Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify156.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

prune2.0ms (0.1%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_2436`
26×	`add-sqr-sqrt_binary64_2457`
21×	`distribute-lft-out_binary64_2389`
18×	`times-frac_binary64_2442`
15×	`add-cube-cbrt_binary64_2468`
14×	`sqrt-prod_binary64_2451`
6×	`associate-/r*_binary64_2382`
5×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
4×	`pow1_binary64_2494`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384` `sqrt-div_binary64_2452`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `pow1/2_binary64_2513` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `sqrt-pow1_binary64_2453`

Counts

3 → 71

Calls

3 calls:

13.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series184.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

125.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify88.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4933	1538
1	4933	1538

prune87.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

Compiler

Compiled 1368 to 1023 computations (25.2% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
0.2b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
3.9b	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
6.8b	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))

rewrite70.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`sqrt-div_binary64_2452`
52×	`*-un-lft-identity_binary64_2436`
38×	`add-sqr-sqrt_binary64_2457`
34×	`sqrt-prod_binary64_2451`
32×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
28×	`associate-*r/_binary64_2380`
26×	`add-cube-cbrt_binary64_2468`
21×	`pow1_binary64_2494`
16×	`frac-sub_binary64_2445`
12×	`distribute-lft-out_binary64_2389` `frac-times_binary64_2446` `times-frac_binary64_2442`
11×	`swap-sqr_binary64_2403`
9×	`pow1/2_binary64_2513` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `sqrt-pow1_binary64_2453`
8×	`associate-*l/_binary64_2381`
7×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461` `associate-r_binary64_2378` `associate-l_binary64_2379`
6×	`add-log-exp_binary64_2472`
5×	`pow-prod-up_binary64_2503`
4×	`sub-div_binary64_2443` `associate-/r*_binary64_2382` `unswap-sqr_binary64_2404`
3×	`associate-/l*_binary64_2383` `pow-prod-down_binary64_2504` `pow-unpow_binary64_2510` `pow-pow_binary64_2505` `pow-sqr_binary64_2409`
2×	`associate-/r/_binary64_2384` `cube-div_binary64_2462`
1×	`prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `*-commutative_binary64_2369` `div-inv_binary64_2433` `diff-log_binary64_2525` `rem-cube-cbrt_binary64_2458` `pow2_binary64_2514` `sqrt-unprod_binary64_2455` `div-exp_binary64_2484` `flip3--_binary64_2440` `cbrt-unprod_binary64_2466` `cube-mult_binary64_2463` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `unpow3_binary64_2499` `sqr-pow_binary64_2408` `frac-2neg_binary64_2447` `sqrt-pow2_binary64_2454` `pow-plus_binary64_2496` `rem-square-sqrt_binary64_2448` `flip--_binary64_2411` `distribute-rgt-out--_binary64_2392` `sub-neg_binary64_2429`

Counts

4 → 163

Calls

4 calls:

15.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
12.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)

series221.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
46.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
36.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))

simplify87.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4939	3308
1	4939	3308

prune422.0ms (12.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	175	4	179

Merged error: 0b

Counts

179 → 4

Compiler

Compiled 6454 to 5236 computations (18.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
0.2b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
6.8b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_2436`
23×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468`
20×	`cbrt-prod_binary64_2464`
16×	`sqrt-prod_binary64_2451`
14×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461`
12×	`times-frac_binary64_2442`
9×	`distribute-lft-out_binary64_2389`
7×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
6×	`add-log-exp_binary64_2472` `pow1_binary64_2494`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r*_binary64_2382` `sqrt-div_binary64_2452` `cube-div_binary64_2462`
3×	`associate-/l*_binary64_2383` `pow-unpow_binary64_2510` `pow-pow_binary64_2505`
2×	`associate-/r/_binary64_2384` `cube-mult_binary64_2463` `unpow3_binary64_2499` `sqr-pow_binary64_2408` `cbrt-div_binary64_2465`
1×	`pow1/3_binary64_2515` `cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `rem-cube-cbrt_binary64_2458` `rem-cbrt-cube_binary64_2459` `pow1/2_binary64_2513` `div-exp_binary64_2484` `sum-log_binary64_2524` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `sqrt-pow2_binary64_2454` `sqrt-pow1_binary64_2453`

Counts

4 → 112

Calls

4 calls:

13.0ms	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
11.0ms	(+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
9.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))

series231.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
48.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
32.0ms	(+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
28.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5056	2185

prune126.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Merged error: 0b

Counts

128 → 4

Compiler

Compiled 2118 to 1642 computations (22.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite64.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64_2436`
92×	`add-sqr-sqrt_binary64_2457`
79×	`sqrt-prod_binary64_2451`
76×	`times-frac_binary64_2442`
57×	`distribute-lft-out_binary64_2389`
47×	`add-cube-cbrt_binary64_2468`
42×	`associate-r_binary64_2378`
11×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
7×	`pow1_binary64_2494`
6×	`associate-/l_binary64_2383` `add-log-exp_binary64_2472` `associate-/r_binary64_2382` `unswap-sqr_binary64_2404` `associate-l_binary64_2379`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384`
2×	`prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `div-exp_binary64_2484` `cbrt-unprod_binary64_2466` `sqrt-div_binary64_2452`
1×	`-commutative_binary64_2369` `pow-prod-down_binary64_2504` `pow1/2_binary64_2513` `associate-r/_binary64_2380` `sum-log_binary64_2524` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `sqrt-pow1_binary64_2453`

Counts

4 → 160

Calls

4 calls:

26.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

series339.0ms (10%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
107.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
32.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
24.0ms	(sqrt.f64 (+.f64 x 1))

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5079	3818

prune191.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	172	4	176

Merged error: 0b

Counts

176 → 4

Compiler

Compiled 3642 to 2306 computations (36.7% saved)

regimes85.0ms (2.5%)

Compiler: Compiled 726 to 602 computations (17.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample768.0ms (22.7%)

Algorithm

1×

intervals

Results

232.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 371 to 309 computations (16.7% saved)

Details

analyze3.0ms (0.1%)

sample12.0ms (0.4%)

simplify156.0ms (4.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite28.0ms (0.8%)

series184.0ms (5.4%)

simplify88.0ms (2.6%)

prune87.0ms (2.6%)

localize16.0ms (0.5%)

rewrite70.0ms (2.1%)

series221.0ms (6.5%)

simplify87.0ms (2.6%)

prune422.0ms (12.5%)

localize9.0ms (0.3%)

rewrite50.0ms (1.5%)

series231.0ms (6.8%)

simplify66.0ms (2%)

prune126.0ms (3.7%)

localize7.0ms (0.2%)

rewrite64.0ms (1.9%)

series339.0ms (10%)

simplify64.0ms (1.9%)

prune191.0ms (5.6%)

regimes85.0ms (2.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample768.0ms (22.7%)

Profiling