Details

sample145.0ms

Algorithm

intervals

Results

70.0ms	112×	body	1280	valid
26.0ms	19×	body	2560	valid
21.0ms	61×	body	640	valid
5.0ms	22×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune10.0ms

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: 38.8b

Counts

2 → 1

localize17.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
4.5b	(tan (+ x eps))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

13.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (tan (+ x eps)) (tan x))
26.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4924	335
1	4924	335

prune112.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 14.0b

Counts

32 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

14.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
11.0ms	(* (tan x) (tan eps))
21.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
34.0ms	(+ (tan x) (tan eps))
35.0ms	(* (tan x) (tan eps))
174.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5109	1563

prune306.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	83	15	98
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	90	17	107

Merged error: 13.8b

Counts

107 → 17

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan eps) (tan eps))
2.3b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

25×	`tan-quot`
18×	`pow1`
16×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-times` `associate-r/` `associate-l*`
7×	`associate-r`
6×	`associate-*l/` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `frac-sub` `cbrt-unprod`
3×	`swap-sqr` `*-commutative` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 94

Calls

4 calls:

12.0ms	(* (tan x) (* (tan eps) (tan eps)))
8.0ms	(* (tan x) (tan eps))
10.0ms	(* (tan eps) (tan eps))
22.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series636.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (tan x) (* (tan eps) (tan eps)))
36.0ms	(* (tan x) (tan eps))
17.0ms	(* (tan eps) (tan eps))
538.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4983	1623
1	4983	1623

prune308.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	105	18	123

Merged error: 13.8b

Counts

123 → 18

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos eps) 2)
0.3b	(* (tan x) (tan eps))
0.3b	(pow (sin eps) 2)
2.3b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`tan-quot`
8×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`frac-sub`
3×	`frac-times` `associate-r/` `associate-r` `associate-l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `associate-*l/` `pow-exp` `associate--l+` `flip-+` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

4.0ms	(pow (cos eps) 2)
8.0ms	(* (tan x) (tan eps))
4.0ms	(pow (sin eps) 2)
22.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series632.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos eps) 2)
39.0ms	(* (tan x) (tan eps))
6.0ms	(pow (sin eps) 2)
581.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5031	1586

prune252.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	90	16	106

Merged error: 13.8b

Counts

106 → 16

regimes390.0ms

Accuracy

84.8% (1.1b remaining)

Error of 15.1b against oracle of 14.0b and baseline of 21.2b

bsearch134.0ms

Steps

Iters	Range		Point
7	9.791429827998993e-113	8.123214819136605e-111	7.958520989490561e-111
9	-1.8479730676440648e-18	-5.583288742464845e-24	-8.944935459056774e-23

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	95
1	88	95

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	3343×	body	1280	valid
809.0ms	570×	body	2560	valid
698.0ms	1824×	body	640	valid
191.0ms	756×	body	320	valid
84.0ms	1154×	body	80	valid
59.0ms	353×	body	160	valid

Details

sample145.0ms

simplify6.0ms

prune10.0ms

localize17.0ms

rewrite21.0ms

series66.0ms

simplify73.0ms

prune112.0ms

localize19.0ms

rewrite58.0ms

series336.0ms

simplify72.0ms

prune306.0ms

localize30.0ms

rewrite56.0ms

series636.0ms

simplify63.0ms

prune308.0ms

localize41.0ms

rewrite42.0ms

series632.0ms

simplify46.0ms

prune252.0ms

regimes390.0ms

bsearch134.0ms

simplify3.0ms

end0.0ms

sample4.5s

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