Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample42.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	72×	body	1024	valid
6.0ms	120×	body	128	valid
5.0ms	35×	body	512	valid
3.0ms	10×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify180.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (0%)

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

Error

34.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_3084`
14×	`*-un-lft-identity_binary64_3068` `add-sqr-sqrt_binary64_3090`
6×	`cancel-sign-sub-inv_binary64_3034`
5×	`add-cube-cbrt_binary64_3103`
4×	`difference-of-squares_binary64_3037` `add-log-exp_binary64_3107`
3×	`distribute-lft-out--_binary64_3020` `pow1_binary64_3129`
2×	`distribute-lft-out_binary64_3019` `add-cbrt-cube_binary64_3104` `add-exp-log_binary64_3106` `sqrt-div_binary64_3085`
1×	`rem-sqrt-square_binary64_3081` `diff-log_binary64_3160` `flip3-+_binary64_3071` `pow1/2_binary64_3148` `sqrt-pow1_binary64_3086` `sub-neg_binary64_3061` `flip--_binary64_3043` `flip3--_binary64_3072` `flip-+_binary64_3042`

Counts

2 → 40

Calls

4 calls:

17.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series83.0ms (0.6%)

Counts

2 → 8

Calls

2 calls:

53.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
30.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 170 to 142 computations (16.5% saved)

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5272	570

prune118.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	2	49

Error

0.2b

Counts

49 → 2

Compiler

Compiled 551 to 360 computations (34.7% saved)

localize13.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_3068`
24×	`sqrt-prod_binary64_3084`
21×	`distribute-lft-out_binary64_3019`
18×	`times-frac_binary64_3074`
16×	`add-sqr-sqrt_binary64_3090`
15×	`add-cube-cbrt_binary64_3103`
7×	`add-exp-log_binary64_3106`
6×	`associate-/r*_binary64_3012`
5×	`add-cbrt-cube_binary64_3104` `pow1_binary64_3129` `add-log-exp_binary64_3107`
3×	`flip3-+_binary64_3071` `associate-/l*_binary64_3013` `flip-+_binary64_3042`
2×	`associate-/r/_binary64_3014` `sqrt-div_binary64_3085` `div-exp_binary64_3119`
1×	`rem-sqrt-square_binary64_3081` `pow-flip_binary64_3142` `pow1/2_binary64_3148` `sqrt-pow1_binary64_3086` `sum-log_binary64_3159` `+-commutative_binary64_2998` `inv-pow_binary64_3153` `rec-exp_binary64_3118` `div-inv_binary64_3065` `1-exp_binary64_3112` `cbrt-undiv_binary64_3102` `frac-2neg_binary64_3079` `clear-num_binary64_3067`

Counts

3 → 75

Calls

6 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series93.0ms (0.6%)

Counts

3 → 11

Calls

3 calls:

35.0ms	(sqrt.f64 (+.f64 x 1))
33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
25.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 182 to 168 computations (7.7% saved)

simplify193.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	4856	1208
1	4856	1208

prune228.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	9	88

Error

0.0b

Counts

88 → 9

Compiler

Compiled 1317 to 963 computations (26.9% saved)

localize27.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite287.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_3068`
700×	`sqrt-prod_binary64_3084`
594×	`times-frac_binary64_3074`
280×	`distribute-lft-out_binary64_3019`
254×	`add-sqr-sqrt_binary64_3090`
252×	`add-cube-cbrt_binary64_3103`
36×	`associate-/l*_binary64_3013`
28×	`sqrt-div_binary64_3085`
24×	`associate-/r/_binary64_3014`
18×	`associate-/r*_binary64_3012`
17×	`add-exp-log_binary64_3106`
14×	`flip3-+_binary64_3071` `flip-+_binary64_3042`
12×	`div-inv_binary64_3065`
11×	`add-cbrt-cube_binary64_3104`
8×	`pow1_binary64_3129` `div-exp_binary64_3119`
4×	`cbrt-undiv_binary64_3102` `add-log-exp_binary64_3107`
3×	`pow-flip_binary64_3142` `pow1/2_binary64_3148` `sqrt-pow1_binary64_3086`
2×	`rem-sqrt-square_binary64_3081` `rec-exp_binary64_3118` `1-exp_binary64_3112` `frac-2neg_binary64_3079` `clear-num_binary64_3067`
1×	`inv-pow_binary64_3153` `associate-/l/_binary64_3015`

Counts

4 → 453

Calls

8 calls:

61.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.0ms	(sqrt.f64 (+.f64 1 x))

series171.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
46.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
39.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
36.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 408 to 368 computations (9.8% saved)

simplify422.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune1.8s (12.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	460	5	465
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	465	9	474

Error

0.0b

Counts

474 → 9

Compiler

Compiled 11567 to 8519 computations (26.4% saved)

localize27.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)
0.3b	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite141.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`*-un-lft-identity_binary64_3068`
168×	`sqrt-prod_binary64_3084`
96×	`distribute-lft-out_binary64_3019`
90×	`times-frac_binary64_3074`
66×	`unpow-prod-down_binary64_3147`
50×	`add-sqr-sqrt_binary64_3090`
49×	`add-cube-cbrt_binary64_3103`
11×	`sqr-pow_binary64_3040`
10×	`associate-/l*_binary64_3013` `add-exp-log_binary64_3106`
9×	`associate-/r*_binary64_3012`
6×	`add-cbrt-cube_binary64_3104` `pow1_binary64_3129` `add-log-exp_binary64_3107`
4×	`sqrt-div_binary64_3085`
3×	`flip3-+_binary64_3071` `pow-unpow_binary64_3145` `div-exp_binary64_3119` `flip-+_binary64_3042`
2×	`pow-to-exp_binary64_3137` `associate-/r/_binary64_3014` `pow-exp_binary64_3136`
1×	`rem-sqrt-square_binary64_3081` `pow1/2_binary64_3148` `sqrt-pow1_binary64_3086` `pow-pow_binary64_3140` `sum-log_binary64_3159` `+-commutative_binary64_2998` `div-inv_binary64_3065` `cbrt-undiv_binary64_3102` `frac-2neg_binary64_3079` `clear-num_binary64_3067`

Counts

4 → 177

Calls

8 calls:

46.0ms	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
18.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)
15.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series158.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)
39.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
36.0ms	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
28.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 372 to 334 computations (10.2% saved)

simplify217.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4873	6538
1	4873	6538

prune588.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	189	9	198

Error

Counts

198 → 9

Compiler

Compiled 5155 to 3610 computations (30% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	280	2086
1	280	2086

regimes213.0ms (1.5%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 1226 to 985 computations (19.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample9.3s (64%)

Algorithm

1×

intervals

Results

425.0ms	2042×	body	1024	valid
231.0ms	4263×	body	128	valid
149.0ms	971×	body	512	valid
60.0ms	233×	body	2048	valid
49.0ms	491×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 3689 to 2965 computations (19.6% saved)

Pareto

0.591162989490023

Details

analyze5.0ms (0%)

sample42.0ms (0.3%)

simplify180.0ms (1.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite29.0ms (0.2%)

series83.0ms (0.6%)

simplify100.0ms (0.7%)

prune118.0ms (0.8%)

localize13.0ms (0.1%)

rewrite53.0ms (0.4%)

series93.0ms (0.6%)

simplify193.0ms (1.3%)

prune228.0ms (1.6%)

localize27.0ms (0.2%)

rewrite287.0ms (2%)

series171.0ms (1.2%)

simplify422.0ms (2.9%)

prune1.8s (12.2%)

localize27.0ms (0.2%)

rewrite141.0ms (1%)

series158.0ms (1.1%)

simplify217.0ms (1.5%)

prune588.0ms (4%)

simplify54.0ms (0.4%)

regimes213.0ms (1.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.3s (64%)

Profiling