Details

sample87.0ms

Algorithm

intervals

Results

40.0ms	104×	body	1280	valid
18.0ms	20×	body	2560	valid
13.0ms	65×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	34×	body	80	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 38.4b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite11.0ms

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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series134.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune137.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 15.1b

Counts

32 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
4.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 1 (* (tan x) (tan eps)))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
13.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series634.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- 1 (* (tan x) (tan eps)))
90.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
348.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify122.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	343	662
1	1170	624
2	4756	614
3	5001	614

prune209.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	61	13	74
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	64	17	81

Merged error: 15.0b

Counts

81 → 17

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
4.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
29.8b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
6.0ms	(pow (* (tan x) (tan eps)) 3)
23.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series671.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan x) (tan eps))
123.0ms	(pow (* (tan x) (tan eps)) 3)
364.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
93.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	384	787
1	1733	744
2	5002	743

prune439.0ms

Filtered

94 candidates to 65 candidates (69.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	94	17	111

Merged error: 15.0b

Counts

111 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
4.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

5.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
7.0ms	(* (tan x) (sin eps))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series602.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
94.0ms	(/ (* (tan x) (sin eps)) (cos eps))
63.0ms	(* (tan x) (sin eps))
353.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	785
1	1424	711
2	5001	699

prune193.0ms

Filtered

82 candidates to 60 candidates (73.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	82	17	99

Merged error: 15.0b

Counts

99 → 17

Details

sample87.0ms

simplify5.0ms

prune2.0ms

localize12.0ms

rewrite11.0ms

series134.0ms

simplify75.0ms

prune137.0ms

localize19.0ms

rewrite26.0ms

series634.0ms

simplify122.0ms

prune209.0ms

localize18.0ms

rewrite40.0ms

series671.0ms

simplify51.0ms

prune439.0ms

localize16.0ms

rewrite37.0ms

series602.0ms

simplify47.0ms

prune193.0ms

regimes178.0ms

bsearch2.0ms

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