Details

analyze2.7s (3.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5015	432
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample2.2s (2.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
11.0ms	103×	body	128	nan
5.0ms	47×	body	128	invalid

Compiler

Compiled 7751 to 10193 computations (-31.5% saved)

simplify41.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6100	27

prune4.0ms (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

16.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
13.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite250.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

67×	`add-exp-log_binary64_798`
38×	`add-sqr-sqrt_binary64_782`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
19×	`div-exp_binary64_811` `associate-r_binary64_700`
17×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
15×	`times-frac_binary64_766`
13×	`associate-l_binary64_701`
10×	`pow-exp_binary64_828` `unswap-sqr_binary64_728`
7×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `associate-*r/_binary64_702` `div-inv_binary64_757`
2×	`pow-to-exp_binary64_829` `*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow-prod-down_binary64_831`

Counts

4 → 116

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series2.1s (2.5%)

Error

7.3b

Counts

4 → 57

Calls

4 calls:

820.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
690.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
332.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
187.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5385	3695

prune240.0ms (0.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	162	11	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Error

6.3b

Counts

174 → 11

Compiler

Compiled 4050 to 2202 computations (45.6% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite358.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

179×	`add-exp-log_binary64_798`
88×	`prod-exp_binary64_809`
52×	`div-exp_binary64_811`
28×	`add-cbrt-cube_binary64_796`
25×	`pow-exp_binary64_828`
24×	`add-sqr-sqrt_binary64_782`
14×	`cbrt-unprod_binary64_793`
13×	`associate-l_binary64_701`
11×	`add-cube-cbrt_binary64_795` `-un-lft-identity_binary64_760` `associate-r*_binary64_700`
10×	`unswap-sqr_binary64_728`
8×	`cbrt-undiv_binary64_794`
7×	`pow1_binary64_821` `unpow-prod-down_binary64_839` `times-frac_binary64_766` `sqrt-prod_binary64_776`
5×	`pow-to-exp_binary64_829`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `associate-*r/_binary64_702` `div-inv_binary64_757`
2×	`*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow-prod-down_binary64_831`

Counts

4 → 132

Calls

4 calls:

20.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6275 to 2349 computations (62.6% saved)

series3.3s (3.9%)

Error

5.8b

Counts

4 → 57

Calls

4 calls:

1.8s	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
752.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
405.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
212.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4400 to 3685 computations (16.3% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5096	4664

prune294.0ms (0.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	189	11	200

Error

5.6b

Counts

200 → 11

Compiler

Compiled 5966 to 2573 computations (56.9% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

3.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))

rewrite388.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

69×	`add-exp-log_binary64_798`
59×	`add-cbrt-cube_binary64_796`
46×	`add-sqr-sqrt_binary64_782`
43×	`times-frac_binary64_766`
40×	`cbrt-prod_binary64_791` `associate-r_binary64_700`
31×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
26×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
21×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
7×	`pow1_binary64_821`
5×	`unswap-sqr_binary64_728` `associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`sqrt-prod_binary64_776`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

4 → 139

Calls

4 calls:

20.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
14.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6977 to 2660 computations (61.9% saved)

series2.0s (2.4%)

Error

5.4b

Counts

4 → 48

Calls

4 calls:

1.2s	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
398.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
193.0ms	(/.f64 (.f64 M D) (.f64 2 d))
193.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4724 to 3057 computations (35.3% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4975	3925
1	4975	3925

prune369.0ms (0.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	2	7	9
Picked	0	1	1
Done	1	0	1
Total	187	11	198

Error

5.4b

Counts

198 → 11

Compiler

Compiled 7833 to 2988 computations (61.9% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

3.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.3b	(/.f64 (*.f64 M D) d)
4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))

rewrite444.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

Rules

62×	`add-exp-log_binary64_798`
52×	`add-cbrt-cube_binary64_796`
48×	`add-sqr-sqrt_binary64_782`
45×	`times-frac_binary64_766`
40×	`cbrt-prod_binary64_791` `associate-r_binary64_700`
33×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
23×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
19×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
7×	`pow1_binary64_821`
5×	`unswap-sqr_binary64_728` `associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-/r*_binary64_704`
3×	`sqrt-prod_binary64_776`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l*_binary64_705`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

4 → 139

Calls

4 calls:

30.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
20.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 9526 to 2642 computations (72.3% saved)

series2.1s (2.5%)

Error

5.4b

Counts

4 → 48

Calls

4 calls:

1.2s	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
445.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
230.0ms	(/.f64 (.f64 M D) (.f64 2 d))
180.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 6407 to 3565 computations (44.4% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4978	4859
1	4978	4859

prune433.0ms (0.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	186	12	198

Error

5.4b

Counts

198 → 12

Compiler

Compiled 10933 to 2923 computations (73.3% saved)

regimes3.0s (3.6%)

Accuracy

Total 4.1b remaining (47.9%)

Threshold costs 0b (0%)

Compiler

Compiled 39982 to 29523 computations (26.2% saved)

bsearch0.0ms (0%)

simplify19.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	160	90
1	160	90

Remove

(sort M D)

Compiler

Compiled 110 to 64 computations (41.8% saved)

end0.0ms (0%)

sample1.1min (75.6%)

Algorithm

1×

intervals

Results

659.0ms	8000×	body	128	valid
375.0ms	3142×	body	128	nan
147.0ms	1165×	body	128	invalid

Compiler

Compiled 236474 to 309602 computations (-30.9% saved)

Details

analyze2.7s (3.1%)

sample2.2s (2.6%)

simplify41.0ms (0%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite250.0ms (0.3%)

series2.1s (2.5%)

simplify69.0ms (0.1%)

prune240.0ms (0.3%)

localize25.0ms (0%)

rewrite358.0ms (0.4%)

series3.3s (3.9%)

simplify105.0ms (0.1%)

prune294.0ms (0.3%)

localize21.0ms (0%)

rewrite388.0ms (0.5%)

series2.0s (2.4%)

simplify79.0ms (0.1%)

prune369.0ms (0.4%)

localize39.0ms (0%)

rewrite444.0ms (0.5%)

series2.1s (2.5%)

simplify65.0ms (0.1%)

prune433.0ms (0.5%)

regimes3.0s (3.6%)

bsearch0.0ms (0%)

simplify19.0ms (0%)

end0.0ms (0%)

sample1.1min (75.6%)

Profiling