Details

analyze454.0ms (7.3%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	170×	body	80	valid
9.0ms	35×	body	1280	valid
9.0ms	29×	body	2560	valid
2.0ms	8×	body	640	valid
1.0ms	26×	body	80	nan
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	10×	body	80	invalid
0.0ms	3×	body	160	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

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: 34.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/l*_binary64` `insert-posit16`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

11.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series456.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify121.0ms (2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5418	2087

prune142.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 6.0b

Counts

88 → 10

Compiler

Compiled 2298 to 1260 computations (45.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.6b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
16.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series927.0ms (15%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
322.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5446	4765

prune215.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	143	10	153

Merged error: 6.0b

Counts

153 → 10

Compiler

Compiled 4659 to 2482 computations (46.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.9b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

13.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series663.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
130.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5189	2522

prune131.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 6.0b

Counts

107 → 10

Compiler

Compiled 2928 to 1745 computations (40.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`associate-l_binary64` `prod-exp_binary64` `insert-posit16`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series449.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
119.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4916	2127
1	4916	2127

prune103.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 6.0b

Counts

105 → 10

Compiler

Compiled 2277 to 1283 computations (43.7% saved)

regimes160.0ms (2.6%)

Compiler: Compiled 603 to 483 computations (19.9% saved)

bsearch103.0ms (1.7%)

Steps

Iters	Range		Point
10	2.115647444246942e+83	1.7550062663401127e+100	1.2904769892397663e+98
7	1.9343849523291177e-203	7.437319578326407e-202	2.278112172640853e-203
8	-9.49638545728917e+40	-2.89384459733206e+37	-9.296819166068998e+40

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	101	92
1	101	92

end0.0ms (0%)

sample1.5s (24.9%)

Algorithm

1×

intervals

Results

314.0ms	1042×	body	2560	valid
292.0ms	5260×	body	80	valid
212.0ms	832×	body	1280	valid
87.0ms	448×	body	640	valid
40.0ms	105×	body	5120	valid
36.0ms	685×	body	80	nan
29.0ms	199×	body	320	valid
21.0ms	383×	body	80	invalid
12.0ms	114×	body	160	valid

Compiler

Compiled 321 to 244 computations (24% saved)

Details

analyze454.0ms (7.3%)

sample42.0ms (0.7%)

simplify114.0ms (1.8%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series456.0ms (7.4%)

simplify121.0ms (2%)

prune142.0ms (2.3%)

localize12.0ms (0.2%)

rewrite54.0ms (0.9%)

series927.0ms (15%)

simplify96.0ms (1.5%)

prune215.0ms (3.5%)

localize13.0ms (0.2%)

rewrite36.0ms (0.6%)

series663.0ms (10.7%)

simplify122.0ms (2%)

prune131.0ms (2.1%)

localize15.0ms (0.2%)

rewrite38.0ms (0.6%)

series449.0ms (7.3%)

simplify125.0ms (2%)

prune103.0ms (1.7%)

regimes160.0ms (2.6%)

bsearch103.0ms (1.7%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample1.5s (24.9%)

Profiling