Details

analyze473.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	37×	body	2560	valid
9.0ms	164×	body	80	valid
6.0ms	25×	body	1280	valid
4.0ms	18×	body	640	valid
2.0ms	31×	body	80	nan
1.0ms	9×	body	320	valid
0.0ms	7×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series516.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4936	2053
1	4936	2053

prune131.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 6.0b

Counts

87 → 8

Compiler

Compiled 2150 to 1173 computations (45.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite85.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
363×	`*-un-lft-identity_binary64`
289×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`
71×	`associate-/r*_binary64`
40×	`sqrt-prod_binary64`
37×	`distribute-lft-out--_binary64`
25×	`add-exp-log_binary64`
17×	`div-inv_binary64`
15×	`div-exp_binary64`
13×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64`
5×	`associate-/r/_binary64`
4×	`insert-posit16`
3×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 356

Calls

4 calls:

27.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series550.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify233.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4989	16357
1	4989	16357

prune688.0ms (11.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	365	3	368
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	368	8	376

Merged error: 5.9b

Counts

376 → 8

Compiler

Compiled 12752 to 7095 computations (44.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series382.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
69.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify120.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5018	1286

prune110.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 5.9b

Counts

76 → 8

Compiler

Compiled 2615 to 1428 computations (45.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series380.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
72.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
72.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify121.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5018	1286

prune109.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	68	8	76

Merged error: 5.9b

Counts

76 → 8

Compiler

Compiled 2654 to 1489 computations (43.9% saved)

regimes184.0ms (3%)

Compiler: Compiled 438 to 345 computations (21.2% saved)

bsearch69.0ms (1.1%)

Steps

Iters	Range		Point
8	2.464908267438983e-79	3.7760870647051616e-76	5.0643624800958176e-79
9	-8.261437727097627e+107	-3.2562849158014094e+102	-1.6000356618606551e+106

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample1.6s (25.5%)

Algorithm

1×

intervals

Results

325.0ms	1013×	body	2560	valid
304.0ms	5145×	body	80	valid
247.0ms	932×	body	1280	valid
95.0ms	449×	body	640	valid
42.0ms	243×	body	320	valid
41.0ms	105×	body	5120	valid
36.0ms	642×	body	80	nan
23.0ms	394×	body	80	invalid
12.0ms	113×	body	160	valid

Compiler

Compiled 239 to 177 computations (25.9% saved)

Details

analyze473.0ms (7.7%)

sample45.0ms (0.7%)

simplify109.0ms (1.8%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series516.0ms (8.4%)

simplify130.0ms (2.1%)

prune131.0ms (2.1%)

localize13.0ms (0.2%)

rewrite85.0ms (1.4%)

series550.0ms (8.9%)

simplify233.0ms (3.8%)

prune688.0ms (11.2%)

localize15.0ms (0.2%)

rewrite24.0ms (0.4%)

series382.0ms (6.2%)

simplify120.0ms (2%)

prune110.0ms (1.8%)

localize14.0ms (0.2%)

rewrite24.0ms (0.4%)

series380.0ms (6.2%)

simplify121.0ms (2%)

prune109.0ms (1.8%)

regimes184.0ms (3%)

bsearch69.0ms (1.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.6s (25.5%)

Profiling