Details

analyze1.6s (17%)

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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	66×	body	128	nan
2.0ms	31×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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

25.8b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
4.1b	(.f64 (.f64 x y) z)
9.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite109.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

22.7b

Rules

18×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
11×	`add-sqr-sqrt_binary64_11012`
10×	`pow1_binary64_11051` `add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
9×	`sqrt-prod_binary64_11006`
6×	`add-log-exp_binary64_11029` `prod-exp_binary64_11039` `cbrt-unprod_binary64_11023` `times-frac_binary64_10996` `associate-/r*_binary64_10934`
4×	`sqrt-div_binary64_11007`
3×	`flip3--_binary64_10994` `flip--_binary64_10965` `div-exp_binary64_11041` `cbrt-undiv_binary64_11024` `pow-prod-down_binary64_11061` `associate-r_binary64_10930`
2×	`associate-/r/_binary64_10936`
1×	`pow1/2_binary64_11070` `sqrt-pow1_binary64_11008` `rem-sqrt-square_binary64_11003` `frac-2neg_binary64_11001` `clear-num_binary64_10989` `div-inv_binary64_10987` `associate-/l_binary64_10935` `associate-l_binary64_10931` `-commutative_binary64_10921` `diff-log_binary64_11082` `sub-neg_binary64_10983` `cancel-sign-sub-inv_binary64_10956`

Counts

4 → 76

Calls

4 calls:

9.0ms	(/.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)

series825.0ms (8.6%)

Error

4.3b

Counts

4 → 66

Calls

4 calls:

415.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
138.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
131.0ms	(-.f64 (.f64 z z) (.f64 t a))
87.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 2979 to 2080 computations (30.2% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5001	2278

prune112.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

4.1b

Counts

143 → 8

Compiler

Compiled 2558 to 492 computations (80.8% 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))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
2.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite126.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

36×	`times-frac_binary64_10996`
34×	`add-sqr-sqrt_binary64_11012`
33×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
24×	`sqrt-prod_binary64_11006` `associate-r_binary64_10930`
18×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
10×	`pow1_binary64_11051`
6×	`add-log-exp_binary64_11029` `sqrt-div_binary64_11007` `prod-exp_binary64_11039` `cbrt-unprod_binary64_11023` `associate-/r*_binary64_10934`
4×	`flip3--_binary64_10994` `flip--_binary64_10965` `associate-/r/_binary64_10936`
3×	`pow-prod-down_binary64_11061` `div-exp_binary64_11041` `cbrt-undiv_binary64_11024` `associate-/l*_binary64_10935`
2×	`div-inv_binary64_10987`
1×	`pow1/2_binary64_11070` `sqrt-pow1_binary64_11008` `rem-sqrt-square_binary64_11003` `associate-r/_binary64_10932` `associate-l_binary64_10931` `-commutative_binary64_10921` `diff-log_binary64_11082` `sub-neg_binary64_10983` `cancel-sign-sub-inv_binary64_10956` `frac-2neg_binary64_11001` `clear-num_binary64_10989`

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)

series882.0ms (9.2%)

Error

4.1b

Counts

4 → 71

Calls

4 calls:

434.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
147.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
134.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
120.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 3299 to 2437 computations (26.1% saved)

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5489	3448

prune128.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Error

4.1b

Counts

191 → 9

Compiler

Compiled 3631 to 681 computations (81.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(.f64 (.f64 x y) z)
9.3b	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite121.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

30×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
28×	`sqrt-div_binary64_11007`
12×	`prod-exp_binary64_11039` `cbrt-unprod_binary64_11023`
11×	`pow1_binary64_11051`
9×	`add-sqr-sqrt_binary64_11012`
8×	`flip3--_binary64_10994` `flip--_binary64_10965` `associate-/r/_binary64_10936`
7×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
6×	`sqrt-prod_binary64_11006` `div-exp_binary64_11041` `cbrt-undiv_binary64_11024`
4×	`add-log-exp_binary64_11029` `frac-times_binary64_11000`
3×	`pow-prod-down_binary64_11061` `associate-r_binary64_10930`
2×	`pow1/2_binary64_11070` `sqrt-pow1_binary64_11008` `rem-sqrt-square_binary64_11003` `associate-l/_binary64_10933` `associate-r/_binary64_10932`
1×	`frac-2neg_binary64_11001` `times-frac_binary64_10996` `clear-num_binary64_10989` `div-inv_binary64_10987` `associate-/l_binary64_10935` `associate-/r_binary64_10934` `associate-l_binary64_10931` `*-commutative_binary64_10921`

Counts

4 → 81

Calls

4 calls:

20.0ms	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (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	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 3190 to 365 computations (88.6% saved)

series878.0ms (9.2%)

Error

4.1b

Counts

4 → 67

Calls

4 calls:

445.0ms	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
150.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
138.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
95.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 4689 to 2762 computations (41.1% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4967	2657
1	4967	2657

prune127.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	148	9	157

Error

4.1b

Counts

157 → 9

Compiler

Compiled 4003 to 724 computations (81.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
6.7b	(.f64 x (.f64 z y))
9.3b	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
25.4b	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))

rewrite133.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

30×	`sqrt-prod_binary64_11006`
24×	`add-sqr-sqrt_binary64_11012`
21×	`*-un-lft-identity_binary64_10990`
20×	`pow1_binary64_11051` `add-cube-cbrt_binary64_11025` `times-frac_binary64_10996`
19×	`associate-r_binary64_10930`
18×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
9×	`pow-prod-down_binary64_11061` `prod-exp_binary64_11039` `cbrt-unprod_binary64_11023`
6×	`add-log-exp_binary64_11029`
4×	`associate-/r/_binary64_10936` `associate-l_binary64_10931`
3×	`sqrt-pow1_binary64_11008` `flip3--_binary64_10994` `flip--_binary64_10965` `rem-sqrt-square_binary64_11003`
2×	`sqrt-div_binary64_11007` `div-inv_binary64_10987` `*-commutative_binary64_10921`
1×	`pow1/2_binary64_11070` `inv-pow_binary64_11075` `pow-flip_binary64_11064` `associate-*r/_binary64_10932` `diff-log_binary64_11082` `sub-neg_binary64_10983` `cancel-sign-sub-inv_binary64_10956`

Counts

4 → 97

Calls

4 calls:

14.0ms	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
6.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 x (.f64 z y))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2553 to 811 computations (68.2% saved)

series828.0ms (8.7%)

Error

4.1b

Counts

4 → 61

Calls

4 calls:

439.0ms	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
130.0ms	(-.f64 (.f64 z z) (.f64 t a))
121.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
97.0ms	(.f64 x (.f64 z y))

Compiler

Compiled 2936 to 2162 computations (26.4% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4964	2646
1	4964	2646

prune119.0ms (1.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	157	10	167

Error

4.1b

Counts

167 → 10

Compiler

Compiled 3091 to 953 computations (69.2% saved)

regimes1.2s (12.7%)

Accuracy

Total 3.5b remaining (51.5%)

Threshold costs 0b (0%)

Compiler

Compiled 7031 to 4866 computations (30.8% saved)

bsearch85.0ms (0.9%)

Steps

Iters	Range		Point
7	1.6649724030372628e+78	3.178613165835006e+79	2.1061885535903113e+79
10	-1.244265765983219e+137	-1.4125163247586248e+127	-1.4998636024609424e+127

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	61
1	73	61

Remove

(sort t a)

(sort x y)

Compiler

Compiled 160 to 84 computations (47.5% saved)

end0.0ms (0%)

sample1.7s (18.2%)

Algorithm

1×

intervals

Results

412.0ms	8000×	body	128	valid
105.0ms	2223×	body	128	nan
44.0ms	829×	body	128	invalid

Compiler

Compiled 936 to 645 computations (31.1% saved)

Details

analyze1.6s (17%)

sample50.0ms (0.5%)

simplify54.0ms (0.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite109.0ms (1.1%)

series825.0ms (8.6%)

simplify93.0ms (1%)

prune112.0ms (1.2%)

localize10.0ms (0.1%)

rewrite126.0ms (1.3%)

series882.0ms (9.2%)

simplify59.0ms (0.6%)

prune128.0ms (1.3%)

localize13.0ms (0.1%)

rewrite121.0ms (1.3%)

series878.0ms (9.2%)

simplify82.0ms (0.9%)

prune127.0ms (1.3%)

localize12.0ms (0.1%)

rewrite133.0ms (1.4%)

series828.0ms (8.7%)

simplify93.0ms (1%)

prune119.0ms (1.2%)

regimes1.2s (12.7%)

bsearch85.0ms (0.9%)

simplify27.0ms (0.3%)

end0.0ms (0%)

sample1.7s (18.2%)

Profiling