Details

analyze292.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample49.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	116×	body	256	valid
9.0ms	285×	pre	128	true
8.0ms	49×	body	512	valid
7.0ms	91×	body	128	valid
2.0ms	29×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 52.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite36.0ms (0.7%)

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` `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 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series527.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
130.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune100.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

Compiler

Compiled 2000 to 1189 computations (40.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series864.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
301.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune151.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Merged error: 0b

Counts

114 → 6

Compiler

Compiled 3141 to 1931 computations (38.5% 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 c (*.f64 a 4))))))
0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite31.0ms (0.6%)

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-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_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 → 71

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series672.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

345.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
68.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune106.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	84	5	89

Merged error: 0b

Counts

89 → 5

Compiler

Compiled 2225 to 1383 computations (37.8% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
0.7b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`cube-div_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

11.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series432.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
125.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
66.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4920	1752
1	4920	1752

prune102.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	83	5	88

Merged error: 0b

Counts

88 → 5

Compiler

Compiled 2224 to 1443 computations (35.1% saved)

regimes47.0ms (0.8%)

Compiler: Compiled 396 to 321 computations (18.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	29
1	66	29

end0.0ms (0%)

sample1.6s (28.5%)

Algorithm

1×

intervals

Results

430.0ms	3770×	body	256	valid
281.0ms	8833×	pre	128	true
256.0ms	1468×	body	512	valid
165.0ms	2762×	body	128	valid
45.0ms	833×	body	128	nan

Compiler

Compiled 179 to 144 computations (19.6% saved)

Details

analyze292.0ms (5.3%)

sample49.0ms (0.9%)

simplify68.0ms (1.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite36.0ms (0.7%)

series527.0ms (9.5%)

simplify97.0ms (1.8%)

prune100.0ms (1.8%)

localize16.0ms (0.3%)

rewrite51.0ms (0.9%)

series864.0ms (15.6%)

simplify73.0ms (1.3%)

prune151.0ms (2.7%)

localize13.0ms (0.2%)

rewrite31.0ms (0.6%)

series672.0ms (12.1%)

simplify83.0ms (1.5%)

prune106.0ms (1.9%)

localize20.0ms (0.4%)

rewrite34.0ms (0.6%)

series432.0ms (7.8%)

simplify72.0ms (1.3%)

prune102.0ms (1.8%)

regimes47.0ms (0.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (28.5%)

Profiling