Details

analyze310.0ms (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	77×	body	1024	valid
4.0ms	47×	body	512	valid
2.0ms	109×	body	128	valid
1.0ms	6×	body	2048	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify96.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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: 38.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.5b	(-.f64 (exp.f64 x) 1)

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_782`
30×	`*-un-lft-identity_binary64_760`
21×	`times-frac_binary64_766`
15×	`add-cube-cbrt_binary64_795`
10×	`difference-of-squares_binary64_729`
7×	`associate-/r*_binary64_704`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

2 → 63

Calls

2 calls:

11.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series47.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
10.0ms	(-.f64 (exp.f64 x) 1)

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4915	1129
1	4915	1129

prune63.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

Compiler

Compiled 959 to 474 computations (50.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.4b	(*.f64 x 1/12)

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_799`
8×	`*-un-lft-identity_binary64_760`
7×	`add-sqr-sqrt_binary64_782`
5×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
4×	`sum-log_binary64_851`
3×	`associate-r_binary64_700` `associate-l_binary64_701`
2×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `div-inv_binary64_757` `associate-+r+_binary64_692` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

3 → 44

Calls

3 calls:

9.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
6.0ms	(+.f64 1/2 (/.f64 1 x))
4.0ms	(*.f64 x 1/12)

series32.0ms (1%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(*.f64 x 1/12)
11.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
8.0ms	(+.f64 1/2 (/.f64 1 x))

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5239	576

prune42.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	53	3	56

Merged error: 0.0b

Counts

56 → 3

Compiler

Compiled 721 to 576 computations (20.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
3.5b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite76.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_766`
237×	`*-un-lft-identity_binary64_760`
153×	`add-sqr-sqrt_binary64_782`
109×	`add-cube-cbrt_binary64_795`
88×	`difference-of-sqr--1_binary64_731`
64×	`distribute-lft-out_binary64_711`
42×	`associate-/r*_binary64_704`
22×	`unpow2_binary64_825` `sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
11×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796` `associate-/l*_binary64_705`
9×	`add-exp-log_binary64_798`
8×	`flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734`
6×	`div-inv_binary64_757`
4×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow1_binary64_821`
2×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `+-commutative_binary64_690` `sum-log_binary64_851` `clear-num_binary64_759`

Counts

4 → 258

Calls

4 calls:

18.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
12.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(+.f64 (exp.f64 x) 1)

series152.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
50.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
23.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
6.0ms	(+.f64 (exp.f64 x) 1)

simplify102.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5050	8086

prune328.0ms (10.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	270	3	273

Merged error: 0.0b

Counts

273 → 3

Compiler

Compiled 6475 to 3714 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (exp.f64 x) 1))
0.0b	(/.f64 (exp.f64 x) (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))))
3.5b	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
3.5b	(-.f64 (exp.f64 x) 1)

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_782`
51×	`*-un-lft-identity_binary64_760`
42×	`exp-prod_binary64_812`
40×	`log-pow_binary64_849`
33×	`times-frac_binary64_766`
30×	`add-cube-cbrt_binary64_795`
14×	`difference-of-squares_binary64_729`
11×	`associate-/r*_binary64_704`
9×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799` `pow1_binary64_821`
8×	`exp-sum_binary64_806`
7×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `log-prod_binary64_846`
6×	`add-cbrt-cube_binary64_796`
5×	`add-exp-log_binary64_798`
3×	`associate-/l*_binary64_705` `sub-neg_binary64_753`
2×	`diff-log_binary64_852` `exp-diff_binary64_808` `rem-exp-log_binary64_800`
1×	`log-div_binary64_847` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `rem-log-exp_binary64_801` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 122

Calls

4 calls:

9.0ms	(/.f64 (exp.f64 x) (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))))
6.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
6.0ms	(exp.f64 (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series218.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (exp.f64 x) (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))))
83.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
24.0ms	(exp.f64 (-.f64 (exp.f64 x) 1))
9.0ms	(-.f64 (exp.f64 x) 1)

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5630	1913

prune99.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

Compiler

Compiled 1823 to 963 computations (47.2% saved)

regimes113.0ms (3.6%)

Compiler: Compiled 1330 to 960 computations (27.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample1.1s (35.9%)

Algorithm

1×

intervals

Results

359.0ms	2640×	body	1024	valid
110.0ms	1398×	body	512	valid
79.0ms	3009×	body	128	valid
45.0ms	277×	body	2048	valid
33.0ms	676×	body	256	valid
0.0ms	3×	body	2048	invalid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 365 to 267 computations (26.8% saved)

Details

analyze310.0ms (9.8%)

sample24.0ms (0.8%)

simplify96.0ms (3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite21.0ms (0.7%)

series47.0ms (1.5%)

simplify75.0ms (2.4%)

prune63.0ms (2%)

localize6.0ms (0.2%)

rewrite22.0ms (0.7%)

series32.0ms (1%)

simplify71.0ms (2.2%)

prune42.0ms (1.3%)

localize9.0ms (0.3%)

rewrite76.0ms (2.4%)

series152.0ms (4.8%)

simplify102.0ms (3.2%)

prune328.0ms (10.3%)

localize6.0ms (0.2%)

rewrite37.0ms (1.2%)

series218.0ms (6.9%)

simplify74.0ms (2.3%)

prune99.0ms (3.1%)

regimes113.0ms (3.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (35.9%)

Profiling