Details

sample92.0ms

Algorithm

intervals

Results

50.0ms	113×	body	1280	valid
12.0ms	56×	body	640	valid
12.0ms	14×	body	2560	valid
4.0ms	22×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 34.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
3.0b	(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))

series41.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
17.0ms	(tan (+ x eps))

simplify73.0ms

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

prune66.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 13.4b

Counts

32 → 8

localize11.0ms

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))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series196.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	994

prune166.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	91	15	106

Merged error: 13.3b

Counts

106 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

12.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series201.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
22.0ms	(+ (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
103.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify65.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	561	1286
1	2547	1185
2	5001	1184

prune169.0ms

Filtered

83 candidates to 111 candidates (-33.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 13.3b

Counts

126 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
8.1b	(cbrt (* (tan x) (tan eps)))
8.1b	(cbrt (* (tan x) (tan eps)))
8.1b	(cbrt (* (tan x) (tan eps)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`tan-quot`
9×	`add-sqr-sqrt` `cbrt-div`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
4.0ms	(cbrt (* (tan x) (tan eps)))
4.0ms	(cbrt (* (tan x) (tan eps)))
4.0ms	(cbrt (* (tan x) (tan eps)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
37.0ms	(cbrt (* (tan x) (tan eps)))
40.0ms	(cbrt (* (tan x) (tan eps)))
37.0ms	(cbrt (* (tan x) (tan eps)))

simplify50.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	225	972
1	537	881
2	1575	811
3	5002	801

prune77.0ms

Filtered

53 candidates to 64 candidates (-20.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	66	13	79

Merged error: 12.2b

Counts

79 → 13

regimes387.0ms

Accuracy

73.9% (1.9b remaining)

Error of 15.4b against oracle of 13.5b and baseline of 20.7b

bsearch55.0ms

Steps

Iters	Range		Point
7	1.8618356104618278e-71	1.294272862403199e-69	6.045793054883833e-71
4	-1.3562651067764176e-33	-7.5134825004128385e-34	-7.610973216732956e-34

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	57	27
2	57	27

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3281×	body	1280	valid
589.0ms	685×	body	2560	valid
384.0ms	1794×	body	640	valid
112.0ms	783×	body	320	valid
50.0ms	1107×	body	80	valid
35.0ms	350×	body	160	valid

Details

sample92.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series41.0ms

simplify73.0ms

prune66.0ms

localize11.0ms

rewrite31.0ms

series196.0ms

simplify44.0ms

prune166.0ms

localize15.0ms

rewrite38.0ms

series201.0ms

simplify65.0ms

prune169.0ms

localize17.0ms

rewrite24.0ms

series215.0ms

simplify50.0ms

prune77.0ms

regimes387.0ms

bsearch55.0ms

simplify2.0ms

end0.0ms

sample2.7s

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