Details

analyze77.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample83.0ms (0.1%)

Algorithm

1×

intervals

Results

45.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify237.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5395	79

prune8.0ms (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

53.2b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize38.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))

37.2b

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

45.4b

(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite1.4s (1.5%)

Algorithm

1×	rewrite-expression-head

Error

37.9b

Rules

86×	`times-frac_binary64_2130`
66×	`associate-/r/_binary64_2070`
60×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
58×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
40×	`frac-times_binary64_2134`
39×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
32×	`associate-*r/_binary64_2066`
28×	`difference-of-squares_binary64_2093`
25×	`add-cube-cbrt_binary64_2159`
21×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
20×	`associate-*l/_binary64_2067`
19×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
14×	`associate-/l*_binary64_2069` `difference-of-sqr-1_binary64_2094`
9×	`div-inv_binary64_2121` `associate-/l/_binary64_2071`
8×	`pow1_binary64_2185`
7×	`associate-/r*_binary64_2068`
3×	`add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `associate-r_binary64_2064`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`flip3--_binary64_2128` `flip--_binary64_2099` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-l_binary64_2065` `*-commutative_binary64_2055`

Counts

3 → 193

Calls

3 calls:

85.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

56.0ms

(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

27.0ms

(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 16828 to 6236 computations (62.9% saved)

series18.5s (18.6%)

Error

10.9b

Counts

3 → 70

Calls

3 calls:

15.7s

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

1.3s

(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

904.0ms

(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 22980 to 16071 computations (30.1% saved)

simplify424.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4961	25227
1	4961	25227

prune1.9s (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	256	7	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	7	264

Error

7.9b

Counts

264 → 7

Compiler

Compiled 21825 to 9972 computations (54.3% saved)

localize1.0ms (0%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series1.0ms (0%)

Error: 7.9b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune19.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

7.9b

Counts

7 → 7

Compiler

Compiled 188 to 119 computations (36.7% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
35.2b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite4.5s (4.5%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

606×	`*-un-lft-identity_binary64_2124`
587×	`times-frac_binary64_2130`
379×	`add-sqr-sqrt_binary64_2146`
210×	`add-cube-cbrt_binary64_2159`
150×	`associate-r_binary64_2064`
129×	`distribute-lft-out_binary64_2075`
74×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
70×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
56×	`associate-l_binary64_2065`
54×	`associate-/r/_binary64_2070`
37×	`difference-of-sqr-1_binary64_2094`
33×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
27×	`div-inv_binary64_2121` `flip3-+_binary64_2127` `flip-+_binary64_2098`
22×	`associate-/l*_binary64_2069`
16×	`associate-/r*_binary64_2068` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`pow1_binary64_2185` `unswap-sqr_binary64_2092`
5×	`associate-/l/_binary64_2071`
4×	`add-log-exp_binary64_2163`
3×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-*r/_binary64_2066`
2×	`flip3--_binary64_2128` `flip--_binary64_2099`
1×	`pow-prod-down_binary64_2195` `frac-times_binary64_2134` `associate-l/_binary64_2067` `-commutative_binary64_2055`

Counts

4 → 497

Calls

4 calls:

335.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
45.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
22.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
18.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 41545 to 19607 computations (52.8% saved)

series17.2s (17.3%)

Error

7.9b

Counts

4 → 86

Calls

4 calls:

12.7s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
2.7s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
495.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
333.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 27607 to 18932 computations (31.4% saved)

simplify707.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

583 → 583

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5022	47888

prune5.3s (5.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	578	5	583
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	581	9	590

Error

7.9b

Counts

590 → 9

Compiler

Compiled 48829 to 23570 computations (51.7% saved)

localize66.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))))
35.2b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.4b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite10.4s (10.5%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

1737×	`times-frac_binary64_2130`
1559×	`*-un-lft-identity_binary64_2124`
694×	`add-sqr-sqrt_binary64_2146`
641×	`add-cube-cbrt_binary64_2159`
398×	`distribute-lft-out_binary64_2075`
290×	`associate-r_binary64_2064`
220×	`add-exp-log_binary64_2162`
128×	`div-exp_binary64_2175`
126×	`distribute-lft-out--_binary64_2076`
103×	`associate-/r*_binary64_2068`
100×	`add-cbrt-cube_binary64_2160`
95×	`associate-/r/_binary64_2070`
56×	`associate-l_binary64_2065`
53×	`cbrt-undiv_binary64_2158`
52×	`div-inv_binary64_2121`
51×	`prod-exp_binary64_2173`
45×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
21×	`cbrt-unprod_binary64_2157`
15×	`1-exp_binary64_2168` `rec-exp_binary64_2174`
14×	`unswap-sqr_binary64_2092`
7×	`pow1_binary64_2185` `associate-/l*_binary64_2069`
4×	`add-log-exp_binary64_2163` `associate-/l/_binary64_2071`
3×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `frac-times_binary64_2134` `un-div-inv_binary64_2122` `associate-l/_binary64_2067` `-commutative_binary64_2055` `inv-pow_binary64_2209` `pow-flip_binary64_2198`

Counts

4 → 899

Calls

4 calls:

548.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))))
73.0ms	(/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))))
21.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
19.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 79000 to 39302 computations (50.3% saved)

series16.9s (17.1%)

Error

7.9b

Counts

4 → 86

Calls

4 calls:

12.6s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))))
2.6s	(/.f64 1 (/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))))
558.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
331.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 27803 to 19132 computations (31.2% saved)

simplify1.1s (1.1%)

Algorithm

1×	egg-herbie

Counts

985 → 985

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4981	80343
1	4981	80343

prune9.9s (10%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	984	1	985
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	986	8	994

Error

7.9b

Counts

994 → 8

Compiler

Compiled 83365 to 40763 computations (51.1% saved)

regimes2.5s (2.5%)

Accuracy

Total 3.2b remaining (29%)

Threshold costs 0b (0%)

Compiler

Compiled 20960 to 12401 computations (40.8% saved)

bsearch59.0ms (0.1%)

Steps

Iters	Range		Point
6	7.343783868413149e+136	1.098576901623832e+138	8.49297746379161e+137

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	89
1	47	89

end0.0ms (0%)

sample7.7s (7.8%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
330.0ms	8000×	pre	128	true

Compiler

Compiled 5295 to 3136 computations (40.8% saved)

Details

analyze77.0ms (0.1%)

sample83.0ms (0.1%)

simplify237.0ms (0.2%)

prune8.0ms (0%)

localize38.0ms (0%)

rewrite1.4s (1.5%)

series18.5s (18.6%)

simplify424.0ms (0.4%)

prune1.9s (1.9%)

localize1.0ms (0%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify11.0ms (0%)

prune19.0ms (0%)

localize39.0ms (0%)

rewrite4.5s (4.5%)

series17.2s (17.3%)

simplify707.0ms (0.7%)

prune5.3s (5.3%)

localize66.0ms (0.1%)

rewrite10.4s (10.5%)

series16.9s (17.1%)

simplify1.1s (1.1%)

prune9.9s (10%)

regimes2.5s (2.5%)

bsearch59.0ms (0.1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample7.7s (7.8%)

Profiling