Details

analyze3.2s (12.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample318.0ms (1.3%)

Algorithm

1×

intervals

Results

175.0ms	131×	body	2048	valid
54.0ms	74×	body	1024	valid
18.0ms	305×	pre	128	true
12.0ms	27×	body	512	valid
10.0ms	11×	body	2048	overflowed
9.0ms	17×	body	1024	overflowed
5.0ms	2×	body	4096	valid
2.0ms	16×	body	128	valid
2.0ms	5×	body	512	overflowed
2.0ms	6×	body	256	valid
1.0ms	11×	body	128	overflowed
1.0ms	5×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify197.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5217	37

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

60.2b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize34.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(exp.f64 (*.f64 b eps))
0.0b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
0.2b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.9b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite72.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_759`
26×	`*-un-lft-identity_binary64_737`
15×	`cancel-sign-sub-inv_binary64_703`
11×	`add-cube-cbrt_binary64_772`
10×	`add-log-exp_binary64_776` `difference-of-squares_binary64_706`
9×	`flip3--_binary64_741` `flip--_binary64_712`
7×	`associate-l_binary64_678` `associate-r_binary64_677`
6×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `pow1_binary64_798`
5×	`distribute-lft-out--_binary64_689` `sub-neg_binary64_730` `difference-of-sqr-1_binary64_707`
4×	`frac-times_binary64_747` `distribute-lft-in_binary64_686` `distribute-rgt-in_binary64_687`
3×	`diff-log_binary64_829`
2×	`associate-l/_binary64_680` `associate-r/_binary64_679`
1×	`unswap-sqr_binary64_705` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `pow-prod-down_binary64_808` `*-commutative_binary64_668`

Counts

4 → 96

Calls

8 calls:

24.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
9.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
9.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
0.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

series706.0ms (2.9%)

Counts

4 → 43

Calls

4 calls:

355.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
153.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
109.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
89.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 2260 to 1715 computations (24.1% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5504	2752

prune462.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	8	140

Error

48.8b

Counts

140 → 8

Compiler

Compiled 4521 to 1941 computations (57.1% saved)

localize30.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (*.f64 (+.f64 a b) eps))
0.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(exp.f64 (*.f64 a eps))
2.9b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
6.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite69.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
14×	`add-sqr-sqrt_binary64_759`
12×	`*-un-lft-identity_binary64_737`
10×	`add-log-exp_binary64_776`
9×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786`
6×	`add-cube-cbrt_binary64_772` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `cancel-sign-sub-inv_binary64_703`
4×	`pow1_binary64_798` `flip3--_binary64_741` `flip--_binary64_712` `difference-of-squares_binary64_706`
2×	`associate-/r/_binary64_683` `diff-log_binary64_829` `associate-l/_binary64_680` `distribute-lft-out--_binary64_689` `sub-neg_binary64_730` `difference-of-sqr-1_binary64_707` `associate-/l/_binary64_684` `associate-r/_binary64_679`
1×	`exp-prod_binary64_789` `frac-2neg_binary64_748` `exp-to-pow_binary64_799` `clear-num_binary64_736` `associate-/l_binary64_682` `associate-/r_binary64_681` `div-inv_binary64_734` `rem-exp-log_binary64_777` `times-frac_binary64_743`

Counts

4 → 75

Calls

8 calls:

31.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
10.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.0ms	(exp.f64 (*.f64 a eps))
0.0ms	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))

series784.0ms (3.2%)

Counts

4 → 42

Calls

4 calls:

494.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (*.f64 b eps)))
148.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
73.0ms	(exp.f64 (*.f64 a eps))
68.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

Compiler

Compiled 1746 to 1289 computations (26.2% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4994	2108
1	4994	2108

prune295.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	121	4	125

Error

0.3b

Counts

125 → 4

Compiler

Compiled 2867 to 1130 computations (60.6% saved)

localize27.0ms (0.1%)

Local error

Found 8 expressions with local error:

6.0b	(/.f64 (*.f64 b eps) a)
0.0b	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
0.0b	(+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a))))
0.0b	(+.f64 eps (/.f64 (*.f64 b eps) a))
0.0b	(+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a))))
0.0b	(+.f64 eps (/.f64 (*.f64 b eps) a))
0.0b	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
6.0b	(/.f64 (*.f64 b eps) a)

rewrite79.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-log-exp_binary64_776`
11×	`*-un-lft-identity_binary64_737`
9×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
8×	`frac-add_binary64_745`
6×	`flip3-+_binary64_740` `add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `flip-+_binary64_711`
5×	`sum-log_binary64_828`
4×	`pow1_binary64_798` `associate-*r/_binary64_679`
3×	`associate-+r+_binary64_669` `associate-/r*_binary64_681` `+-commutative_binary64_667` `distribute-lft-out_binary64_688` `times-frac_binary64_743`
2×	`div-inv_binary64_734` `cbrt-undiv_binary64_771` `div-exp_binary64_788`
1×	`distribute-lft-in_binary64_686` `cbrt-unprod_binary64_770` `frac-2neg_binary64_748` `prod-exp_binary64_786` `clear-num_binary64_736` `associate-/l*_binary64_682` `distribute-rgt-in_binary64_687`

Counts

4 → 67

Calls

8 calls:

30.0ms	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
16.0ms	(+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a))))
10.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))
9.0ms	(/.f64 (*.f64 b eps) a)
0.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))

series1.0s (4.2%)

Counts

4 → 53

Calls

4 calls:

425.0ms	(+.f64 (/.f64 1 a) (+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a)))))
314.0ms	(+.f64 (/.f64 1 b) (.f64 1/2 (+.f64 eps (/.f64 (.f64 b eps) a))))
189.0ms	(/.f64 (*.f64 b eps) a)
120.0ms	(+.f64 eps (/.f64 (*.f64 b eps) a))

Compiler

Compiled 1381 to 1198 computations (13.3% saved)

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5032	2315

prune240.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

0.0b

Counts

124 → 5

Compiler

Compiled 2627 to 1287 computations (51% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 1 a) (/.f64 1 b))
0.0b	(+.f64 (/.f64 1 a) (/.f64 1 b))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_737`
7×	`distribute-lft-out_binary64_688`
6×	`times-frac_binary64_743`
4×	`div-inv_binary64_734`
3×	`add-log-exp_binary64_776` `add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759`
1×	`add-cbrt-cube_binary64_773` `flip3-+_binary64_740` `add-exp-log_binary64_775` `frac-add_binary64_745` `pow1_binary64_798` `flip-+_binary64_711` `+-commutative_binary64_667` `sum-log_binary64_828`

Counts

1 → 19

Calls

2 calls:

26.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))
0.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))

series97.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

97.0ms

(+.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 102 to 126 computations (-23.5% saved)

simplify147.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4871	341
1	4871	341

prune35.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	31	5	36

Error

0.0b

Counts

36 → 5

Compiler

Compiled 294 to 224 computations (23.8% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	375	1668
1	375	1668

regimes498.0ms (2%)

Accuracy

Total 3.3b remaining (97.8%)

Threshold costs 0b (0%)

Compiler

Compiled 3291 to 2400 computations (27.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample16.1s (64.9%)

Algorithm

1×

intervals

Results

5.8s	4076×	body	2048	valid
1.8s	2409×	body	1024	valid
386.0ms	9662×	pre	128	true
341.0ms	360×	body	2048	overflowed
332.0ms	568×	body	1024	overflowed
320.0ms	731×	body	512	valid
115.0ms	291×	body	512	overflowed
69.0ms	251×	body	256	valid
66.0ms	517×	body	128	valid
41.0ms	16×	body	4096	valid
37.0ms	293×	body	128	overflowed
36.0ms	147×	body	256	overflowed
5.0ms	3×	body	2048	invalid

Compiler

Compiled 3323 to 2415 computations (27.3% saved)

Pareto

-0.6355700953240039

Details

analyze3.2s (12.7%)

sample318.0ms (1.3%)

simplify197.0ms (0.8%)

prune6.0ms (0%)

localize34.0ms (0.1%)

rewrite72.0ms (0.3%)

series706.0ms (2.9%)

simplify94.0ms (0.4%)

prune462.0ms (1.9%)

localize30.0ms (0.1%)

rewrite69.0ms (0.3%)

series784.0ms (3.2%)

simplify99.0ms (0.4%)

prune295.0ms (1.2%)

localize27.0ms (0.1%)

rewrite79.0ms (0.3%)

series1.0s (4.2%)

simplify137.0ms (0.6%)

prune240.0ms (1%)

localize9.0ms (0%)

rewrite29.0ms (0.1%)

series97.0ms (0.4%)

simplify147.0ms (0.6%)

prune35.0ms (0.1%)

simplify41.0ms (0.2%)

regimes498.0ms (2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample16.1s (64.9%)

Profiling