Details

sample702.0ms

Algorithm

intervals

Results

367.0ms	90×	body	1280	valid
263.0ms	55×	body	2560	valid
32.0ms	66×	body	640	valid
9.0ms	26×	body	320	valid
4.0ms	7×	body	80	valid
3.0ms	12×	body	160	valid

simplify753.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune7.0ms

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: 29.7b

Counts

2 → 1

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (sin x))
1.6b	(- x (tan x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

15.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
11.0ms	(- x (tan x))

series70.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (sin x))
36.0ms	(- x (tan x))

simplify110.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4864	1145
1	4864	1145

prune181.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.2b	(* x 9/40)
19.3b	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

10.0ms	(* (pow x 4) -27/2800)
9.0ms	(* x (* x 9/40))
7.0ms	(* x 9/40)
15.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (pow x 4) -27/2800)
6.0ms	(* x (* x 9/40))
4.0ms	(* x 9/40)
11.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

simplify100.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune195.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (log (pow (exp x) 9/40)))
0.1b	(* (pow x 4) -27/2800)
2.9b	(log (pow (exp x) 9/40))
22.4b	(+ (* x (log (pow (exp x) 9/40))) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

35×	`log-prod`
26×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
14×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
12×	`add-exp-log`
10×	`associate-l`
9×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`associate-r` `sqr-pow`
6×	`pow1`
4×	`prod-exp` `unswap-sqr`
3×	`rem-log-exp` `sum-log`
2×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 103

Calls

4 calls:

10.0ms	(* x (log (pow (exp x) 9/40)))
8.0ms	(* (pow x 4) -27/2800)
4.0ms	(log (pow (exp x) 9/40))
16.0ms	(+ (* x (log (pow (exp x) 9/40))) (+ -1/2 (* (pow x 4) -27/2800)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* x (log (pow (exp x) 9/40)))
7.0ms	(* (pow x 4) -27/2800)
71.0ms	(log (pow (exp x) 9/40))
19.0ms	(+ (* x (log (pow (exp x) 9/40))) (+ -1/2 (* (pow x 4) -27/2800)))

simplify114.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4951	1037
1	4951	1037

prune300.0ms

Filtered

78 candidates to 115 candidates (-47.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	115	3	118

Merged error: 0.0b

Counts

118 → 3

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 3)
1.6b	(- (pow x 3) (pow (sin x) 3))
1.6b	(- x (tan x))
24.6b	(/ (- (pow x 3) (pow (sin x) 3)) (* (- x (tan x)) (+ (* x x) (* (sin x) (+ x (sin x))))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
49×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
16×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`frac-times`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

5.0ms	(pow (sin x) 3)
25.0ms	(- (pow x 3) (pow (sin x) 3))
6.0ms	(- x (tan x))
42.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (- x (tan x)) (+ (* x x) (* (sin x) (+ x (sin x))))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow (sin x) 3)
24.0ms	(- (pow x 3) (pow (sin x) 3))
20.0ms	(- x (tan x))
75.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (- x (tan x)) (+ (* x x) (* (sin x) (+ x (sin x))))))

simplify132.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5054	3053

prune350.0ms

Filtered

88 candidates to 159 candidates (-80.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	159	3	162

Merged error: 0.0b

Counts

162 → 3

regimes157.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch77.0ms

Steps

Iters	Range		Point
10	0.01683730658649282	12785707414306.22	0.022487938951425535
10	-0.2101619750885166	-2.51237587459879e-12	-0.025787172413692064

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	33
1	49	33

end0.0ms

sample11.9s

Algorithm

intervals

Results

7.3s	1675×	body	2560	valid
2.9s	2738×	body	1280	valid
918.0ms	1817×	body	640	valid
305.0ms	945×	body	320	valid
110.0ms	466×	body	160	valid
50.0ms	359×	body	80	valid

Details

sample702.0ms

simplify753.0ms

prune7.0ms

localize40.0ms

rewrite39.0ms

series70.0ms

simplify110.0ms

prune181.0ms

localize18.0ms

rewrite45.0ms

series27.0ms

simplify100.0ms

prune195.0ms

localize20.0ms

rewrite44.0ms

series190.0ms

simplify114.0ms

prune300.0ms

localize37.0ms

rewrite89.0ms

series130.0ms

simplify132.0ms

prune350.0ms

regimes157.0ms

bsearch77.0ms

simplify3.0ms

end0.0ms

sample11.9s

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