Details

analyze4.0s (14.6%)

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

Compiler

Compiled 19 to 19 computations (0% saved)

sample115.0ms (0.4%)

Algorithm

1×

intervals

Results

43.0ms	256×	body	128	valid
16.0ms	112×	body	128	nan
5.0ms	39×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	6100	27

prune6.0ms (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

12.8b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
10.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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

Counts

4 → 116

Calls

4 calls:

23.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
15.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
11.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series3.2s (11.6%)

Counts

4 → 72

Calls

4 calls:

1.1s	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
1.0s	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
763.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
259.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3175 to 3028 computations (4.6% saved)

simplify175.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4969	4504
1	4969	4504

prune519.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	177	11	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	11	189

Error

3.7b

Counts

189 → 11

Compiler

Compiled 4642 to 2475 computations (46.7% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
4.3b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.2b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))

rewrite95.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64_798`
91×	`prod-exp_binary64_809`
40×	`div-exp_binary64_811`
30×	`add-cbrt-cube_binary64_796`
25×	`pow-exp_binary64_828`
23×	`associate-r_binary64_700`
22×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
11×	`cbrt-unprod_binary64_793` `times-frac_binary64_766`
8×	`rec-exp_binary64_810` `1-exp_binary64_804`
7×	`pow1_binary64_821`
6×	`cbrt-undiv_binary64_794` `unpow-prod-down_binary64_839`
5×	`pow-to-exp_binary64_829`
4×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `associate-l_binary64_701`
3×	`sqrt-prod_binary64_776` `div-inv_binary64_757`
2×	`unpow2_binary64_825` `sqrt-div_binary64_777` `sqr-pow_binary64_732` `*-commutative_binary64_691`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `sqrt-pow1_binary64_778` `associate-/r_binary64_704` `associate-/l_binary64_705` `associate-*r/_binary64_702` `pow1/2_binary64_840` `clear-num_binary64_759` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 130

Calls

4 calls:

24.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
16.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
14.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
12.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series2.8s (10.3%)

Counts

4 → 62

Calls

4 calls:

1.1s	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
801.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
710.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
267.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2776 to 2698 computations (2.8% saved)

simplify159.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5282	3937

prune568.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	192	11	203

Error

3.7b

Counts

203 → 11

Compiler

Compiled 4585 to 2855 computations (37.7% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
5.9b	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))

rewrite156.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64_798`
85×	`div-exp_binary64_811`
79×	`prod-exp_binary64_809`
64×	`times-frac_binary64_766`
60×	`add-sqr-sqrt_binary64_782`
33×	`add-cbrt-cube_binary64_796`
30×	`pow-exp_binary64_828`
25×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
22×	`associate-r_binary64_700`
18×	`unpow-prod-down_binary64_839`
15×	`unswap-sqr_binary64_728`
14×	`associate-l_binary64_701` `cbrt-prod_binary64_791`
13×	`cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
11×	`associate-/l*_binary64_705`
7×	`div-inv_binary64_757` `pow1_binary64_821`
6×	`unpow2_binary64_825` `pow-to-exp_binary64_829` `sqr-pow_binary64_732`
4×	`add-log-exp_binary64_799`
3×	`sqrt-prod_binary64_776`
2×	`frac-2neg_binary64_771` `associate-/r*_binary64_704` `sqrt-div_binary64_777` `clear-num_binary64_759`
1×	`rem-sqrt-square_binary64_773` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `frac-times_binary64_770` `associate-r/_binary64_702` `pow1/2_binary64_840` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 182

Calls

4 calls:

56.0ms	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
23.0ms	(/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
14.0ms	(/.f64 (.f64 M D) (.f64 2 d))
12.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))

series3.6s (13.1%)

Counts

4 → 62

Calls

4 calls:

1.5s	(/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
1.1s	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
765.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
234.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3069 to 2895 computations (5.7% saved)

simplify206.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4953	6164
1	4953	6164

prune659.0ms (2.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	244	11	255

Error

3.7b

Counts

255 → 11

Compiler

Compiled 6813 to 3469 computations (49.1% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (*.f64 M D) d)
4.3b	(.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) d) 3) 8)) 2))
6.2b	(.f64 (.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8)) 2)) (/.f64 1 l))
24.0b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8))

rewrite217.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64_766`
133×	`cbrt-prod_binary64_791`
116×	`unpow-prod-down_binary64_839`
107×	`add-sqr-sqrt_binary64_782`
88×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
85×	`associate-r_binary64_700`
58×	`add-exp-log_binary64_798`
43×	`cube-prod_binary64_788`
32×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
16×	`div-inv_binary64_757`
10×	`div-exp_binary64_811`
9×	`unswap-sqr_binary64_728` `sqr-pow_binary64_732`
8×	`cbrt-unprod_binary64_793`
6×	`cube-mult_binary64_790` `unpow3_binary64_826` `pow1_binary64_821`
5×	`pow-exp_binary64_828` `pow-to-exp_binary64_829`
4×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799` `associate-l_binary64_701` `rec-exp_binary64_810` `1-exp_binary64_804`
3×	`associate-/r*_binary64_704`
2×	`unpow2_binary64_825` `*-commutative_binary64_691`
1×	`pow1/3_binary64_842` `frac-2neg_binary64_771` `associate-/l_binary64_705` `cbrt-div_binary64_792` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `un-div-inv_binary64_758`

Counts

4 → 235

Calls

4 calls:

74.0ms	(.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) d) 3) 8)) 2))
51.0ms	(.f64 (.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8)) 2)) (/.f64 1 l))
16.0ms	(cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8))
10.0ms	(/.f64 (*.f64 M D) d)

series2.3s (8.5%)

Counts

4 → 45

Calls

4 calls:

1.1s	(.f64 (.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8)) 2)) (/.f64 1 l))
766.0ms	(.f64 h (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) d) 3) 8)) 2))
281.0ms	(cbrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 M D) d) 3) 8))
204.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 2064 to 2064 computations (0% saved)

simplify268.0ms (1%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	5050	6187

prune1.1s (3.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	280	11	291

Error

3.7b

Counts

291 → 11

Compiler

Compiled 8283 to 5396 computations (34.9% saved)

regimes2.3s (8.2%)

Accuracy

Total 5.0b remaining (51.6%)

Threshold costs 0b (0%)

Compiler

Compiled 12245 to 11293 computations (7.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify33.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	229	111
1	229	111

Compiler

Compiled 148 to 100 computations (32.4% saved)

end0.0ms (0%)

sample4.8s (17.2%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
457.0ms	3191×	body	128	nan
185.0ms	1320×	body	128	invalid

Compiler

Compiled 831 to 745 computations (10.3% saved)

Details

analyze4.0s (14.6%)

sample115.0ms (0.4%)

simplify83.0ms (0.3%)

prune6.0ms (0%)

localize29.0ms (0.1%)

rewrite88.0ms (0.3%)

series3.2s (11.6%)

simplify175.0ms (0.6%)

prune519.0ms (1.9%)

localize32.0ms (0.1%)

rewrite95.0ms (0.3%)

series2.8s (10.3%)

simplify159.0ms (0.6%)

prune568.0ms (2.1%)

localize40.0ms (0.1%)

rewrite156.0ms (0.6%)

series3.6s (13.1%)

simplify206.0ms (0.7%)

prune659.0ms (2.4%)

localize44.0ms (0.2%)

rewrite217.0ms (0.8%)

series2.3s (8.5%)

simplify268.0ms (1%)

prune1.1s (3.8%)

regimes2.3s (8.2%)

bsearch3.0ms (0%)

simplify33.0ms (0.1%)

end0.0ms (0%)

sample4.8s (17.2%)

Profiling