Details

analyze2.4s (25.9%)

Algorithm

1×

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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
7.0ms	91×	body	80	nan
3.0ms	34×	body	80	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5038	27

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

Merged error: 12.8b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
8.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`associate-l_binary64`
10×	`unswap-sqr_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 120

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
10.0ms	(/.f64 (.f64 M D) (.f64 2 d))
10.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (10.9%)

Counts

4 → 12

Calls

4 calls:

516.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
296.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
167.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
46.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5535	2933

prune180.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	7	133

Merged error: 7.1b

Counts

133 → 7

Compiler

Compiled 3343 to 1937 computations (42.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
5.6b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64`
121×	`prod-exp_binary64`
43×	`div-exp_binary64`
33×	`add-cbrt-cube_binary64`
30×	`pow-exp_binary64`
23×	`associate-r_binary64` `add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
19×	`cbrt-unprod_binary64`
11×	`associate-l_binary64`
9×	`cbrt-prod_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`pow-to-exp_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `unpow2_binary64` `sqr-pow_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 149

Calls

4 calls:

21.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
14.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

series877.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

332.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
308.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
189.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
47.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5596	3602

prune213.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	160	8	168

Merged error: 6.9b

Counts

168 → 8

Compiler

Compiled 4444 to 2318 computations (47.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.6b	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
33×	`add-cbrt-cube_binary64`
28×	`associate-r_binary64`
26×	`times-frac_binary64`
24×	`div-exp_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`cbrt-prod_binary64`
15×	`cbrt-unprod_binary64`
12×	`pow-exp_binary64`
11×	`associate-l_binary64` `unswap-sqr_binary64`
9×	`cbrt-undiv_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64` `associate-l/_binary64`

Counts

4 → 137

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

series742.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

321.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
189.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
187.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5566	3611

prune196.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	149	8	157

Merged error: 6.9b

Counts

157 → 8

Compiler

Compiled 4292 to 2165 computations (49.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
7.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`cbrt-unprod_binary64` `prod-exp_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
7×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `insert-posit16`
3×	`sqrt-prod_binary64`
2×	`associate-/r_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

series517.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

301.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
126.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5087	2223

prune152.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 6.4b

Counts

133 → 12

Compiler

Compiled 3498 to 1754 computations (49.9% saved)

regimes441.0ms (4.7%)

Compiler: Compiled 3520 to 3288 computations (6.6% saved)

bsearch1.0ms (0%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	109	80
1	109	80

end0.0ms (0%)

sample1.8s (19.2%)

Algorithm

1×

intervals

Results

637.0ms	8000×	body	80	valid
252.0ms	2990×	body	80	nan
113.0ms	1341×	body	80	invalid

Compiler

Compiled 345 to 308 computations (10.7% saved)

Details

analyze2.4s (25.9%)

sample50.0ms (0.5%)

simplify100.0ms (1.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite44.0ms (0.5%)

series1.0s (10.9%)

simplify77.0ms (0.8%)

prune180.0ms (1.9%)

localize18.0ms (0.2%)

rewrite58.0ms (0.6%)

series877.0ms (9.4%)

simplify98.0ms (1%)

prune213.0ms (2.3%)

localize17.0ms (0.2%)

rewrite49.0ms (0.5%)

series742.0ms (7.9%)

simplify96.0ms (1%)

prune196.0ms (2.1%)

localize13.0ms (0.1%)

rewrite44.0ms (0.5%)

series517.0ms (5.5%)

simplify113.0ms (1.2%)

prune152.0ms (1.6%)

regimes441.0ms (4.7%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.8s (19.2%)

Profiling