Details

analyze1.7s (15.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5017	231
0	5	5
1	5	5

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

Symmetry

(sort x y)

(sort t a)

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample51.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	79×	body	128	nan
2.0ms	37×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune3.0ms (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

23.9b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
8.4b	(.f64 (.f64 x y) z)
8.6b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
22.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite120.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

17.9b

Rules

18×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
11×	`add-sqr-sqrt_binary64_10671`
10×	`pow1_binary64_10710` `add-cube-cbrt_binary64_10684` `*-un-lft-identity_binary64_10649`
9×	`sqrt-prod_binary64_10665`
6×	`add-log-exp_binary64_10688` `prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `times-frac_binary64_10655` `associate-/r*_binary64_10593`
4×	`sqrt-div_binary64_10666`
3×	`flip3--_binary64_10653` `flip--_binary64_10624` `div-exp_binary64_10700` `cbrt-undiv_binary64_10683` `pow-prod-down_binary64_10720` `associate-r_binary64_10589`
2×	`associate-/r/_binary64_10595`
1×	`pow1/2_binary64_10729` `sqrt-pow1_binary64_10667` `rem-sqrt-square_binary64_10662` `frac-2neg_binary64_10660` `clear-num_binary64_10648` `div-inv_binary64_10646` `associate-/l_binary64_10594` `associate-l_binary64_10590` `-commutative_binary64_10580` `diff-log_binary64_10741` `sub-neg_binary64_10642` `cancel-sign-sub-inv_binary64_10615`

Counts

4 → 76

Calls

4 calls:

17.0ms	(/.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))

Compiler

Compiled 1787 to 278 computations (84.4% saved)

series768.0ms (7%)

Error

1.8b

Counts

4 → 61

Calls

4 calls:

405.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
128.0ms	(-.f64 (.f64 z z) (.f64 t a))
100.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
90.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 2549 to 1794 computations (29.6% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5276	2071

prune108.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	8	138

Error

1.7b

Counts

138 → 8

Compiler

Compiled 2401 to 431 computations (82% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
0.4b	(-.f64 (.f64 z z) (.f64 t a))
4.6b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
22.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite140.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

76×	`times-frac_binary64_10655`
47×	`add-sqr-sqrt_binary64_10671`
46×	`add-cube-cbrt_binary64_10684` `*-un-lft-identity_binary64_10649`
33×	`sqrt-prod_binary64_10665`
25×	`associate-/r*_binary64_10593`
18×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
7×	`div-exp_binary64_10700` `cbrt-undiv_binary64_10683` `associate-/l*_binary64_10594`
6×	`add-log-exp_binary64_10688`
5×	`pow1_binary64_10710`
4×	`sqrt-div_binary64_10666` `div-inv_binary64_10646`
3×	`flip3--_binary64_10653` `flip--_binary64_10624`
2×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `frac-2neg_binary64_10660` `clear-num_binary64_10648` `associate-/l/_binary64_10596`
1×	`pow1/2_binary64_10729` `sqrt-pow1_binary64_10667` `rem-sqrt-square_binary64_10662` `associate-/r/_binary64_10595` `diff-log_binary64_10741` `sub-neg_binary64_10642` `cancel-sign-sub-inv_binary64_10615`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
7.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
7.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 3488 to 515 computations (85.2% saved)

series817.0ms (7.5%)

Error

1.7b

Counts

4 → 67

Calls

4 calls:

407.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
139.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
126.0ms	(-.f64 (.f64 z z) (.f64 t a))
104.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 2798 to 2072 computations (25.9% saved)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4970	4095
1	4970	4095

prune140.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	199	8	207

Error

1.7b

Counts

207 → 8

Compiler

Compiled 3969 to 626 computations (84.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
4.6b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
22.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite130.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

36×	`times-frac_binary64_10655`
34×	`add-sqr-sqrt_binary64_10671`
33×	`add-cube-cbrt_binary64_10684` `*-un-lft-identity_binary64_10649`
24×	`sqrt-prod_binary64_10665` `associate-r_binary64_10589`
18×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
10×	`pow1_binary64_10710`
6×	`add-log-exp_binary64_10688` `sqrt-div_binary64_10666` `prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `associate-/r*_binary64_10593`
4×	`flip3--_binary64_10653` `flip--_binary64_10624` `associate-/r/_binary64_10595`
3×	`pow-prod-down_binary64_10720` `div-exp_binary64_10700` `cbrt-undiv_binary64_10683` `associate-/l*_binary64_10594`
2×	`div-inv_binary64_10646`
1×	`pow1/2_binary64_10729` `sqrt-pow1_binary64_10667` `rem-sqrt-square_binary64_10662` `associate-r/_binary64_10591` `associate-l_binary64_10590` `-commutative_binary64_10580` `diff-log_binary64_10741` `sub-neg_binary64_10642` `cancel-sign-sub-inv_binary64_10615` `frac-2neg_binary64_10660` `clear-num_binary64_10648`

Counts

4 → 112

Calls

4 calls:

13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
6.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2928 to 440 computations (85% saved)

series788.0ms (7.2%)

Error

1.7b

Counts

4 → 65

Calls

4 calls:

396.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
129.0ms	(-.f64 (.f64 z z) (.f64 t a))
126.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
99.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 2759 to 2068 computations (25% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4973	3197
1	4973	3197

prune120.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	177	8	185

Error

1.7b

Counts

185 → 8

Compiler

Compiled 3400 to 574 computations (83.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
7.4b	(.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))))))
23.0b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
23.0b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite165.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

40×	`add-sqr-sqrt_binary64_10671`
36×	`times-frac_binary64_10655`
33×	`associate-r_binary64_10589`
30×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
29×	`add-cube-cbrt_binary64_10684` `*-un-lft-identity_binary64_10649`
20×	`sqrt-prod_binary64_10665`
16×	`cbrt-prod_binary64_10680`
9×	`div-exp_binary64_10700` `prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `cbrt-undiv_binary64_10683`
7×	`associate-l_binary64_10590`
6×	`pow1_binary64_10710` `cbrt-div_binary64_10681`
4×	`add-log-exp_binary64_10688` `unswap-sqr_binary64_10617`
3×	`flip3--_binary64_10653` `flip--_binary64_10624` `div-inv_binary64_10646` `associate-/r*_binary64_10593`
2×	`pow1/3_binary64_10731` `sqrt-div_binary64_10666` `associate-/r/_binary64_10595`
1×	`pow-prod-down_binary64_10720` `frac-times_binary64_10659` `associate-l/_binary64_10592` `associate-r/_binary64_10591` `-commutative_binary64_10580` `frac-2neg_binary64_10660` `clear-num_binary64_10648` `associate-/l_binary64_10594`

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))))))
4.0ms	(/.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)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 4632 to 478 computations (89.7% saved)

series1.7s (15.8%)

Error

1.7b

Counts

4 → 64

Calls

4 calls:

857.0ms	(.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))))))
373.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
215.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
204.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 6002 to 4165 computations (30.6% saved)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5051	5583

prune168.0ms (1.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	179	8	187

Error

1.7b

Counts

187 → 8

Compiler

Compiled 5782 to 765 computations (86.8% saved)

regimes1.1s (10.2%)

Accuracy

Total 2.9b remaining (47.7%)

Threshold costs 0b (0%)

Compiler

Compiled 8935 to 5852 computations (34.5% saved)

bsearch92.0ms (0.8%)

Steps

Iters	Range		Point
9	8.598321735256545e+145	1.4388240342212295e+153	1.7098713886106964e+148
10	-2.1623449021339623e+158	-6.746602197204488e+140	-3.308504810282927e+151

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	43
1	72	43

Remove

(sort t a)

Compiler

Compiled 174 to 120 computations (31% saved)

end0.0ms (0%)

sample2.3s (21.2%)

Algorithm

1×

intervals

Results

641.0ms	8000×	body	128	valid
100.0ms	2263×	body	128	nan
40.0ms	800×	body	128	invalid

Compiler

Compiled 1058 to 702 computations (33.6% saved)

Details

analyze1.7s (15.4%)

sample51.0ms (0.5%)

simplify53.0ms (0.5%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite120.0ms (1.1%)

series768.0ms (7%)

simplify66.0ms (0.6%)

prune108.0ms (1%)

localize11.0ms (0.1%)

rewrite140.0ms (1.3%)

series817.0ms (7.5%)

simplify81.0ms (0.7%)

prune140.0ms (1.3%)

localize10.0ms (0.1%)

rewrite130.0ms (1.2%)

series788.0ms (7.2%)

simplify88.0ms (0.8%)

prune120.0ms (1.1%)

localize14.0ms (0.1%)

rewrite165.0ms (1.5%)

series1.7s (15.8%)

simplify96.0ms (0.9%)

prune168.0ms (1.5%)

regimes1.1s (10.2%)

bsearch92.0ms (0.8%)

simplify42.0ms (0.4%)

end0.0ms (0%)

sample2.3s (21.2%)

Profiling