)

simplify72.0ms (1.3%)

prune120.0ms (2.2%)

localize10.0ms (0.2%)

rewrite40.0ms (0.7%)

series247.0ms (4.5%)

simplify79.0ms (1.4%)

prune92.0ms (1.7%)

localize15.0ms (0.3%)

rewrite37.0ms (0.7%)

series254.0ms (4.6%)

simplify79.0ms (1.4%)

prune75.0ms (1.4%)

regimes798.0ms (14.4%)

bsearch37.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (27.9%)

Profiling