Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample40.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	68×	body	1024	valid
7.0ms	136×	body	128	valid
3.0ms	24×	body	512	valid
2.0ms	9×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify283.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune4.0ms (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: 29.4b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite76.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_2465`
88×	`times-frac_binary64_2471`
85×	`add-sqr-sqrt_binary64_2487`
37×	`add-cube-cbrt_binary64_2500`
34×	`cancel-sign-sub-inv_binary64_2431`
27×	`distribute-lft-out_binary64_2416`
22×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
11×	`associate-/r*_binary64_2409`
9×	`difference-of-sqr-1_binary64_2435`
7×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-/l*_binary64_2410`
6×	`associate-/r/_binary64_2411`
5×	`add-log-exp_binary64_2504`
3×	`flip--_binary64_2440` `div-inv_binary64_2462` `pow1_binary64_2526` `flip3--_binary64_2469`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `frac-2neg_binary64_2476`
1×	`sub-neg_binary64_2458` `diff-log_binary64_2557` `frac-sub_binary64_2474`

Counts

3 → 147

Calls

3 calls:

47.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series170.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

107.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
32.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
30.0ms	(/.f64 x (+.f64 x 1))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5369	2774

prune274.0ms (5.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	2	157

Merged error: 0.0b

Counts

157 → 2

Compiler

Compiled 3038 to 2139 computations (29.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
2.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1))))
16.8b	(/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1)))

rewrite101.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
24×	`times-frac_binary64_2471`
18×	`associate-/r/_binary64_2411`
16×	`add-cube-cbrt_binary64_2500` `cancel-sign-sub-inv_binary64_2431`
14×	`flip--_binary64_2440` `flip3--_binary64_2469`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`frac-times_binary64_2475`
7×	`difference-of-squares_binary64_2434` `associate-/l*_binary64_2410`
5×	`add-log-exp_binary64_2504` `associate-/r*_binary64_2409`
4×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `distribute-lft-out_binary64_2416`
3×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `pow1_binary64_2526`
2×	`associate-/l/_binary64_2412` `clear-num_binary64_2464` `div-sub_binary64_2470` `frac-2neg_binary64_2476`
1×	`flip3-+_binary64_2468` `associate--r-_binary64_2404` `flip-+_binary64_2439` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `diff-log_binary64_2557` `prod-exp_binary64_2514` `frac-sub_binary64_2474` `cbrt-unprod_binary64_2498`

Counts

3 → 101

Calls

3 calls:

53.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1))))
14.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1)))
11.0ms	(/.f64 x (+.f64 x 1))

series172.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1))))
40.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 1 1)) (*.f64 (-.f64 x 1) (-.f64 x 1)))
36.0ms	(/.f64 x (+.f64 x 1))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5103	1960

prune195.0ms (3.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	110	2	112

Merged error: 0.0b

Counts

112 → 2

Compiler

Compiled 2611 to 1781 computations (31.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 3 (pow.f64 x 3))
0.7b	(/.f64 -1 (*.f64 x x))
5.8b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite105.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64_2465` `times-frac_binary64_2471`
39×	`add-sqr-sqrt_binary64_2487`
35×	`add-cube-cbrt_binary64_2500`
13×	`associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `cancel-sign-sub-inv_binary64_2431`
12×	`cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
10×	`add-cbrt-cube_binary64_2501`
9×	`unpow3_binary64_2531`
8×	`add-log-exp_binary64_2504`
6×	`distribute-lft-out_binary64_2416` `associate-/l*_binary64_2410`
5×	`div-exp_binary64_2516`
4×	`cube-mult_binary64_2495` `div-inv_binary64_2462` `sqr-pow_binary64_2437` `distribute-rgt-out_binary64_2418`
3×	`cbrt-undiv_binary64_2499` `pow1_binary64_2526` `frac-sub_binary64_2474`
2×	`difference-of-squares_binary64_2434` `clear-num_binary64_2464` `distribute-lft-out--_binary64_2417` `diff-log_binary64_2557` `frac-2neg_binary64_2476`
1×	`flip3-+_binary64_2468` `associate--r+_binary64_2401` `flip--_binary64_2440` `sum-log_binary64_2556` `flip-+_binary64_2439` `distribute-rgt1-in_binary64_2421` `pow-exp_binary64_2533` `sub-neg_binary64_2458` `pow-to-exp_binary64_2534` `prod-exp_binary64_2514` `flip3--_binary64_2469` `frac-add_binary64_2473` `cbrt-unprod_binary64_2498`

Counts

3 → 119

Calls

3 calls:

59.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
16.0ms	(/.f64 3 (pow.f64 x 3))
9.0ms	(/.f64 -1 (*.f64 x x))

series147.0ms (3%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(/.f64 3 (pow.f64 x 3))
54.0ms	(/.f64 -1 (*.f64 x x))
34.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4961	2020
1	4961	2020

prune160.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Merged error: 0b

Counts

130 → 3

Compiler

Compiled 2615 to 1849 computations (29.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (pow.f64 x 5))
0.1b	(*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))
9.6b	(-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5))))
50.7b	(/.f64 (-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))) (pow.f64 x 6))

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_2465`
24×	`add-sqr-sqrt_binary64_2487`
22×	`add-cube-cbrt_binary64_2500`
21×	`times-frac_binary64_2471`
12×	`unpow-prod-down_binary64_2544`
11×	`add-exp-log_binary64_2503`
10×	`add-log-exp_binary64_2504`
8×	`add-cbrt-cube_binary64_2501`
7×	`associate-/r*_binary64_2409`
6×	`pow1_binary64_2526`
4×	`sqr-pow_binary64_2437` `associate-r_binary64_2405`
3×	`div-exp_binary64_2516` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`flip3-+_binary64_2468` `associate--r+_binary64_2401` `distribute-lft-in_binary64_2414` `flip--_binary64_2440` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `associate-*r/_binary64_2407` `distribute-rgt-in_binary64_2415` `diff-log_binary64_2557` `distribute-lft-out_binary64_2416` `flip3--_binary64_2469`
1×	`neg-log_binary64_2558` `*-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `associate--l-_binary64_2403` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `pow-exp_binary64_2533` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `pow-to-exp_binary64_2534` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `neg-sub0_binary64_2460` `cbrt-unprod_binary64_2498`

Counts

4 → 99

Calls

4 calls:

18.0ms	(*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))
12.0ms	(/.f64 (-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))) (pow.f64 x 6))
10.0ms	(-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5))))
10.0ms	(+.f64 (pow.f64 x 3) (pow.f64 x 5))

series541.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(+.f64 (pow.f64 x 3) (pow.f64 x 5))
197.0ms	(*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))
77.0ms	(/.f64 (-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5)))) (pow.f64 x 6))
48.0ms	(-.f64 (neg.f64 (pow.f64 x 4)) (*.f64 3 (+.f64 (pow.f64 x 3) (pow.f64 x 5))))

simplify93.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5048	2994

prune225.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Merged error: 0b

Counts

114 → 3

Compiler

Compiled 2926 to 2301 computations (21.4% saved)

regimes193.0ms (3.9%)

Compiler: Compiled 1876 to 1448 computations (22.8% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	74
1	120	74

end0.0ms (0%)

sample1.8s (36.3%)

Algorithm

1×

intervals

Results

318.0ms	2036×	body	1024	valid
183.0ms	4275×	body	128	valid
121.0ms	979×	body	512	valid
42.0ms	205×	body	2048	valid
42.0ms	505×	body	256	valid

Compiler

Compiled 931 to 717 computations (23% saved)

Details

analyze8.0ms (0.2%)

sample40.0ms (0.8%)

simplify283.0ms (5.7%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite76.0ms (1.5%)

series170.0ms (3.4%)

simplify77.0ms (1.6%)

prune274.0ms (5.5%)

localize10.0ms (0.2%)

rewrite101.0ms (2%)

series172.0ms (3.4%)

simplify79.0ms (1.6%)

prune195.0ms (3.9%)

localize9.0ms (0.2%)

rewrite105.0ms (2.1%)

series147.0ms (3%)

simplify112.0ms (2.3%)

prune160.0ms (3.2%)

localize15.0ms (0.3%)

rewrite60.0ms (1.2%)

series541.0ms (10.9%)

simplify93.0ms (1.9%)

prune225.0ms (4.5%)

regimes193.0ms (3.9%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.8s (36.3%)

Profiling